Home

An Integrated, Modular Simulation System for Education and

1. AT N E o A i I PU n Ti la Tm M l i il i MILL Time sec Figure 30 CHIRP Time and Frequency Plots from CessnaTransfer Function frequency analysis is a oscillation of the controls starting at a low frequency then progressing to as high a frequency as the pilot can attain without exceeding strict safety limits The maneuver is called a CHIRP Note that in figure 30 the input the magnitude stays constant while in the output the magnitude drops off This is characteristic for a damped second order system On the right of the figure is the Frequency plot bode plot processed by CIFER Compare the bode plot from CIFER to the bode plot in Figure 29 Note that in the Figure 29 the magnitude line breaks down and then stays slanted In the CIFER plot the magnitude line breaks back up This is incorrect However notice the third coherence plot Coherence is a measure of the linearity of the system the accuracy of the output data at the corresponding frequency The same frequency where the coherence plot breaks downward is the frequency that the magnitude breaks upward The coherence plot tells the user that where the magnitude breaks upward the data is no longer valid CIFER is also able to fit a low order first or second order transfer function to the bode plot The original transfer function was obtained by doing a second order fit to the frequency data within the frequency range w
2. input cpp else Snoopy LandAC aircraft cpp this function displays the program version number void DisplayVersion cprintf EEEEFEEEEEEEEEEEEEEFEEEEREEEEEEEEEE r n cprintf NEMO cprint f QEEEEFEEEEEEEEEEFEEEFEEEEEEEEEECEEEE Nr Nn gotoxy 4 2 cprintf Snoopy Linear Flight Simulator Version i i c MAJ VER MIN VER VER LET gotoxy 4 6 104 program entry point void main int argc char argv window 1 1 80 25 conio h set a text window clrscr conio h clear the screen textcolor 7 conio h set the text color oldVmode byte MK FP 0x40 0x49 store the text mode opMode FLIGHT assume normal operating mode ParseCLP argc argv parse command line args if opMode HELP if this is a help run DisplavHelp then displav the command exit 0 list and exit if opMode VERSION DisplayVersion exit 0 StartUp controler GetControls Snoopy input cpp run one control pass to initialize the state vector main flight loop while controler Exit 4 input cpp check for exit command controler GetControls Snoopy input cpp get control settings Snoopy RunFModel aircraft cpp run flight model GroundApproach if UpdateView Snoopy aircraft cpp make the next frame Terminate View switch file or memory error UpdateView if opMode DEBUG if not debugging
3. g uPtrs 0 set amp altimeter int uPtrs 0 jk set amp altimeter 4000 set amp pitch8Ball uPtrs 1 set amp rol18Ball uPtrs 2 set amp yaw8Ball uPtrs 3 set amp dirGyro uPtrs 4 set amp gMeter uPtrs 5 set amp vertDevPoint uPtrs 6 set amp rudderBall uPtrs 7 set amp aoaIndicator uPtrs 8 set machIndicator uPtrs 9 set amp airspeed uPtrs 10 set amp sideslipAngle uPtrs 11 set amp leftEngRPM uPtrs 12 set amp rightEngRPM uPtrs 13 set amp verspeedIndicator uPtrs 14 set krightNozz tuPtrs 15 set amp leftNozz uPtrs 16 set amp internalPress uPtrs 17 set amp courseDirIndicator uPtrs 18 set amp cdHorIndicator uPtrs 19 set amp cdVerIndicator uPtrs 20 set amp rightEngTemp uPtrs 21 set amp leftEngTemp uPtrs 22 set amp rightEngFuel uPtrs 23 set amp leftEngFuel uPtrs 24 set amp pTotGauge uPtrs 25 111 set amp yawForceOut uPtrs 26 set amp rollForceOut uPtrs 27 set amp pitchForceOut uPtrs 28 setup for d a void DACCardInit struct DAC card short channel unsigned short count unsigned short addri float voltage voltage 0 if card gt nBits gt 16 card gt nBits lt 2 printf DAC error Cannot set for d bits n card gt nBits card gt maxCount unsigned short 1 lt lt card gt nBits
4. STheta sin Theta SPhi sin Phi SPsi sin Psi CTheta cos Theta CPhi cos Phi CPsi cos Psi TTheta STheta CTheta SecTheta 1 0 if CTheta 0 0 SecTheta 1 0 CTheta PhiDot p q SPhi r CPhi TTheta This is the Euler angle transformation ThetaDot q CPhi r SPhi from body to world coordinates PsiDot q SPhi r CPhi SecTheta This transforms velocity components to world coordinates 149 xDot u CTheta CPsi v SPhi STheta CPsi CPhi SPsi w CPhi STheta CPsi SPhi SPsi yDot u CTheta SPsi v SPhi STheta SPsi CPhi CPsi w CPhi STheta SPsi SPhi CPsi zDot u STheta v SPhi CTheta w CPhi CTheta Theta 3 0 ThetaDot OldThetaDot 2 0 dt Euler angle integration Phi 3 0 PhiDot OldPhiDot 2 0 dt Psi 3 0 PsiDot OldPsiDot 2 0 dt xx 3 0 xDot 0ldxDot 2 0 dt position integration yy 7 3 0 yDot OldyDot 2 0 dt zz 3 0 zDot OldzDot 2 0 dt OlduDot uDot Update the derivatives for the integrations OldvDot vDot OldwDot wDot OldpDot pDot OldqDot qDot OldrDot rDot OldThetaDot ThetaDot OldPhiDot PhiDot OldPsiDot PsiDot OldxDot xDot OldyDot yDot OldzDot zDot handle bounds checking on roll and yaw at 180 or 180 if Phi gt pi Phi pi Phi pi else if Phi lt pi Phi pi Phi pi if Psi gt pi Psi pi Psi pi else if Psi lt pi Psi pi Psi pi
5. int newVal define MDL_UPDATE Change to undef to remove function tif defined MDL UPDATE Function mdlUpdate Abstract T This function is called once for every major integration time step Discrete states are typically updated here but this function is useful di for performing any tasks that should only take place once per integration step static void mdlUpdate SimStruct S int_T tid endif MDL UPDATE define MDL DERIVATIVES Change to undef to remove function if defined MDL DERIVATIVES Function mdlDerivatives static void mdlDerivatives SimStruct S endif MDL_DERIVATIVES void PCLabCardInit struct PCLabCard card qe dCard new DACCard 12 card gt dalLow 0 0 5 0 2 0 0 if dCard printf PCLabCard Unable to allocate memory for DAC n outportb card gainCtrl 0x00 outportb card modeCtrl 0x01 float doConversion struct ADCChannel Chan struct PCLabCard Card float value unsigned short bHigh bLow flag 1 if Chan gt cNumber gt Card gt nADChannels printf PCLabCard Analog channel d is out of range n Chan cNumber outportb Card muxCtrl Chan cNumber outportb Card gt softAD Oxff delay 1 while flag bHigh inportb Card gt adHigh bLow inportb Card adLow flag bHigh amp 0x10 Chan gt adcount bHigh lt lt 8 bLow amp Ox00ff value Cha
6. newVal doConversion amp pitchTrimDef amp aToD12 newVal 0 4 newVal 0 6 oldVals 2 oldVals 2 newVal y 2 int newVal newVal doConversion amp pitchTrimPos amp aToD12 newVal 0 4 newVal 0 6 oldVals 3 oldVals 3 newVal y 3 int newVal newVal doConversion amp pitchVelocity amp aToD12 newVal 0 4 newVal 0 6 oldVals 4 oldVals 4 newVal y 4 int newVal newVal doConversion amp rollPos amp aToD12 newVal 0 4 newVal 0 6 oldVals 5 oldVals 5 newVal y 5 int newVal newVal doConversion amp rollForce amp aToD12 newVal 0 4 newVal 0 6 oldVals 6 oldVals 6 newVal y 6 int newVal newVal doConversion amp rollTrimDef amp aToD12 newVal 0 4 newVal 0 6 oldVals 7 oldVals 7 newVal 120 y 7 int newVal newVal doConversion amp rollTrimPos amp aToD12 newVal 0 4 newVal 0 6 oldVals 8 oldVals 8 newVal y 8 int newVal newVal doConversion amp rollVelocity amp aToD12 newVal 0 4 newVal 0 6 oldVals 9 oldVals 9 newVal y 9 int newVal newVal doConversion amp rudderPos amp aToD12 newVal 0 4 newVal 0 6 oldVals 10 oldVals 10 newVal y 10 int newVal newVal doConversion amp rudderForce aToD12 newVal 0 4 newVal 0 6 oldVals 11 oldVals 11 newVal y 11 int newVal newVal doConversion amp rudderTrimPos amp aToD12 newVal 0 4 ne
7. 1 card gt gainVtoCounts float card maxCount card pLimit card gt nLimit card gt vOffset card nLimit for channel 0 channel lt card gt nChannels channel if channel gt card gt nChannels printf DACCard channel d is out of range n channel if card gt vDefault gt card gt pLimit card gt vDefault lt card nLimit if errorChecking printf DACCard Voltage 1 3f is out of range n card vDefault voltage voltage gt card gt pLimit card gt pLimit card nLimit count unsigned short card gt gainVtoCounts voltage card vOffset addrl card gt baseAddr channel lt lt 1 outpw addrl count Setup for Dac channel void DACChannelInit struct DACChannel chan struct DAC Card float min max if chan gt channelNumber gt Card gt nChannels printf DACCard channel d is out of range n chan channelNumber else chan gt addr Card gt baseAddr chan gt channelNumber lt lt 1 if chan gt min chan gt max min Card gt nLimit max Card pLimit chan gt gain float Card gt maxCount max min 112 else chan gt gain float Card maxCount chan maxV chan gt minV chan gt offset chan gt min void set struct DACChannel Chan float value unsigned short count float checkMin checkMax if Chan max Chan gt minV checkMin Chan gt maxV chec
8. 153 oe sAcB sAsB cA Fzb oe Test data FxWind 100 FyWind 30 FzWind 300 u 100 v 50 w 50 SERRA Trio functions frrst seek atan w u alpha beta asin v AirSpeed Salpha asin w AlphaSpeed 57 3 alpha acos u AlphaSpeed 57 3 Sbeta asin v AirSpeed 57 3 just lift and drag FxBody FxWind cos alpha cos beta FzWind sin alpha FyBody FxWind sin beta Fzbody FxWind sin alpha cos beta FzWind cos alpha with side force FxBody FxWind cos alpha cos beta FyWind cos alpha sin beta FzWind sin alpha FyBody FxWind sin beta FyWind cos beta Fzbody FxWind sin alpha cos beta FyWind sin beta sin alpha FzWind cos alpha Without trig functions oe computers are VERY SLOW at trig functions and fast at mult ok at divide oe SA w AlphaSpeed oe cA u Alphaspeed oe sB v Airspeed oe cB AlphaSpeed Airspeed vSquared u u w w 154 AirSpeed sqrt v v vSquared AlphaSpeed sqrt vSquared combo v AlphaSpeed AirSpeed FxBody FxWind u AirSpeed FyWind u combo FzWind w AlphaSpeed FyBody FxWind v AirSpeed FyWind AlphaSpeed AirSpeed FzBody FxWind w AirSpeed FyWind w combo FzWind u AlphaSpeed 155 Standard Atmosphere Simulink S function Ef S function std_atms File std_atms c This C file S function estimates the values for
9. The combination of several technologies maturing at the same time along with the advent of low cost powerful computing hardware and software packages has allowed the creation of a modeling system that is much more powerful than the components that make up the system Tools have been assembled to rapidly create high resolution high fidelity flight simulations Simulink Ref 3 with Real Time Workshop Ref 4 provide a user friendly simulation environment that eliminates the need for a skilled programmer to produce most types of simulations Simulink RTW generate c programming source and a stand alone executable from a Simulink symbolic diagram in one step providing true Pictures to Code capability as represented in Figure 1 _ FS UPGRADE CONTROL STICK Matlab Simulink S Functions Non linear 6 DOF EOM or Auto code state space or Augmented transfer function non linear aircraft Student pilot simulation Command output Compiled C code Visu Cues Simulated Simulated Cockpit instruments View Figure 1 General User Progress Pictures to Code Simulink is a graphical user interface for The Mathworks MA Trix LABoratory Matlab dynamic system simulation software Essentially Simulink is an environment that allows a user to program a problem graphically Two additional capabilities allow the system the power and flexibility required to provide unlimited growth of the basic system The first is an Applic
10. Time Invariant LTI systems in Matlab to obtain time histories to compare to each other and the 6DOF simulation The LTI systems used a unit step input while the 6 DOF model used a 2 degree step input to scale the response so that they could be compared on a time history The perturbation was kept small in the 6 DOF in an attempt to keep the dynamics as close to the linearized system as possible however the stepsize could still be large enough to introduce the nonlinear effects for the non linear model Note that in all the graphs the 6 DOF response is the dotted line The first axis compared was the pitch in the short period Figure 20 shows the two state space models have very similar short period Impulse Response Pitch Angle 0 5 F State Space 4 o 6 DOF EA o 1 l A 2 ENS 2 ine 1 5 F 4 2 la Ba 25 E S l l l l l l l l z 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 Time sec Figure 20 Theta to Elevator Short Period Longitudinal Dynamics wn and damping while the 6 DOF is less damped and higher frequency The Long period dynamics show similar differences between the state space models and the 6 DOF The wn is higher and less damped than the state space but the time constants are the same The pitch angle response figure 21 is one where the state space models differed The natural frequency of the 6 DOF model falls between the two state space models The 6 DOF model shown in Figure 18 has the correction for t
11. handling qualities specifications Ref 37 as possible using the control architecture and CONDUIT software to fine tune the control gains 72 Modifications Required to Fly The model of the SH 2f was a 6 DOF state space model of the helicopter The model Figure 28 required fewer modification to fly than the X 29a as there were Matlab 5 1 Simulink 2 1 p gt theta body phi body gt psi body 0 1 m Ms u body Simulation Delay P radisec y body a radisec control inputs sif D gt w body ux ca Pa Demux 1 rad seo To Graphics gt gt j x i Control System Actuators Aircraft xdi Dynamics y ft y_out an z out a i ES phi deg sec 9 phi out i From Ctrl Arena2 Theta deg sec theta_out ft sec2kts pi psi deg sec i out Figure 28 SH 2F Block Diagram outputs for airspeed as well as all the linear and rotational rates and positions The Flybox input was included in the model and wired up to the inputs and the graphics and HUD were wired to the outputs of the model the timing block was included and set Observations of Flight Model The procedure for setting the timing of the model to real time was still not complete during the testing of the SH 2f The timing error was found after a engineer familiar with the dynamics of the helicop
12. The most simple and therefore the first kind of model used to analyze a new aircraft is a linearized first or second order transfer function model The basic flying qualities can be estimated from these simple models with very acceptable results for a first pass estimation Using relatively few equations a first cut gross estimate can be made of the flying qualities of a proposed aircraft The derivatives are estimated from statistical data collected from sources like the Air Force DATCOM The most simple model created using the Simulink RTW environment was a transfer function model The model was built up from loops to provide rate information to the Euler function block Figure 15 shows the same model as a transfer function a series of loop closures and a w 2 S2 2 z ws w 2 Y Step Transfer Fcn psition i ce egratori Scope1 rate gt gt input position gt Transfer function Figure 15 2 Order Transfer functions 49 subsystem with inputs and outputs The Simulink diagram was built up using variables in the blocks to allow the use of a initialization file to load the natural frequency cn and damping 6 variables into the model This allows one model to be used and modified quickly by loading various init files with variations in the model parameters Transfer function models treat an aircraft as a linear or rotational spring mass system The model has no motion except by
13. amp d12 DACChannelInit amp altimeter amp d16 DACChannelInit amp pitch8Ball amp d16 DACChannelInit amp roll8Ball amp d16 DACChannelInit amp yaw8Ball amp d16 DACChannelInit amp rudderBall amp d16 DACChannelInit amp airspeed amp d16 DACChannelInit amp dirGyro amp d16 DACChannelInit amp gMeter amp d16 DACChannelInit amp aoaIndicator amp d16 DACChannelInit amp machIndicator amp d16 DACChannelInit amp sideslipAngle amp d16 DACChannelInit amp leftEngRPM amp d16 DACChannelInit amp rightEngRPM amp d16 DACChannelInit amp verspeedIndicator amp d16 110 DACChannelInit amp rightNozz amp d12 DACChannelInit amp leftNozz amp d12 DACChannelInit amp internalPress amp d12 DACChannelInit amp courseDirIndicator amp d12 DACChannelInit amp cdHorIndicator amp d12 DACChannelInit amp leftEngTemp amp d12 DACChannelInit amp rightEngTemp amp d12 DACChannelInit amp leftEngFuel amp d12 DACChannelInit amp rightEngFuel amp d12 DACChannelInit amp pTotGauge amp d12 DACChannelInit amp yawForceOut amp d12 DACChannelInit amp rollForceOut amp d12 DACChannelInit amp pitchForceOut amp d12 endif MDL START Function mdlOutputs Abstract y 2 u static void mdlOutputs SimStruct S int T tid InputRealPtrsType uPtrs ssGetInputPortRealSignalPtrs S 0 printf Working
14. amp d16 DACCardInit amp d12 DACChannelInit amp altimeter amp d16 DACChannelInit amp pitch8Ball d16 DACChannelInit amp roll8Ball amp d16 DACChannelInit amp yaw8Ball amp d16 DACChannelInit amp rudderBall amp d16 DACChannelInit sairspeed amp d16 DACChannelInit amp dirGyro amp d16 DACChannelInit amp gMeter amp d16 DACChannelInit amp aoaIndicator amp d16 DACChannelInit amp sideslipAngle amp d16 DACChannelInit amp leftEngRPM amp d16 DACChannelInit amp rightEngRPM amp d16 DACChannelInit amp verspeedIndicator amp d16 DACChannelInit amp yawForceOut amp d12 DACChannelInit amp rollForceOut amp d12 DACChannelInit amp pitchForceOut amp d12 endif MDL_START Function mdlOutputs Abstract y 2 u static void mdlOutputs SimStruct S int T tid 127 InputRealPtrsType uPtrs ssGetInputPortRealSignalPtrs S 0 real T y ssGetOutputPortRealSignal S 0 set amp airspeed uPtrs 0 printf Working g uPtrs 0 set amp altimeter int uPtrs 1 set amp altimeter 4000 set amp pitch8Ball uPtrs 2 set amp rol18Ball uPtrs 3 set amp yaw8Ball uPtrs 4 set dirGyro uPtrs 4 set amp rudderBall uPtrs 7 set amp gMeter uPtrs 5 set amp aoaIndicator uPtrs 6 set amp sideslipAngle uPtrs 7 set amp leftEngRPM uPtrs 8 set amp rightEngRPM uPt
15. blitscreen bkground Image display the new frame else else if debugging VectorDump do the screen dump ji checkpt 4 update progress flag Terminate Normal program termination main 105 Instrument D A Simulink S function VAZZEEZZZZZZZZZZZZZZZIZI RRR A A E E E E IIR II ZI K A A ZI ZZZ id MODULE al inst c AUTHOR S Friz Anderson Douglas Hiranaka DATE September 25 1998 Copyright c ALL RIGHTS RESERVED REVISION HISTORY REV AUTHOR DATE DESCRIPTION 1 0 crf 11 5297 Creation cabtest cpp Es c dkh 6 11 98 reduced to instruments only o dkh 7 11 98 put into c mex S function format S mex See simulink src sfuntmpl doc Copyright c 1990 1998 by The MathWorks Inc All Rights Reserved Revision 1 3 This S function block sends values to the instruments from the computer to the PhEagle flight sim cab This is the a basic version of the outputs to Che Sim cab sending out only the altitude airspeed attitude direction g s angle of attack side slip L rpm R rpm Vertical speed and the forces back to the sim cab stick The stick positions are read in the stick block ph stick c kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkikkkkkkkxix define S FUNCTION NAME al inst define S FUNCTION LEVEL 2 include include include include include include include include i
16. yaw due to rudder Beta 0 0 Beta is the Side slip angle Alpha 0 0 u u0 cos Beta cos Alpha v u0 sin Beta w u0 sin Alpha Thrust CD 5 Rho Area u0 u0 trim thrust drag Deflect_Rudder 0 0 initialize Deflect_Aileron 0 0 Deflect_Elevator 0 0 Alpha 0 0 Beta 0 0 pre calculate the trig functions theta pitch angle psi yaw angle phi roll angle Theta 0 Psi 0 Phi 0 STheta sin Theta SPhi sin Phi SPsi sin Psi CTheta cos Theta CPhi cos Phi 144 CPsi cos Psi TTheta tan Theta SecTheta 1 0 if CTheta gt le 6 SecTheta 1 0 CTheta AE u_Trim u0 UpdateState tendif MDL INITIALIZE CONDITIONS ENTRY POINT FOR FLIGHT MODEL LOOP This function takes as parameters references to a state vect structure containing the control input from the current pass as well as the values for all other aircraft data from the previous pass Function mdlOutputs Abstract static void mdlOutputs SimStruct S int T tid Function mdlOutputs Abstract x This function is called once for every major integration time step Control vector Deflect_Elevator uPtrs 0 Deflect_Aileron uPtrs 1 Deflect_Rudder uPtrs 2 Rho uPtrs 3 Fx uPtrs 4 Fy uPtrs 5 Fz uPtrs 6 PitchingMoment uPtrs 7 Rolling
17. 40 To confirm the program code several complete stand alone simulators and IO functions were written to test the new code before incorporating them into S functions Where graphics and joystick input were required for verification the Snoopy IO package was used Virtually all of the stand alone program code that was created for use in the Cal Poly simulation lab has been converted to S functions The components have become part of a simulation laboratory using the same hardware and software through the conversion of the pieces to S functions To verify the CMEX S function a first order Euler then a second order numerical integrator using a Runge Kutta 4 integration method were placed into the S function template and imported into Simulink blocks The Euler block was tested against a Simulink first order transfer function using the Euler integration scheme The RK4 integrator test code uses three different damping ratios corresponding to the commanded pitch roll and yaw angles The test sent three step input signals to the integrators The results were compared to the same system set up using second order transfer functions and the built in Simulink RK4 integrators Both functions matched with the Simulink functions with less than 0 596 difference The next step was to create a transfer function model of the same system as the custom S function block The values were entered into the block the time step was set to the same value and Runge Kut
18. D to A Starting with the c code created for PhEagle I a Simulink D A S function was created to provide input to a simulation from the PheEagle stick pedals and throttles The code had to be converted to c code to function inside the S function template The process of converting the D A driver to c necessitated several changes to the original code C uses classes as a structure to construct programs C provides flexibility by allowing generalized functions to be created Since c is an extension of the c language all of the extensions had to be duplicated within the scope of the c language Since the flexibility and complexity of overloaded classes were not required for simulation the specific cases required for the S functions were cut and pasted from the c classes Creating the D A S function required a new data structure simplification of the function structure separation of the D A and A D functionality from a single function and simplified error trapping To keep the functions as simple as possible the A D and D A functions were separated into an input block and an output block respectivly The 43 D A output block is the code for both the 12 and 16 bit D A cards This is possible because both cards use the same code with different base addresses and different offsets for the resolution used by each card C pointer arithmetic is still powerful enough to provide the flexibility to handle 12 and 16 bit addressing in the same fu
19. Ref Airforce DATCOM Alpha and Beta and control derivatives are per radian forcesmoments has been modified to use the Airforce DATCOM techniques The data and conversion use the Navion example in Flight Sability and Control Robert C Nelson McGraw Hill Inc 1989 143 Parameter Value Description Name Dimensionless stability derivatives logitudinal CL dp 12 Lift CD dp 13 Drag CLAlpha dp 24 Lift curve slope per radian CDAlpha dp 27 Drag curve slope CmAlpha 7 dp 18 Pitching moment curve slope CLAlphaDot dp 25 CmAlphaDot dp 19 Pitching moment to angle of attack rate CLq dp 26 Change in lift to pitch rate Cmq dp 20 Pitch damping CLm 0 0 CDM 0 0 CmM 0 0 CLDelE dp 30 heave to elevator CmDelE dp 32 Pitch control to elevator Note sign gt up Cm0 dp 15 ji Dimensionless stability derivatives lateral CyBeta dp 43 Sway ClBeta dp 33 roll rate to beta dihedral CnBeta dp 38 yaw rate to beta Clp dp 34 roll damping Cnp dp 39 yaw moment to roll rate Clr dp 35 roll moment to yaw rate Cnr dp 40 yaw damping C1DelA dp 36 roll control CnDelA dp 41 yaw due to aileron adverse yaw CyDelR dp 47 sway to rudder ClDelR dp 37 roll rate due to rudder CnDelR dp 42
20. The second order system acts like a spring damper system with the natural frequency and damping ratio variable The second order system is used to model the short period oscillations of an aircraft s longitudinal pitch and lateral yaw axis Each axis is isolated dynamically providing 23 great control over the model dynamics Usually the system would be described as a state space as described by Equation1 Integrating a state space usually requires a single technique of numerical integration Part of the reason for creating the model was to Equation 1 X s AXG BU s Y s CX s DU s demonstrate Euler and Runge Kutta numerical integration techniques Each model was set up to use separate numerical integrators for each output axis To perform the first order integration s a Euler numerical integrator was created and tested using Matlab Matlab was selected to take advantage of its interpreted language which uses a syntax very similar to c Note that by rearranging the terms of a first order transfer function equations 2 4 the Euler technique is derived The results Equation 2 10 Y 86 s 10 U de Equation 3 de 100 10 dt Equation 4 d0 106dt 10dedt from the coded Euler integrator were compared to the Euler integrator supplied by Mathworks When the resulting plots overlaid exactly for the same input and time step the function was included in the simulator 24 The integration of the second order sy
21. VSound void estimate Function mdlTerminate double LESE fk fk fk fk TBase PBase Value for sea ssGetInputPortRealSignalPtrs S 0 ssGetOutputPortRealSignal S 0 level TEMPERATURE in K T0 288 16 is std Value for sea level PRESSURE in N m 2 PO 101325 0 Altitude m Temp if Alt lt 11000 0 TempK T0 LapseRatel Alt LS std eee K Press N m 2 Density N Kg 3 Acolustic Vel Press P0 pow TempK T0 9 81 LapseRatel R if Alt gt 11000 0 amp amp Alt lt 25000 0 PBase TempK Press 22700 216 66 PBase exp 9 81 Alt 11000 0 R TempK if Alt gt 25000 0 TBase 216 66 PBase 2527 3 TempK Alt 25000 0 LapseRate2 TBase Press PBase pow TempK TBase 9 81 LapseRate2 R Density Press R TempK VSound sqrt Y R TempK return Abstract No termination needed but we are required to have this routine static void mdlTerminate SimStruct S 158 M Sec kkkxxj ifdef MATLAB MEX FILE Is this file being compiled as a MEX file include simulink c MEX file interface mechanism telse include cg_sfun h Code generation registration function endif 159 Euler Coordinate Transform and Integrator Simulink S function KI de de in in File to_euler c Abstract x y Z psi theta phi 2 eul
22. ch 4 transforming the lift and oe drag vectors calulated in airpath axis to body axis All forces oe calulated in airpath axis must be transformed to the body axis The oe Fy was added to the force vector then the transoform was expanded oe to pass the y force through The final matrix takes all three axis oe forces from airpath to the aircraft body axis system Without the oe transform the only place a simulation is valid is in trim Without oe the transform the dynammics are slightly off and the flight path is oe significanly in error The transform maps some of the lift to drag oe and some of the drag to down Alpha and side force Beta oe oe This transform must tbe done before any body axis forces eg thrust oe are added to the system oe oe Inputs NA oe Outputs NA oe oe Usage wind2body oe oe Doug Hiranaka oe Cal Poly San Luis Obispo oe San Luis Obispo CA oe Created 12 30 98 oe Last Modified oe Do this twice once using trig functions and once using oe trig definitions oe oe This will be a two axis rotation A Alpha B Beta s sin c cos oe combining wind to beta oe cB sB 0 Dw oe sB cB 0 Fyw oe Or 0 1 1 bw oe and beta to body oe cA 0 sA X1 oe o m o xi Z1 oe a D o e D de to get oe CACB CAsB sA Fxb oe sB cB 0 Eyb
23. float pDot qDot rDot uDot vDot wDot Function mdlInitializeSizes Abstract Setup sizes of the various vectors Ef static void mdlInitializeSizes SimStruct S ssSetNumSFcnParams S NUM PARAMS if ssGetNumSFcnParams S ssGetSFcnParamsCount S return Parameter mismatch will be reported by Simulink tifdef oldtype ssSetNumContStates S 0 ssSetNumDiscStates S 0 tendif if ssSetNumInputPorts S 1 return ssSetInputPortWidth S 0 10 ssSetNumInputs S 3 ssSetDirectFeedThrough S 1 ssSetInputPortDirectFeedThrough S 0 1 if ssSetNumOutputPorts S 1 return ssSetOutputPortWidth S 0 20 ssSetNumOutputs S 6 ssSetNumSampleTimes S 1 Take care when specifying exception free code see sfuntmpl doc ssSetOptions S SS OPTION EXCEPTION FREE CODE Function mdlInitializeSampleTimes Abstract 142 Specifiy that we inherit our sample time from the driving block el static void mdlInitializeSampleTimes SimStruct S ssSetSampleTime S 0 INHERITED SAMPLE TIME ssSetOffsetTime S 0 0 0 define MDL INITIALIZE CONDITIONS Change to undef to remove function tif defined MDL INITIALIZE CONDITIONS Function mdlInitializeConditions Abstract Initialize the state Note that if this S function is placed hi with in an enabled subsystem which is configured to reset states this routine will be called during t
24. include lt stdlib h gt include lt math h gt define NUM_PARAMS 1 define INPUT_FILE_PARAM ssGetSFcnParam S 0 define SAD FILE NAME mxGetString INPUT FILE PARAM fname 99 define N COLS 100 max number of characters per line in input file define readline c f if fgets c N COLS f free c printf Not enough memory void Accelerate void ForcesMoments void read derivs char fname double dp void UpdateState void Wind2Body float FxWind float FyWind float FzWind double AirSpeed define pi 3 14159 define g 32 17 ft sec 2 141 define Deg2Rad 0 01745329 define Rad2Deg 57 2957795 define TwicePi 2 0 pi define HalfPi pi 2 0 char fname 100 double dp 50 properties float Rho Mass Ixx Iyy Izz Ixz Ixy Iyz Area Span Chord xx x states kkkkkl float u v w p Ar Y Theta Phi Psi xx yy zz Alpha Beta dt float STheta SPhi SPsi CTheta CPhi CPsi TTheta SecTheta derivatives float CL CD CLAlpha CDAlpha CmAlpha CLAlphaDot CmAlphaDot CLq Cmq CLm CDM CmM CLDelE CmDelE Cm0 CyBeta ClBeta CnBeta Clp Cnp Clr Cnr ClDelA CnDelA CyDelR ClDelR CnDelR xx x Controls KKK KK float Deflect_Elevator Deflect_Aileron Deflect_Rudder Forces moments static float Fx Fy Fz PitchingMoment RollingMoment YawingMoment static double Thrust Accelerations
25. oe 23 right engine fuel 0 100 oe 24 left eengione fuel 0 100 oe 25 ptotal 0 7000 0 left Nozzel 0 700 knots oe 7 internal pressure Beta side slip 15 degrees deg o 8 Course Deviation indicator 110 10 percent rpm oe 9 cd Horizontal indicator 10 110 percent rpm oe 10 cd Vertical Indicator 6000 feet min ft min de Stick forces CAUTION Pilot must be in CAB when used oe 26 pitch force 4 1 lbs 114 oe oe o oe o oe oe oe 27 roll force 4 1 lbs 28 yaw force 4 1 lbs NOTE this is a help block only there is no function attached to this m file Doug Hiranaka 9 27 98 Copyright c 1998 by Penguin Aeronautics 115 Stick D A Simulink S function VAZZEEZZZZZZZZZZZZZZZIZIZZ ZZZZZZZIZII ZZZ IIR RR ZZZ RR MODULE al_stick c AUTHOR S Fritz Anderson Doug Hiranaka DATE September 25 1998 Copyright c ALL RIGHTS RESERVED Cal Poly San Luis Obispo 1998 REVISION HISTORY x REV AUTHOR DATE DESCRIPTION 0 ert 11 5 97 Creation cabtest cpp Sub dkh 6 11 98 reduced to stick only 32 dkh 7 11 98 put into s mex format S mex See simulink src sfuntmpl doc S mex Copyright c 1990 1998 by The MathWorks Inc All Rights Reserved Revision 1 3 This S function block Reads the commanded stick position from the PhEagle flight sim cab This is the a basic version of the inputs from the Sim cab sending out on
26. this function provides a dump of the aircraft state vector values see the struct definition in AIRCRAFT H If debug is true it is output with the proper header and footer for a realtime dump If debug is false it is formatted to be output at the end of the program void VectorDump int i state_vect tSV tSV state_vect Snoopy gotoxy 3 1 cprintf State vector realtime dump i l ViewParamDump 35 i Snoopy ACDump 35 i i 3 gotoxy 3 i cprintf right aileron oe H tSV aileron_pos gotoxy 3 i de H cprintf left aileron tSV aileron pos gotoxy 3 i oe m cprintf elevator tSV elevator pos gotoxy 3 i 100 reports program status at termination knows whether this is an abnormal term void Terminate oe Pe cprintf rudder gotoxy 3 i oe m cprintf throttle gotoxy 3 i oe amp cprintf ignition gotoxy 3 i ge e cprintf engine on gotoxy 3 i ge e cprintf prop rpm gotoxy 3 i ge m cprintf fuel level gotoxy 3 i ge m cprintf x coordinate gotoxy 3 i ge m cprintf y coordinate gotoxy 3 i ge m cprintf z coordinate gotoxy 3 i oe th cprintf pitch gotoxy 3 i oe Fh cprintf effect pitch gotoxy 3 i oe th cprintf roll gotoxy 3 i oe th cp
27. 0 d12 nChannels 16 d12 vDefault 0 0 errorChecking DACChannel 16 bit channels altimeter channelNumber 14 altimeter minV 0 0 altimeter maxV 6e4 pitch8Ball channelNumber 5 pitch8Ball minV 0 5 pi pitch8Ball maxV 0 5 pi roll8Ball channelNumber 1 roll8Ball minV pi roll8Ball maxV pi yaw8Ball channelNumber 2 yaw8Ball minV pi yaw8Ball maxV pi rudderBall channelNumber 7 rudderBall minV 1 0 rudderBall maxV 1 0 airspeed channelNumber 10 airspeed minV 0 0 airspeed maxV 700 0 dirGyro channelNumber 3 dirGyro minV pi dirGyro maxV pi gMeter channelNumber 4 gMeter minV 4 gMeter maxV 9 aoaIndicator channelNumber 8 aoalIndicator minV 10 aoaIndicator maxV 40 sideslipAngle channelNumber 11 sideslipAngle minV 15 sideslipAngle maxV 15 0 0 turns off 1 truns on 126 leftEngRPM channelNumber 12 leftEngRPM minV 110 leftEngRPM maxV 10 rightEngRPM channelNumber 13 rightEngRPM minV 10 rightEngRPM maxV 110 verspeedIndicator channelNumber 15 verspeedIndicator minV sqrt 6000 verspeedIndicator maxV sqrt 6000 DACChannel 12 bit channels yawForceOut channelNumber 11 yawForceOut minV 1 yawForceOut maxV 1 rollForceOut channelNumber 12 rollForceOut minV 1 rollForceOut maxV 1 pitchForceOut channelNumber 13 pitchForceOut minV 1 pitchForceOut maxV 1 errorChecking 1 DACCardInit
28. 1 1b MB first beta 9 26 1992 da MB publication release 8 23 1995 2 0 mickRacky second edition update 6 10 1998 D Hiranaka modified with rk4 variables Description oec This file contains definitions for structures and prototypes of interface functions for the aircraft model posa i e EE Ho Ho Ho ifndef AIRCRAFT_H define AIRCRAFT H This is the aircraft model state vector tvpe It holds the current state of the aircraft controls attitude and velocities as well as the current view status This struct is modified bv the functions in aircraft cpp input cpp and fsmain cpp However the onlv declaration of this tvpe in the current version is in fsmain cpp The other modules get it bv reference during function calls struct state vect int aileron pos aileron position 15 to 15 int elevator_pos elevator position 15 to 15 int throttle_pos throttle position 0 to 16 int rudder pos rudder position 15 to 15 boolean buttonl stick buttons true if pressed boolean button2 boolean ignition on ignition state on off true false boolean engine on engine running if true int rpm rpm of engine byte fuel gallons of fuel byte fuelConsump fuel consumption in gallons hr int x pos current location on world x int y pos current location on world y int z pos current location on world z double pitch rotation abo
29. 6 DOF model The alpha and beta inputs allow the model to take in angle of attack and sideslip angles from a state space model and have the aircraft oriented correctly The wind axis velocity components are transformed through the Euler angles to the world axis Finally the wind axis velocity components in world coordinates are integrated to get a change in position in the world coordinate axis To test the block the velocity and angle rates were connected to constant value blocks in Simulink and integrated for several seconds Once the proper dynamics were 52 observed the Euler block was flown using the stick and no other dynamics to confirm the correct responses to the commanded input rates Trim Attitude and Speed Since the model is linear and actual aircraft are highly nonlinear the model is valid only for small perturbations from the initial trim conditions It is difficult to see when the model has departed from the conditions where the model is valid Since the same model is available in the three levels of complexity a side by side comparison of the models is possible Feel Transfer function and state space models are perfect for setting up and determining the feel system dynamics Models with known dynamics can be quickly created to test various states fed back to the feel system to determine if feeding back the state has positive negative or no effects on the handling qualities The effects of the feel system itself can be mo
30. 99 Copyright c 1998 99 by Penguin Aeronautics wn approx 6 zeta approx 6 create a tranfer function system num 36 3271 den 1 8 2998 36 3271 181 9 create a frequency vector w 0 1 0 1 100 mag phase bode num den w convert the magnatude to db db 220 10g10 mag figure plot the bode results on a single plot subplot 211 semilogx w db r title Amplitude Response db vs freq grid subplot 212 semilogx w phase r title Phase Response degree vs freq grid Sor use a LTI system Sys tf num den bode sys create a time history of the data figure impulse sys figure rlocus sys sgrid 182
31. By making the feel proportional to the dynamic pressure and Nz the actual feel of an aircraft can be 65 modeled By feeding back any of the other states the effect on handling qualities can be investigated 66 Control System Closed Loop Using Simulink Real time workshop PhEagle II allows engineers the capability to rapidly create simulations of closed loop flight control systems These can be systems closed around state space or full nonlinear aircraft models The ability to model closed loop control systems allows students and professional engineers to fly the aircraft flight control system to confirm analysis of the control laws Classic linear analysis only looks at one or two axis at a time Flying the model tells the engineer right away if there is something that requires more detailed analysis or optimization Flying the closed loop full state model of the Kaman SH 2f gave a researcher insight to behaviors in the aircraft that were part of the physical system that could not be compensated with the flight control system User manual Intranet Internet Using a combination of intranet and internet web pages the documentation for the simulation laboratory is maintained on the host computer with the basic instructions being the home page of the browser on the PhEagle computer The rest of the information publicly available will be kept on the locus web server http locus aero calpoly edu sim Source code for the PhEagle II will be kept
32. ERA OAS II SA KE a a TFT RATI N ifndef sticki h define sticki h include lt conio h gt ifdef _MSVC_ define inport addr _inpw addr define inportb addr _inp addr define outportb addr val _outp addr val endif define inportb addr inp addr define outportb addr val outp addr val struct PCLabCard unsigned short int addr register addresses unsigned short maxADCount minADVoltage maxADVoltage nADChannels nDAChannels base ento cntl cnt2 cntCtrl dalLow dalHigh da2Low da2High adLow adHigh diLow diHigh Celi gainCtrl muxCtrl modeCtrl softAD doLow doHigh remember to cut an paste the da code requred struct ADCChannel short cNumber float minV float maxV unsigned short adcount float gain float offset Me void PCLabCardInit struct PCLabCard card float doConversion struct ADCChannel Chan void ADCChannelInit struct ADCChannel chan tendif struct PCLabCard Card struct PCLabCard card 139 Abbreviated Stick Help file function pitch roll yaw r throttle l throttle ph stick ph stick c Simulink RTW s function Pheagle Flight sim cab input E oe pitch roll yaw r throttle l throttle ph stick oe This is a basic input block that reads stick pedal and throttle oe positions from the Pheagle sim cab The forces are done with oe the instrument output block so that all the input and all the oe o
33. MDL_INITIALIZE CONDITIONS static int near readjoy STICK s int mode int mask int nread int delay register int i register Uint m unsigned int t xl yl x2 y2 minxl minyl minx2 miny2 int js tt ntimes minxl minyl minx2 miny2 OxffffU avoid compiler warning memset s gt a 0 sizeof s 7a for ntimes 0 i JS_TIMEOUT t READING xl yl x2 y2 t outp JS_PORT 0 set trigger for m mask m while JS_READ m amp amp 1 LEALI break tt READING js JS READ m if js 0x01 xl tt m amp 0x01 if js amp 0x02 yl tt m amp 0x02 if js amp 0x04 x2 tt m amp 0x04 if js amp 0x08 y2 tt m amp 0x08 if minx1 gt xi t minxl xi if minyl gt vi t minyl vi if minx2 gt x2 t minx2 x2 if miny2 gt y2 t miny2 y2 if ntimes nread read more break 170 if 0 i delay delay tt 1234 for i 10 i gt 0 tt 19 js m mask s a 0 js amp 0x01 0 minxl analog 1 s a 1 js amp 0x02 0 minyl analog 2 s a 2 js amp 0x04 0 minx2 analog 3 s a 3 js amp 0x08 0 miny2 analog 4 js JS READ s b 0 js amp 0x10 button 1 s b 1 js amp 0x20 button 2 s b 2 js amp 0x40 button 3
34. Ref 13 CIFER is a set of utilities tied together with a common interface that process time domain Ref 12 frequency sweep data into frequency domain data bode plots Conducting a manual frequency sweep CHIRP provides data for the program to process into transfer functions and stability derivatives CIFER includes a utility to fit low order transfer functions Ref 17 to the high order identified systems Data created for the Cal Poly simulation lab tutorial was processed using CIFER and a simple Simulink model The model and data were incorporated into a internet based tutorial to demonstrate system identification to users of the Cal Poly simulation lab A flight data collection system created in the Cal Poly flight controls lab provides the capability to collect frequency data for existing aircraft The system uses low cost consumer grade sensors sending signals through a pem cia A D card to a laptop personal computer The system created is flexible powerful inexpensive expandable verified and easy to use fulfilling all of the original design objectives The software code generator was also verified and includes the tools and techniques that can be used to verify future simulation models PhEagle I PhEagle Hardware Sim Cab The heart of pilot in the loop simulation is the interface between the pilot and the simulation Cal Poly s simulation laboratory has a two seat tandem fighter cockpit cab Figure 3 with analog stick
35. SIMULINK S FUNCTION NAVION LATERAL STATE SPACE SETUP ARCHANGEL NAVION LONGITUDIANAL STATE SPACE SETUP ARCHANGLE NAVION COMPLETE STATE SPACE SETUP ARCHANGEL NAVION LATERAL STATE SPACE SETUP NELSON NAVION LONGITUDINAL STATE SPACE SETUP NELSON NAVION COMPLETE STATE SPACE SETUP NELSON NAVION TRANSFER FUNCTION SETUP xi 168 173 174 175 177 178 179 181 List of Tables Table Page Table 1 Aircraft control Stick and Pedal Feedbacks 13 Table 2 State Vector 29 Table 3 SAD File 29 Table 4 Force and Moment Derivative Equations 31 Table 5 Equiations of Motion 31 Table 6 Euler Velocity Equations 32 Table 7 Euler Rate Equations 32 Table 8 Instrument Output 44 Table 9 Cab Inputs 46 List of Figures Figure Title Page Figure 1 General User Progress Pictues to Code 3 Figure 2 FlyBox Inceptor 5 Figure 3 PhEable Simulation Cab 12 Figure 4 F 15 eagle Stick 12 Figure 5 Sibline and Stick Computer 14 Figure 6 Engine Throttles 14 Figure 7 Instructor Station 16 Figure 8 Pheagle Instruments 16 Figure 9 Graphics Front View 17 Figure 10 Pheagle I Distributed parallel Computing 19 Figure 11 BYOFS Original Screen 26 Figure 12 Snoopy Screen 26 Figure 13 Symbolic Model of 6 DOF Functions 28 Figure 14 Screen Shot of World Up VR Player 37 Figure 15 2nd Order Transfer Functions 49 Figure 16 Archangel State Space Model 51 Figure 17 Navion Long Period Longitudinal Dynamics 56 F
36. Siblinc The input to the Siblinc is in the form of reference voltages sent from a PC through an off the shelf digital to analog D A converter card The voltages are amplified in the Siblinc to drive the instruments The Siblink is the tall tower on the left of Figure 5 Figure 5 Siblinc and Stick Computer Stick Computer All of the functions of the stick are handled through a separate analog computer the center tower in Figure 5 The stick computer buffers command inputs from the stick rudder pedals and two throttles Figure 6 to the PC s analog to digital A D Figure 6 Engine Throttles card and sends commands from the PC s D A card through an amplifier to the sick and rudder pedal torque motors The amount of torque generated by the motors can be set statically through the stick computers front panel or by varying the reference voltages from the PC to the stick computer The stick computer also sends back to the IO PC computer stick position force and trim position and velocity Feeding back force to the position virtual spring and damping can be created By feeding back force and damping proportional to any of the modeled states can be used to enhance the handling qualities of an aircraft Ref 25 PhEagle Hardware Computers The heart of the simulation lab is the computer network There are 4 Pentium 166 MHz computers connected by Ethernet to provide the simulation dynamics high resolution texture mapp
37. Table 6 Euler velocity Equations QX gt ucos cos v sindsin cos COos sinV w cospsinOcosYy sinpsiny dY dt ucos siny v sinpsin sinPy cos cosy w cospsin sinwP sIndcosy QZ gt using VSINPCOSO WCOSPHCOSQ Table 7 Euler Rate Equations o ot pt gsin rcoso tano d0 gt qcos rsing dP ot qsin rcos sec out the right wing w down The world axis velocities are integrated to obtain the current position in the world flat earth X North Y East Z toward the center of the earth coordinate axis Table 7 shows how the body axis rates p about the long axis q about the wing axis r about the vehicle vertical axis are combined with the previous Euler angles to obtain the Euler rates The Euler rates are integrated to obtain the current Euler angles Y yaw positive east and 0 degrees north O pitch positive up and 0 degrees level from the horizon flat earth roll positive right wing down 0 degrees no roll Finally the angles are reduced to remain in the first multiple of pi The model was originally created and tested as a Matlab m file program FASAND to demonstrate the coding of 6 DOF equations of motion in a generic programming language The code is functional however on a PC the rate of integration limits the usefulness as a research tool The version intended to be used for batch simulations is the Simulink S function In addition to the basic equations of motion the FASAND code inclu
38. allow a complete verification of the model with an actual aircraft 63 Impulse Response Roll Angle T T T T o o a J State Space 6 DOF 4 10 15 20 25 30 Time sec Figure 23 Roll Angle Response Standard Atmosphere A C MEX S function block was created Figure 24 to replace the hardwired atmosphere function The original function estimated the atmosphere up to the first isothermal layer This limited the function 459 67 Constant to altitudes less than 36 090 ft the cruising fenka PT 00014503 i Pressure Ib in 2 altitude of paar Demux To psi Alt ft A To meters SFunction 01940 Density slug ft 3 To psit The S function ai To ft sec commercial airliners Demux standard atmosphere Figure 24 Atmosphere Conversion from SI to English Units function calculates the pressure temperature density and speed of sound up to 47 kilometers or about 155 000 ft using altitude as an input Using the altitude output from the 6 DOF function required including a unit delay block in the Simulink model to avoid a algebraic loop The delay and initial condition must be set to match the models starting altitude and time step The C MEX S function does the calculations using SI units the conversion to 64 English engineering units is done in Simulink as shown in Figure 24 The block takes in as parameters the
39. being perturbed from a steady state The results are only valid for conditions fairly close to the steady state State space models can model off axis dynamics as well as on axis dynamics with the most sophisticated models able to model all of the coupled dynamics for the condition These are still not as complete as a 6 DOF nonlinear model as aerodynamic and other nonlinear effects occur off the trim condition A model was created with separate longitudinal and lateral state space matrices The derivatives were dimensionalized using Cal Poly Archangel v1 0 software A second state space model figure 16 was created using a state space model used as an example in Ref 33 50 592 to knots u delta ft sec to degl p rad sec alpha delta rad Xft Airspeed 700 knots elevator im CD I Int YU theta delta rad Altimeter 06000 ft Aileron Navion q rad sec Archangel 1 0 q delta rad sec gt Pitch8ball 90 deg Rudder Longitudinal Long output xm to command rad StateSpace per radisec p gt Roll8ball 180 deg Right Throttle beta delata rad phi delta rad gt Do Yaw 180 deg Left Throttle aileron rad Out pl X7 ABUL glint p delta rad p alpha rad Z f gt gmeter 4 49 g Stick ut y Cx Du n p delta rad sec alpha ra gmet
40. beta sideslip 15 deg deg 44 12 Teft engine rpm 10 110 percent rpm 13 right engine rpm 10 110 percent rpm 14 vertical speed indicator 0 60 000 feet 15 vertical speed indicator 0 6 000 feet min 12 bit channels 0 right nozzel 0 100 1 left nozzel 0 100 2 internal pressure 112 psi 3 course deviation indicator 1 4 cd horizontal indicator 1 5 cd vertical indicator 1 5 right engine temp 200 1 400 deg 7 left engine temp 200 1 400 deg 8 left fuel 0 100 percent 9 right fuel 0 100 percent 10 ptotal 0 7 000 psi 11 stick pitch force 1 not calibrated 12 stick roll force 1 not calibrated 13 pedal yaw force 1 not calibrated Input A to D The same changes to the c code were made to the stick pedal and throttle A D functions The function sets the gain and offset so that the input to the model is normalized to 1 Stick The stick was tested by connecting the stick block to a numerical output block and scope to view the numerical and dynamic output from the stick block The stick output units were normalized to allow any commanded units to be set from the Simulink diagram Note that some of the ranges have reversed signs from the rest of the outputs and the throttles are normalized to between 0 and 1 This has no effect on the output from the S Function as the output is a single numerical value per time step Table 9 shows
41. channelNumber 13 rightEngRPM minV 10 rightEngRPM maxV 110 altimeter channelNumber 14 altimeter minV 0 0 altimeter maxV 6e4 verspeedIndicator channelNumber 15 verspeedIndicator minV sqrt 6000 verspeedIndicator maxV sqrt 6000 DACChannel 12 bit channels rightNozz channelNumber 0 rightNozz minV 0 rightNozz maxV 100 leftNozz channelNumber 1 leftNozz minV 0 leftNozz maxV 100 internalPress channelNumber 2 internalPress minV 1 internalPress maxV 12 courseDirIndicator channelNumber 3 courseDirIndicator minV 1 courseDirIndicator maxV 1 cdHorIndicator channelNumber 4 cdHorIndicator minV 1 cdHorIndicator maxV 1 109 cdVerIndicator channelNumber 5 cdVerIndicator minV 1 cdVerIndicator maxV 1 leftEngTemp channelNumber 6 leftEngTemp minV 200 leftEngTemp maxV 1400 rightEngTemp channelNumber 7 rightEngTemp minV 200 rightEngTemp maxV 1400 leftEngFuel channelNumber 8 leftEngFuel minV 0 leftEngFuel maxV 100 rightEngFuel channelNumber 9 rightEngFuel minV 0 rightEngFuel maxV 100 pTotGauge channelNumber 10 pTotGauge minV 0 pTotGauge maxV 7000 yawForceOut channelNumber 11 yawForceOut minV 1 yawForceOut maxV 1 rollForceOut channelNumber 12 rollForceOut minV 1 rollForceOut maxV 1 pitchForceOut channelNumber 13 pitchForceOut minV 1 pitchForceOut maxV 1 errorChecking 1 DACCardInit amp d16 DACCardInit
42. code from c to S functions and for students to create the same simulation after the conversion The conversion from c to S functions took six months whereas Sr level undergraduate students were able to create complex models in hours Research Objectives Originally the objectives of the research were to extend the basic capabilities of the Cal Poly flight simulation laboratory providing a first and second order linear model for the rotational axes of a Cessna 172 in landing mode The model was to be used to perform handling qualities research into the effects of time delay Ref 19 20 21 22 23 24 on the pitch channel of input using Cal Poly s force feedback stick and rudder However after the model was created tested and verified a system was found that allows rapid development of an advanced simulation lab Using The Mathworks Simulink graphical simulation environment as a base along with Real Time Workshop auto coding software to generate simulation executables from the Simulink models a completely modular simulator was established Once the existing modeling software and hardware drivers were incorporated additional software tools were created to provide a system that is inexpensive flexible powerful easy to use and provides students with tools industry and research are just starting to use Ref 9 The Mathworks provides a API for including user created functions in simulations C MEX functions extend the basic matlab scri
43. design from a blank sheet of paper to a flying simulation utilizing a complete set of stability derivatives The project combines computer aided drafting CAD computer aided Engineering CAE computational fluid dynamics and simulation As the project matured and PC s become more powerful the simulation code was ported to a PC and converted to c TCP IP network socket and A D D A drivers were written for the PC s and Graphics were created to work with the Quantum 3D cards Development of PhEagle I Using c to develop the original software for the PhEagle has allowed rapid and structured creation of the basic capabilities of the system The system is run and maintained by student technicians and researchers To change the force set up on the stick or verify the flight model requires an expert programmer familiar with the modeling software and hardware drivers The programmer must have a thorough knowledge of c programming the source code and the hardware as well as control theory The c code is powerful and flexible and allows the system unlimited expansion It does require a substantial investment to learn how the various parts of program code and hardware interact 21 Existing Simulation Tools There are two main types of simulation of fixed wing and rotary wing aircraft batch and real time Both can be further divided into categories that include various combinations of simulated and actual hardware in the loop and piloted and pr
44. flag if Snoopy InitAircraft opMode Terminate Aircraft initialization failed main checkpt 3 update progress flag EraseScreen REV 2 1 display control help void DisplayHelp gotoxy 1 1 cprintf The Waite Group s Flights of Fantasy c 1992 1995 r n cprintf r n cprintf cmd line args display this help screen r n cprintf cprintf cprintf cprintf r n cprintf view control keys cprintf cprintf cprintf Cpr ntf XNrVXn cprintf engine control cprintf cprintf r n cprintf sound control cprintf r n D ord enable debugging dump mode r n W or w enable world traverse mode r n Vor v diplay program version r n Fl look forward r n F2 look right r n F3 look behind r n F4 look left r n I or i toggle ignition engine on off r n increase decrease throttle setting r n S or s toggle sound on off r n cprintf aircraft control pitch up stick back or down arrow r n cprintf pitch down stick forwardd or up arrow r n cprintf left roll stick left or left arrow r n cprintf right roll stick right or right arrow r n cprintf rudder or keys r n cprintf brake tb or B XrNn this function parses the command line parameters Accepted command line parameters are d D start FOF in debu
45. functions were created to expand the basic capabilities of the system Simulink Simulink is an add on package to Matlab that uses a graphical interface to allow rapid modeling of dynamic systems Through the graphical user interface provide by Simulink engineers get a visual representation of connections between the hardware and control system Using Simulink as an interface to the simulation hardware drivers allows 34 the setup of the force feedback system to be performed by non programmers Software tools were created to allow engineers to fly transfer function and state space models that previously would have required expert programmers to create Flying a transfer function allows rapid development of preliminary designs First cut designs use literal factors to estimate the gross handling qualities for a design iteration by using spring and damping values obtained from the literal factors The Transfer functions are then analyzed using frequency domain techniques Finally it is possible to use PhEagle II to fly the equations Gross handling qualities are rapidly evaluated early in a design allowing more time to be spent refining performance and handling characteristics Since the RTW auto coder creates a stand alone DOS executable program students can substitute generic game jovsticks and software graphics for the complex simulation lab IO to allow code generated at the laboratory to be run on any PC The wraparound template that provides t
46. index 1 while t lt tFinal deltaTheta index 10 OldTheta dt 10 deltakE dt Update the derivatives for the integrations OldTheta 01dTheta deltaTheta index theta index OldTheta t t dt time index t index index 1 end Outer loop plot time theta xlabel Time sec ylabel theta grid 90 RK4 Runge Kutta Help file script RK4 SRK4 m Given the transfer function 0 0165 s 2 0 186s 0 0165 solving the differential equation this routine returns the values at the next time step oe In this version we use the fourth order Runge Kutta method oe to integrate oe oe integrate to get current state oe dt time increment oe Theta pitch angle oe deltaE elevator angle oe This function is free to copy and distribute for educational purposes as long oe as this notice is included No guarantee expressed or otherwise is made of the oe accuracy of the code oe Eric Vinande Doug Hiranaka 4 98 oe Copyright c 1998 by Cal Poly San Luis Obispo hold on clear DegToRad 0 01745329 begin inputs K 1 0 wn 0 12845 zeta 0 5 deltaE 1 0 dt 0 5 tFinal 100 Ster end of inputs coefficients for Runge Kutta method 2 0 zeta wn b wn 2 0 c wn 2 0 Theta 1 20 z 1 0 while t lt tFinal kl dt z index 1 ll dt a z index 1 b Theta index 1 K
47. oe 10 Vertical Speed Indicator 6000 feet min ft min oe Stick forces CAUTION Pilot must be in CAB when used oe 11 pitch force 4 1 lbs oe 12 roll force 1 lbs oe 13 yaw force 4 1 lbs oe oe NOTE this is a help block only there is no function oe attached to this m file oe oe Doug Hiranaka 9 27 98 oe Copyright c 1998 by Penguin Aeronautics 131 Abbreviated Stick D A Simulink S function RRO I III RRR IIIA A II IIR A I A A K K k K RR A I a k k k k k MODULE ph_stick c AUTHOR S Fritz Anderson Doug Hiranaka DATE September 25 1998 Copyright c ALL RIGHTS RESERVED Cal Poly San Luis Obispo 1998 REVISION HISTORY x REV AUTHOR DATE DESCRIPTION 0 ert 11 5 97 Creation cabtest cpp Fi iL dkh 6 11 98 reduced to stick only 2 dkh 7 11 98 put into s mex format S mex See simulink src sfuntmpl doc S mex Copyright c 1990 1998 by The MathWorks Inc All Rights Reserved Revision 1 3 This S function block Reads the commanded stick position from the PhEagle flight sim cab This is the a basic version of the inputs from the Sim cab sending out only the stick pedal and throttle position from the cab The forces are set in the instrument block ph inst c E EE EHEHEHEH k k k k k k k k Ck Ck Ck k k k k k ch Ck Ck kCk Ck CkCk Ck Ck Ck k k k k k AA AAA AAA AAA RA AAA AAA ke kk ke ke ek ek e ex f define S FUNCTION NAME ph sti
48. on the PhEagle computer and the FASAND source code on the locus server sim page The www web page describes the facilities and software capabilities of the PhEagle system and the simulation and controls laboratory Verification of Concept To validate the software aspects of the pictures to code concept several models were modified to allow inceptor input and graphics output using NASA Ames RIPTIDE Real time Interactive Prototype Technology Integration Development Environment rapid simulation facility The facility at the time consisted of a SGI ONYX with 4 67 R10000 processors an inceptor Flybox and high resolution texture mapped graphics database which includes a basic heads up display HUD system The RIPTIDE system was verified using a verified GENHEL blade element model of a UH 60 helicopter Three models were used to conduct the test which was done in four stages The Flybox and graphics were tested using a simple transfer function model to test the Euler motion and orientation block A simple one axis state space model of the X 29A in pitch was modified with transfer functions for yaw and roll and given motion with the Euler function A complex state space model of a Kaman SH 2f with a model following flight control system was modified to use the Flybox and graphics And the 6 DOF nonlinear model of a Navion liaison aircraft was connected to the Flybox and graphics and flown CONDUIT The feedback and feedforward gains for the X 29A and th
49. pitch and yaw based on control position and airspeed uDot Fx Mass g STheta q w r v vDot Fy Mass g CTheta SPhi r u p w wDot Fz Mass g CTheta CPhi p v q u tau I Thetadot gt Thetadot tau I w x H pDot q r Iyy Izz Ixx RollingMoment Ixx Ixz Ixx q p Ixx Iyy Izz r Ixz Izz p YawingMoment Izz 1 1 Ixz Ixx Ixz Izz qDot p r Izz Ixx Iyy PitchingMoment Iyy r r p p Ixz Iyy rDot p q Ixx Iyy Izz pDot q r Ixz Izz YawingMoment Izz This function applies the current angular rates of change to the 148 current aircraft rotations and checks for special case conditions such as pitch exceeding 90 degrees void UpdateState float xDot yDot zDot PsiDot ThetaDot PhiDot static float OlduDot OldvDot OldwDot OldpDot OldqDot OldrDot OldPhiDot OldThetaDot OldPsiDot OldxDot OldyDot OldzDot Initialize the previous velocities for the integrator OldxDot 0 0 OldyDot 0 0 OldzDot 0 0 OlduDot 0 0 OldvDot 0 0 OldwDot 0 0 OldpDot 0 0 OldqDot 0 0 OldrDot 0 0 Fx 0 0 Initialize the force and moment variables Fy 0 0 Fz 0 0 PitchingMoment 0 0 RollingMoment 0 0 YawingMoment 0 0 ut 3 0 uDot OlduDot 2 0 dt v 3 0 vDot OldvDot 2 0 dt wt 3 0 wDot OldwDot 2 0 dt p 3 0 pDot OldpDot 2 0 dt q 3 0 qDot 0ldqDot 2 0 dt r 3 0 rDot OldrDot 2 0 dt Precalculate trig functions
50. pitchPos minV 1 0 pitchPos maxV 1 0 pitchForce cNumber 3 pitchForce minV 1 0 pitchForce maxV 1 0 pitchTrimDef cNumber 4 pitchTrimDef minV 1 0 pitchTrimDef maxV 1 0 pitchTrimPos cNumber 5 pitchTrimPos minV 1 0 pitchTrimPos maxV 1 0 pitchVelocity cNumber 6 pitchVelocity minV 1 0 pitchVelocity maxV 1 0 rollPos cNumber 7 rollPos minV 1 0 rollPos maxV 1 0 rollForce cNumber 8 rollForce minV 1 0 rollForce maxV 1 0 rollTrimDef cNumber 9 rollTrimDef minV 1 0 rollTrimDef maxV 1 0 118 rollTrimPos cNumber 10 rollTrimPos minV 1 0 rollTrimPos maxV 1 0 rollVelocity cNumber 11 rollVelocity minV 1 0 rollVelocity maxV 1 0 rudderPos cNumber 12 rudderPos minV 1 0 rudderPos maxV 1 0 rudderForce cNumber 13 rudderForce minV 1 0 rudderForce maxV 1 0 rudderTrimPos cNumber 14 rudderTrimPos minV 1 0 rudderTrimPos maxV 1 0 rudderVelocity cNumber 15 rudderVelocity minV 1 0 rudderVelocity maxV 1 0 Set up for the card and the channels PCLabCardInit amp aToD12 ADCChannelInit amp pitchPos amp aToD12 ADCChannelInit amp pitchForce amp aToD12 ADCChannelInit amp pitchTrimDef amp aToD12 ADCChannelInit amp pitchTrimPos amp aToD12 ADCChannelInit amp pitchVelocity amp aToD12 ADCChannelInit amp rollPos amp aToD12 ADCChannelInit amp rollForce amp aToD12 ADCC
51. qualities research to be conducted A state space is a linear system modeling primary axis the output desired and cross coupling of control input to other axes This capability is being developed as a separate part of system development and will not be described at this time 27 Basic 6 DOF Nonlinear Rigid Body Steady State Subsonic Aerodynamics A single point 6 degree of freedom nonlinear rigid body model of an aircraft Ref 32 was created to provide the basis for more advanced models The simulation has been divided into three main functions Forces and moments accelerations coordinate transform and state update Figure 13 shows a symbolic representation of functions and Unit Delay8 180 1 Psi Unit Detay7 1 gt UnirDetayo 1 lt z Mass M O gt rho hoc P ixx mo uDot mi pu w yy R uDot y 540 izz P izz y Ixz P xz z gt 0 m Fx u vDot 4 4 p vDot di z Fy Piv q a gt Theta L Pip wDot wDot pi 2 99 Elevator Elevator gt ja E N dir gt Aileron i rd pDot DE Aileron Alpha Red Psi pDot Theta Beta RR P Theta Rudder Airspeed Phi r gt Rudder p Beta gt P gt
52. s gt b 3 js amp 0x80 button 4 return m Function mdlOutputs Abstract simply passes states y n Ef static void mdlOutputs SimStruct S int T tid real_T ey ssGetOutputPortRealSignal S 0 int ij double XOut YOut Ulong testno STICK s 1 i 3 for testno 1 i readjoy s 0 3 1 0 This section calibrates the output for a Kraft KC3 stick and normalizes the outputs XOut 1 s a 0 290 0 YOut 1 s gt a 1 290 0 if XOut lt 0 0 XOut 2 3 if YOut lt 0 if XOut gt 0 0 XOut 1 048 0 0 YOut 2 3 0 if YOut gt 0 0 YOut 1 048 y 0 XOut y 1 YOut sE Dati define MDL_UPDATE Change to undef to remove function if defined MDL UPDATE Function mdlUpdate Abstract 171 This function is called once for every major integration time step w Discrete states are typically updated here but this function is useful ke for performing any tasks that should only take place once per integration step kif static void mdlUpdate SimStruct S int T tid endif MDL_UPDATE define MDL_DERIVATIVES Change to undef to remove function tif defined MDL DERIVATIVES Function mdlDerivatives d static void mdlDerivatives SimStruct S endif MDL DERIVATIVES Function mdlTerminate Abstract No termination needed but we are required to have
53. space setup SFASAND Fundamentals of Aircraft Simulation And Nonlinear Dynamics 9 9 9 oe oe o oe oe o oe o oe oe oe oe This is a state space model of the Navion example aircraft template file to set up a state space to run a state space model in Simulink The A and B matricies were dimensional derivatives provided in appendix A of Flight Stability and control Robert C Nelson This Script is free to copy and distribute for educational purposes as long as this notice is included Doug Hiranaka Created 1 99 Last Update Copyright c 1998 99 by Penguin Aeronautics NNavionLonA 0 0448765 0 036 0 32 174 0 369 2 014955 168 8 0 0 0019 0 0396 2 948 0 001 0 NNavionLonB 0 28 2856 11 65435 0 NNavionLonC 10 0 0 0100 0 0 1 50 000 1 NNavionLonD 0 0 0 0 states u w q theta inputs elevator output speed heave pitch rate pitch angle sys ss NNavionLonA NNavionLonB NNavionLonC NNavionLonD statename states inputname inputs outpurname output NNavionLatA 0 2531035 0 1 0 0 182 16 02 8 40 2 19 0 4 448 0 350 0 760 0 010 0 179 NNavionLatB 0 0 0704561 28 73202 2 294273 2228004 4 583323 0 0 NNavionLatC 10 0 0 0100 0010 000 1 NNavionLatD 0 0 00 00 0 0 states beta p r phi inputs aileron rudder Soutput sideslip roll rate yaw rate roll a
54. states required as inputs to the graphics computer 86 References 1 Piaget s Theory of Intellectual Development an Introduction Herbert Ginsburg Sylvia Opper Prentice Hall Inc Englewood Cliffs New Jersey 1969 Anderson F G Biezad D J A Low Cost Flight Simulation for Rapid Handling Qualities Evaluations During Design AIAA 98 4368 SIMULINK Dynamic System Simulation for Matlab The Math Works Inc Using Simulink 1997 SIMULINK Real Time Workshop The Math Works Inc User s Guide 1997 Duda H Hovmark G Forssell L Prediction of Category II Aircraft Pilot Couplings New Experimental Results AIAA 97 399 Buethe S A Deppe P R A Rapid Prototyping System for Inflight Simulation using the Calspan Learjet 25 Military Standard Flying Qualities of Piloted Aircraft MIL STD 1797A 1987 Tischler M B Colbourne J D Morel M R Biezad D J Levine W S and Moldoveanu V CONDUIT A New Multidisciplinary Integration Environment for Flight Control Development NASA TM 112202 USAATCOM Technical Report 97 A 009 June 1997 RIPTIDE http caffeine arc nasa gov riptide Mohammadreza H Mansur 09 15 98 Advances in Aircraft Flight Control Mark B Tischler ed Taylor and Frances Ltd Bristol Pa 1996 pp 35 69 Fletcher J W A Model Structure for Identification of Linear Models of the UH 60 Helicopter in Hover and Forward Flight NASA TM 110362 USAATCOM Technical Report 95 A 008 Augu
55. temperature pressure speed of sound and density from sea level to 35 0 km Original function written as a AERO 215 assignment Inputs Geometric altitude in meters Sea level pressure std P0 1 013 X 10 5 Nm 2 Temperature at Sea level std T0 288 K Outputs rho speed of sound temperature pressure Douglas Hiranaka Cal Poly San Luis Obispo San Luis Obispo CA See simulink src sfuntmpl doc Copyright c 1990 1998 by The MathWorks Inc All Rights Reserved Revision 1 3 Created 1 28 95 Fortran code Last Modified 1 4 99 DH converted to c added hard constant values at the transitions and converted function to S function define S FUNCTION NAME std atms define S FUNCTION LEVEL 2 include lt stdio h gt include lt math h gt include simstruc h define NUM_PARAMS 2 define SEA LEVEL TEMPERATURE PARAM ssGetSFcnParam S 0 define SEA LEVEL PRESSURE PARAM ssGetSFcnParam S 1 define BASE PRESS real T mxGetPr SEA LEVEL PRESSURE PARAM 0 define BASE TEMP real T mxGetPr SEA LEVEL TEMPERATURE PARAM 0 define LapseRatel 0 006489 define LapseRate2 0 003 define Y 1 4 define R 287 05 156 double Alt TempK Press Density VSound T0 P0 Function mdlInitializeSizes Abstract Setup sizes of the various vectors ky static void mdlInitializeSizes SimStruct S ssSetNumSFcnParams S NUM PARAMS if ssGetNumSFcnParams S ssGetSFcnParamsCo
56. 00 gt Ra epee gain fe Noise iter aproxzona TSN seta actuator radi x aes Mx Virim a iS Gra soam dp b 5247 1167 dp assdp a 2 s2 2 dp assdp a 2 49 4309 80s 200 M 18769 f s 80 f 200 ini 52 192 896518769 Diferentiator Antialiasing Filter FE Pitch rate sensor s 200 Pa sesa EN f High Pass nafasing Fiter Fiteri Figure 26 X 29A Block Digram Flying the X 29a provided the least amount of insight to the changes in control laws and handling qualities Developing a procedure for creating the executable code and setting the timing block provided the most information from the model The timing block was written at NASA Ames and the first version required the user to estimate the amount of time that needed to be delayed to reach the end of the time frame The integration was carried out on its own processor and each time step required about a millisecond to compute while the dt for the integration was 16 milliseconds so the timing block had to delay the integration s for 15 milliseconds The first few flights had the delay incorrect resulting in the model flying at a frame rate much faster than real time Once the timing was worked out there remains some questions about the flight model The baseline model was reported to have tendencies toward sluggish responses which was observed flying the ba
57. 33 Using the state space model as well as input from undergraduate students testing the FASAND program several errors were found in the first edition of the text book that were providing dynamics that were inconsistent with an aircraft of the type modeled in the text The roll control derivative was off by two orders of magnitude causing a roll time constant of 17 seconds rather than 0 15 sec The yaw roll Cl r coupling was off by an order of magnitude causing a severe dutch roll The sign for aileron control Cl a was reversed The results produced reversed roll responses in the state space and 6 DOF models Since the FASAND code runs as a batch at close to actual time using fairly large time steps the initial verification consisted of checking various dynamics by hand calculating time constants and damping ratios using the published characteristics To have a complete baseline set of dynamics the stability derivatives were entered into the program Archangel The program dimensionalizes the non dimensional derivatives given a set of initial conditions then combines and arranges the derivatives into two state space systems for the longitudinal and lateral directions A second state space was set up using dervatives published in Ref 33 The two state spaces matched in most places however there were a couple of places that the dynamics differed The State spaces were used to create flying models for the PhEagle lab and to set up as Linearly 60
58. 33 440 Hess R A Theory for Aircraft Handling Qualities Based Upon A Structural Pilot Model J Guid Cont and Dyn vol 12 no 6 1989 pp 792 797 Hess R A Closed Loop Assesment of Flight Simulator Fidelity J Guid Cont and Dyn vol 14 no 1 1991 pp 191 197 Aircraft Dynamics and Automatic Control McRuer Ashkenas and Graham Princeton University Press Princeton New Jersey 1973 Flight Stability and Automatic Control Robert C Nelson McGraw Hill Inc New York 1989 Build You Own Flight Sim in C Programming a 3D Flight Simulator Using OOP Michael Radtke Christopher Lampton Waite Group Press Corte Matdera CA 1996 Introduction to Flight Third Edition John D Anderson Jr McGraw Hill Inc New York 1978 Roscam J AirplaneFlight Dynamics Part I Roscam Aviation and Engineering Corp Ottawa KS 1979 Aeronautical Design Standard Handling Qualities Requirements for Military Aircraft ADS 33 PRF May 13 1996 89 Appendix Euler Help File amp euler m oe Given the transfer function 1 s 10 solving the differential equation oe this routine returns the values at the next time ste oe In this version we use the euler method oe to integrate integrate to get current state oe dt time increment oo Theta pitch angle oe deltaE elevator angle DegToRad 0 01745329 tFinal 1 dt 0 01 OldTheta 0 deltaE 25 DegToRad t 0
59. An Integrated Modular Simulation System for Education and Research A Thesis Presented to the faculty of California State Polytechnic State University In partial fulfillment of the requirements for the degree of Master of Science in Aeronautical Engineeering By Douglas K Hiranaka 1999 Authorization Page I grant permission for the reproduction of this thesis in its entirety or any of its parts without further authorization from me Signature Date Approval Page TITLE An Integrated Modular Simulation System for Education and Research AUTHOR Douglas K Hiranaka DATE SUBMITTED May 10 1999 Dr Daniel J Biezad Advisor Signature Dr Jin Tso Committee Member Signature Dr Jordi Puig suari Committee Member Signature Mohammadreza H Mansur Committee Member Signature jii Abstract An Integrated Modular Simulation System for Education and Research Douglas Hiranaka Simulation is the most powerful learning and research tool in engineering However simulation of aircraft has only been available to students with advanced preparation in aircraft dynamics and programming skills This paper describes the development and evolution of a low cost flight simulation lab into a modular powerful flexible easy to use and accurate flight modeling system With the advent of cheap fast personal computers and powerful software packages flight simulation can be available to a
60. CLadothat Lift due to rate of alpha 27 CLqhat Lift due to pitch rate 28 CDa Drag due to angle of attack 29 CDu Drag due to forward velocity 30 CTXu Change in thrust due to velocity 31 CLdE Lift due to elevator deflection 32 CDdE Drag due to elevator deflection 33 CmdE Pitch control 34 CRollbeta Clbeta Roll due to side slip dihedral effect 35 CRollphat Clp Roll damping 36 CRollrhat Clr Roll due to yaw 37 CRolldA CIdA Roll control 38 CRolldR CIdR Roll due to rudder 39 Cnbeta Yaw due to side slip 40 Cnphat Yaw due to roll dutch roll 4 Cnrhat Yaw damping 42 CndA Yaw due to aileron adverse or proverse yaw 43 CndR Yaw control 44 Cybeta Side damping 45 Cyphat Sway due to roll 46 Cyrhat Sway due to Yaw 47 CydA Sway due to Aileron 48 CydR Sway due to Rudder 30 The model currently uses a Taylor expansion of the forces on a point mass to model the linear accelerations Table 4 Moments are then applied to a rigid body to obtain the rotational accelerations The translational forces are applied to the body in the Table 4 Force and Moment Derivative Equations C FC atC B C qhat C phat C rhat C X0 Xa Xp Xqhat xphat xrhat DI C C gtC ptc qhat C phat C rhat C O Ya YB Yqhat yphat yrhat C a FC qhat C phat C rhat FC Za Zqhat Zphat Zrhat LdelE C delR LdelR C atC prc at C phat C rhat C delA C delR 0 Ma Mqh ph mr
61. Dot OldyDot yDot OldzDot zDot Function mdlTerminate Abstract ik No termination needed but we are required to have this routine Ef static void mdlTerminate SimStruct S ifdef MATLAB MEX FILE Is this file being compiled as a MEX file include simulink c MEX file interface mechanism telse include cg_sfun h Code generation registration function 164 endif 165 Euler Transform Help File function x y Z psi theta phi 2 euler p q r alpha beta u v w 2 euler c Flight sim angle conversion and position integrator E oe oe o oe oe o oe o oe oe o oe o oe oe o oe o oe oe o oe o oe oe o oe o oe oe o oe o oe oe o oe o oe oe o oe o oe oe o oe oe oe x y 2 psi theta phi 2 euler p q r alpha beta u v w returns position vectors x y z and euler angles psi theta and phi from open or closed loop flight control models The inputs required are the angular rates to be provided by the flight model alpha and beta can be zero and airspeed components u v w which can be a gain block providing constant airspeed The routine stores the position x y z states and angle psi theta phi states for the next integration The initial position and angles are input through the s function block parameters in the order x y z psi theta phi Position in feet and angles in degrees The euler angle conversion phiDot p q S
62. E WORK Advanced Aerodynamics Ground effects Transonic Supersonic Hypersonic Helicopter Rotor Dynamics Momentum Theory Blade Element Non Rigid Structures Propulsions Multiple Engine Model Non Centerline Propulsion Complex Modeling of Various Systems Landing Gear Additional Hardware in the Loop Coordinate Transform to Place Eyepoint in Cockpit Simulink Blocks Real time Timing Block for use on a PC Flybox Graphics REFERENCES APPENDIX EULER HELP FILE 84 84 84 84 84 84 84 84 84 84 84 84 84 85 85 85 85 85 85 85 86 87 90 90 RK4 RUNGE KUTTA HELP FILE RK4 RUNGE KUTTA C CLASS TEST FUNCTON SNOOPY 2ND ORDER RK4 CLASS MODIFIED MAIN C CLASS SNOOPY INSTRUMENT D A SIMULINK S FUNCTION INSTRUMENT HELP FILE STICK D A SIMULINK S FUNCTION ABBREVIATED INSTRUMENT D A SIMULINK S FUNCTION ABBREVIATED INSTRUMENT HELP FILE ABBREVIATED STICK D A SIMULINK S FUNCTION HEADER FILE FOR STICK S FUNCTIONS ABBREVIATED STICK HELP FILE SIX DEGREE OF FREEDOM POINT MASS NON LINEAR SIMULINK S FUNCTION SAD FILE NAVION TSF WIND TO BODY AXIS COORDINATE TRANSFORM STANDARD ATMOSPHERE SIMULINK S FUNCTION EULER COORDINATE TRANSFORM AND INTEGRATOR SIMULINK S FUNCTION EULER TRANSFORM HELP FILE 91 93 96 99 106 114 116 124 131 132 138 140 141 152 153 156 160 166 GAME JOYSTICK DRIVER
63. Moment uPtrs 8 YawingMoment uPtrs 9 Output vector values yl0 xx MTS yy yl2 zz y 3 Psi y 4 Theta y 5 Phi ud y 6 u yl7 v ji y 8 w y 10 q y 11 Y y 12 Alpha y 13 Beta y 14 pDot 145 ia y 15 qDot E y 16 rDot y 17 2 uDot y 18 2 vDot y 19 2 wDot QUA InputRealPtrsType uPtrs ssGetInputPortRealSignalPtrs S 0 real T y ssGetOutputPortRealSignal S 0 time_T stepSize stepSize ssGetStepSize S dt stepSize Deflect_Elevator uPtrs 0 take in values from uPtrs Deflect_Aileron uPtrs 1 Deflect_Rudder uPtrs 2 Rho uPtrs 3 Fx uPtrs 4 Fy uPtrs 5 Fz uPtrs 6 PitchingMoment uPtrs 7 RollingMoment uPtrs 8 YawingMoment uPtrs 9 ForcesMoments find the current rates of change Accelerate UpdateState apply them to current rotations y 0 xx send out values through the y vector y 1 yy y 2 zz y 3 Psi y 4 Theta yl5 Phi y 6 ui yl7 v y 8 w y 9 p y 10 q y 11 r y 12 Alpha y 13 Beta y 14 pDot y 15 qDot y 16 rDot y 17 uDot y 18 vDot y 19 wDot This function models the forces and moments acting on the aircraft first the aircraft is treated as a point mass and accelerated linearly then rotational properties are applied and the mass becomes three dimensio
64. Phi r CPhi TTheta thetaDot q CPhi r SPhi psiDot q SPhi r CPhi SecTheta This function reduces angles to values between zero and two Pi The euler velocity conversion xDot u CTheta CPsi v SPhi STheta CPsi CPhi SPsi w CPhi STheta CPsi SPhi SPsi yDot u CTheta SPsitv SPhi STheta SPsi CPhi CPsi w CPhi STheta SPsi SPhi CPsi zDot u STheta v SPhi CTheta w CPhi CTheta inputs p body roll rate nose up Input in Deg Sec q body pitch rate right wing down r body yaw rate nose right alpha angle of attack set to 0 if supplying v amp W beta side slip set to 0 if supplying v amp W u forward If letting this routine do alpha and beta v right wing then v and w whould be 0 w down Ft Sec outputs x position FEET y position z altitude psi euler yaw nose right OUTput in degrees theta euler pitch nose up phi euler roll right wing down States not using s function states x position FEET y position z altitude psi euler yaw Keeps angles in RADIANS theta euler pitch phi euler roll 166 oe oo oo oe oe NOTE this is a help block only there is no function attached to this m file Doug Hiranaka 7 12 98 Copyright c 1998 by Penguin Aeronautics 167 Game Joystick Driver Simulink S function VAZZEEEEZZZZZZZZZZZZZIZZ ZZZ o OO OK II EI OOOO KK k RR I k k k k k k MODULE game stick c AUTHOR S Eyal L
65. SPhi r CPhi SecTheta Theta fmod Theta TwicePi if angle is greater than 2Pi reduce below 2pi Phi fmod Phi TwicePi Psi fmod Psi TwicePi Redo the angles to account for alpha and beta where the aircraft is going not where it is pointed conversion from body to wind axis 163 calulate the trig functions first sAlpha sin alpha cAlpha cos alpha sBeta sin beta cBeta cos beta coordinate transform for the velocity and position from airspeed body axis to world axis uWind u cAlpha cBeta v sBeta w sAlpha cBeta vWind u cAlpha sBeta v cBeta w sAlpha sBeta wWind u sAlpha w cAlpha xDot uWind CTheta CPsi vWind SPhi STheta CPsi CPhi SPsi wWind CPhi STheta CPsi SPhi SPsi yDot uWind CTheta SPsi vWind SPhi STheta SPsi CPhi CPsi wWind CPhi STheta SPsi SPhi CPsi zDot uWind STheta vWind SPhi CTheta wWind CPhi CTheta Theta 3 0 thetaDot OldThetaDot 2 0 dt Pitch Euler angle integration Phi 3 0 phiDot OldPhiDot 2 0 dt roll Psi 3 0 psiDot OldPsiDot 2 0 dt yaw OldThetaDot thetaDot OldPhiDot phiDot OldPsiDot psiDot y 3 Psi Angle output vector yaw DEGREES y 4 Theta Pitch y 5 Phi roll X 3 0 xDot OldxDot 2 0 dt position integration YY 3 0 yDot OldyDot 2 0 dt Z 3 0 zDot OldzDot 2 0 dt y 0 X Position output vector y 1 YY y 2 Z OldxDot x
66. Spiegle is the IO computer containing the A D D A and digital cards that process data to and from the sim cab and also has one of the side views to process Eagle is the main graphics engine that has the front view and HUD to process Phantom is a backup IO computer with Win95 for the backup functions and a partition of Linux to provide remote access to the sim lab for researchers operating off site Phantom is also being set up to provide hardware in the loop support for remotely piloted vehicles using the backup A D D A cards and separate software from the stick IO to use the IO cards for both functions at the same time Using the TCP IP socket software several Silicon Graphics workstations available can be included in the system to provide extra computing power when required The portability of C code allow functions programmed on a PC system to be ported to the Unix computer when more computing power is required 20 PhEagle I Software The software originally written for the simulation system has gone through several generations of development The equations of motion heads up display and handling qualities tasks were originally written in c and Fortran for use on a Silicon Graphics workstation The software was originally encompassed by a project called PANGLOSS named after the ever optimistic character Dr Pangloss in Voltaire s Candide Ref 26 The PANGLOSS project has the lofty goals to create a complete package of software that takes a
67. Terminate SimStruct S ifdef MATLAB MEX FILE Is this file being compiled as a MEX file include simulink c MEX file interface mechanism telse include cg sfun h Code generation registration function endif 151 SAD file Navion tsf 24153 1 Altl ft 0 00237254 2 Densityl slugs ft 3 175 215 3 Ul 175 054 ft sec 0 4 Attitudel rad 184 5 Area ft 92 33 4 6 Span ft 25 7 Chord ft 2750 8 Weight lbs 1048 9 Ixx slug ft 2 3000 10 Iyy slug ft 2 3530 11 Izz slug ft 2 0 12 Ixz slug ft 2 0 41 13 CL1 41 0 05 14 CD1 0 05 15 CTXT 0 16 Cml 0 17 CmTl 0 18 Cmu 0 683 19 Cma 4 36 20 Cmadothat 9 96 21 Cmqhat 0 22 CmTu 0 23 CmTa 0 24 CLu 4 44 25 CLa 0 0 26 CLadothat 3 8 27 CLqhat 0 33 28 CDa 0 29 CDu 0 0 30 CTXu 0 350 31 CLdE 0 00 32 CDdE 0 923 33 CmdE 0 074 34 CRollbeta Clbeta 0 41 35 CRollphat Clp 92 0 107 36 CRollrhat Clr 0 134 37 CRolldA C1dA 0 0107 38 CRolldR CldR 0 071 39 Cnbeta 2 0 20575 40 Cnphat 0 125 41 Cnrhat 0 0035 42 CndA 0 072 43 CndR 0 564 44 Cybeta 0 0 45 Cyphat 0 0 46 Cyrhat 0 47 CydA 0 0 48 CydR 152 Wind to Body Axis Coordinate Transform Sscript wind2body E oe function wind2body m oe oe This script transforms a 3d force vector from the flight path coordinate oe axis to the aircraft body axis through 2 transforms multiplied The oe function is an extension of McRuer et al
68. Wind 0 1 0 sin 6 cos B Ol sin B cos p 0 FyWind sin a 0 cos a 0 0 1 sin a cos B sin a sin B cos a LiftWind 55 difference between the two axes are the angle of attack alpha and the side slip angle beta In actual flight the airpath and aircraft body axes rarely coincide The effects of the difference in angles adds to the overall drag as some of the lift is mapped to the drag and some of the original drag is mapped to the down force Fz of the aircraft and therefore affects the natural frequency and damping of the longitudinal and lateral long period oscillations The simulator originally did not re map the forces calculated in airpath axis to the aircraft body axis The re mapping of the forces changed the dynamics of the model so that there was much less climb associated with a step input of negative up command elevator The re mapping of the forces also affected the natural frequency and damping in the long period phugoid mode Re mapping added damping to the system and decreased the natural frequency Figure 17 shows the changes in wn and 0 Pitch Rate and Angle With and Without Forces to Body Axis 3 T T T Angle 2 pude Angle body 7 Rate Rate body 7 l l l l l l l l 0 20 40 60 80 100 120 140 160 180 200 Figure 17 Navion Long Period Longitudinal Dynamics 56 The model assumes a trim alpha angle and balanced initial moments The program will req
69. ailable The PhEagle I uses the Ethernet to send the data to the graphics hardware PhEagle lionly requires a TCP IP client S function to access the remote graphics computers Graphics is a whole area that can be investigated Since there can be more than one computer processing equations of motion it is conceivable that any number of computers can be added to the network to provide formation or air to air combat simulation A graphics subsystem can be created to handle expansions of the system beyond PhEagle II Network TCP IP A TCP IP communications template block is included to allow for future expansion of the remote parallel processing capabilities of the PhEagle II system The block is being used to send states to the graphics computers The block can also be used for multiple aircraft simulations playback of flight test or earlier simulation data to the graphics system and hardware in the loop simulation 47 Key Features of Simulations Stability and controls engineers use models of varying complexity to analyze and design control systems for aircraft These range from simple first and second order differential equation models of the rotational and linear dynamics of only the primary axis dynamics to complex state space models to full non linear equations of motion models To verify the 6 DOF non linear model two state space models were created and compared to the dynamics of the 6 DOF model Finally a transfer function model was cr
70. ain analysis provides little intuitive basis for the student The hands on learning that spawns mental connections between modal analysis and the time domain is best demonstrated by pilot in the loop simulation Ref 9 Simulink RTW provides a means to create a pilot in the loop simulation Seeing coupled responses such as a Dutch roll mode allows correlation of magnitudes of the motion with the position and rate graphs Aircraft handling qualities analysis has traditionally been conducted by engineers analyzing control systems with Computer Assisted Design CAD packages Using CAD the engineers generate batch time or frequency histories Ref 15 of the designs of the FBW flight control systems The engineers do not interact with the design nor fly the design If a model exhibits complex cross coupling gaining intuition of the plant is impaired The time required to write real time simulation source code for control laws aerodynamic models and the hardware interfaces for a real time simulation prohibits engineers from direct interaction with their designs until the later stages of design when changes are much more difficult The ability to go from pictures to code allow rapid development of prototype systems by substituting hardware drivers for simulated components in an existing simulation then auto generating executable code An example of the flexibility of the system is demonstrated by the difference in the amount of time required to convert the
71. ake care when specifying exception free code see sfuntmpl doc ssSetOptions S SS OPTION EXCEPTION FREE CODE Function mdlInitializeSampleTimes Abstract ik Specifiv that we inherit our sample time from the driving block static void mdlInitializeSampleTimes SimStruct S ssSetSampleTime S 0 INHERITED SAMPLE TIME ssSetOffsetTime S 0 0 0 define MDL START Change to undef to remove function tif defined MDL START Function mdlStart Abstract Initialize the da cards y static void mdlStart SimStruct S unsigned short int addr addr 0x220 aToD12 addr 0x220 aToD12 maxADCount 4095 aToD12 minADVoltage 5 0 aToD12 maxADVoltage 5 0 aToD12 nADChannels 16 aToD12 nDAChannels 2 aToD12 base addr aToD12 cnt0 addr 0 aToDI2 cntl addr 4 1 aToD12 cnt2 addr 2 117 aToD12 aToD12 aToD12 aToD12 aToD12 aToD12 aToD12 aToD12 aToD12 aToD12 aToD12 aToD12 aToD12 aToD12 aToD12 aToD12 cntCtrl addr 3 dalLow addr 4 dalHigh addr 5 da2Low addr 6 da2High addr 7 adLow addr 4 adHigh addr 5 diLow addr 6 diHigh addr 7 cli addr 8 gainCtrl addr 9 muxCtrl addr 10 modeCtrl addr 11 softAD addr 12 doLow addr 13 doHigh addr 14 ADCChannel rThrottle cNumber 0 rThrottle minV 0 0 rThrottle maxV 1 0 lThrottle cNumber 1 lThrottle minV 0 0 lThrottle maxV 1 0 pitchPos cNumber 2
72. ake up a complete aircraft Modeling an aircraft provides the bridge between the theoretical and real world Referring to model each time a new topic is introduced provides reinforcement that each topic is related to a whole discipline Computer simulation provides the kind of modeling that could be available to every engineering student Engineering students have access to personal computers that are used mostly for data reduction and presentation Personal computers have become powerful enough to provide real time simulation of simple aircraft from the desktop Ref 2 Joysticks used for game type simulators are common and drivers exist to allow their use for input to a engineering simulation High resolution scenery exists that is available in the public domain to provide an out the window view The popularity of video games has provided everything for a high fidelity high resolution visual simulation of an aircraft except the equations of motion required to provide the dynamics to the model Cal Poly has been developing a set of the basic equations of motion Ref 2 which exist in several computer languages Since research and education have the same goals the tools used by both disciplines should be the same The tools should be powerful flexible easy to set up and use and provide useful information to the users rapidly and accurately The ideal tool can be used by both students and researchers providing insight at various levels to correspo
73. al the opposite of the base drag the model demonstrated a damped long period with a frequency just slightly higher than the value published for the aircraft There is no provision to model a stall or limit alpha on the main wing or the tail so putting a step input with too great a control deflection produces poor results after a very short interval as the alpha limits of the wing are exceeded Portability The c code for the 6 DOF EOM model was created and debugged using a PC then ported to an IRIX operating system Silicon Graphics Onyx Since the c code uses only generic math functions only minimal changes were required to the code to compile on the Onyx The math model itself required no changes The differences were in the S function interface and the changes were minimal All of the modeling functions for PhEagle II were ported to the SGI to confirm portability The IO functions were not ported as the c code is specific to the IO cards located in the PC s SAD Files The aircraft data used in the S functions are standard aircraft data SAD files written in ASCII format so the input files are portable between the PC s and workstations The SAD files contain physical characteristics describing an aircraft along with non dimensional stability derivatives in a standard order In addition to providing information to the simulator the SAD file can be used to create linearized transfer functions and a state space model of the aircraft 76 Test Set
74. and instrument computers to run the mechanical Figure 3 PhEagle Simulation Cab steam gauge instruments as well as drive the force feedback torque motors for pilot force feedback or state cueing to the center stick and rudder pedal inceptors Sim Cab F 4 F 15 PHantom EAGLE Cal Poly simulation cab on loan from NASA Dryden combines an F 4 Phantom cockpit with the center control stick from a F 15 Eagle Figure 4 providing controls and instrumentation on par with any modern high performance fighter aircraft The cab was originally used to train F 4 pilots then converted to a F 15 stick with force feedback to the pedals and stick to conduct Figure 4 F 15 Eagle Stick handling qualities research The force feedback allows the cab to simulate actual aerodynamic control forces or feed back force or cueing proportional to any of the aircraft s current states for research into the simulated aircraft s handling qualities Ref 25 The hybrid cab contributed to the simulation labs nickname the PhEagle The force feedback stick provides Cal Poly with the ability to perform advanced handling qualities research Handling qualities is defined as flying qualities which allow a mission to be accomplished with ease and precision Ref 7 Feedback of the aircraft states to the pilot is an important quantity to provide good handling qualities Feedback through the controls is important enough to be included in the MIL STD 1797 Ref 7 Military S
75. and output to and from the simulation cab was converted to Simulink S functions A 6 Degree of Freedom model originally created to demonstrate program coding of a point mass model was converted to a S function and verified Several functions were changed and several were added after tools in Simulink and Matlab showed that the model was not producing acceptable results A Euler integrator and coordinate transform S function was created to allow liner transfer function and state space models to be flown in a virtual world Next four models of varying complexity modified to include pilot input and graphical output were flown to verify the concept and the ability of the auto coder to generate stand alone executable program code Starting with a transfer function model 9 then a simple one axis closed loop state space model of a X29 A fixed wing jet anda complex state space model of a Kaman SH2 F with a closed loop flight control system were modified to fly on the system Next a model was created from the ground up to provide fixed wing six degree of freedom nonlinear equations of motion to fly open loop as well as to provide a airframe to wrap closed loop flight controls around The models of the X29 A and SH2 F used for verification of the rapid prototyping capability of the Cal Poly simulation lab had the control law gains optimized using the CONDUIT software NASA s CONDUIT Ref 8 is a set of utilities to perform handling qualities analysis and c
76. ar tog s gt Yaw Force 1 gt Roll Force 1 gt Pitch Force 1 Instruments amp Force code such that the Simulink environment sets the time step for simulation The S function will take and use any size time step for the numerical integrators that environment passes in Passing the time increment into the existing code the new code is not limited to a hard coded dt and can run at whatever time step the rest of the model is using The model uses a course time step of 0 0417 sec 24 HZ for real time simulation and as fine as required for batch simulations The Mathworks supplies integrators that can be used by code in the S functions but for many users that have existing math models Simulink provides the ability to wrap the S function IO around the existing code The equations of motion can then be imported to the Simulink environment as a block to wrap a control system around Mathworks supplies a make script to include all of its libraries 58 that are required to complete the programs The script adds the code then compiles completed code into a 32 bit dynamic link library dll win95 or the equivalent in Unix 59 6 DOF Model Verification The 6 DOF model used a L 17 Navion piston engine propeller driven light Air Force liason aircraft shown in Figure 19 for validation Figure 19 L 17 Navion The aircraft was used to demonstrate stability analysis calculations in Ref
77. ation information and the source can be anything it is possible to play back flight test data or previous simulations by sending the saved state information to the graphics computers using a function to send the data at the correct rate Since the playback is not limited to real time very long period characteristics can be seen by playing the frames back quickly or very short period dynamics can be seen by playing back the data very slowly Network The key to being able to use PC s is the Ethernet network Using a standard TCP IP socket protocol the main simulation computer the Spiegle integrates the equations of motion and sends out position and orientation information to the graphics computers the Eagle and Phantom and state information to and from the IO computer the PhEagle The network can support multiple simulations as sources providing muti aircraft simulations such as formation flight air to air refueling and or aerial combat Parallel Computing Parallel computing is a technique used by super computers to split up tasks to processes that can be done at the same time by separate CPU s Simulation of any kind of vehicle lends it self to parallel processing by having at least five separate tasks that need 18 to be performed at the same time These include Pilot input stick output instruments equations of motion table look up of stability derivatives used by the equations of motion and out the window graphics For a simple f
78. ations Programmer Interface API which allows users to create custom S functions to extend the basic capabilities of the system An S function is a user created Simulink function that uses compiled c code that is dynamically linked to the rest of a simulation S functions are used to write functions to extend the basic capabilities of the Simulink system Since S functions use c code existing models can be included in the Simulink environment allowing use of any of the built in Simulink functions An example is to start with Cal Poly s basic 6 Degree of Freedom airplane model convert the code to an S function then add a auto pilot simply by putting a Proportional Derivative Integral pid function block in a feedback loop To code up and debug a pid compensator would take several days Including one in a Simulink model wiring it up and creating a set of gains requires about an hour A user created S function can include just about any valid c function including calls to hardware and communications Simulink provides its modeling capabilities in batch runs The integration time step can be set to any value but the simulation runs as fast as the processor can perform the calculations Simulink does not come with any functions to delay the code to the actual time increment set by the numerical integration time step An add on product called Real Time Workshop RTW adds real time capability to Simulink along with three other functions First RTW is a au
79. avionLatA ANavionLatB ANavionLatC ANavionLatD statename states inputname inputs outpurname output 173 Navion Longitudianal State Space Setup Archangle Navion longitudianl state space setup SFASAND Fundamentals of Aircraft Simulation And Nonlinear Dynamics This is a state space model of the Navion example aircraft used to validate the FASAND code The A and B matricies were oe obtained from Arcangle 1 0 by inputing the example non dimensional oe derivatives provided in appendix A of Flight stability and oe control Robert C Nelson oe oe This Script is free to copy and distribute for educational purposes as long oe as this notice is included oe oe Doug Hiranaka oe oe Created 8 98 oe Copyright c 1998 99 by Penguin Aeronautics ANavionLonA 0 0448765 6 297068 32 174 0 0 002097989 2 014955 0 T 0 0 0 1 0 01899917 6 906006 0 2 974 ANavionLonB 0 0 1593115 0 11 65435 ANavionLonC 10 0 0 0100 0010 070 0 1 Tz ANavionLonD 0 0 0 0 15 states u alpha theta q inputs elevator output speed angle of attack pitch angle pitch rate aLonSys ss ANavionLonA ANavionLonB ANavionLonC ANavionLonD statename states inputname inputs outpurname output 174 Navion Complete State Space Setup Archangel E Navion complete state space setup FASAND Fundamentals o
80. avionLatD 0 0 00 00 00 0 0 states beta phi p psi Te inputs aileron rudder output sideslip bank angle bank rate yaw angle yaw rate sys ss ANavionLatA ANavionLatB ANavionLatC ANavionLatD statename states inputname inputs oe outpurname output 176 Navion Lateral State Space Setup Nelson navion lateral state space setup SFASAND Fundamentals of Aircraft Simulation And Nonlinear Dynamics This is a state space model of the Navion example aircraft used to validate the FASAND code The A and B matricies were de dimensional derivatives provided in appendix A of Flight oe Stability and control Robert C Nelson oe oe This Script is free to copy and distribute for educational purposes as long oe as this notice is included oe oe Doug Hiranaka oe oe Created 8 98 oe Last Update 1 25 99 DH Corrected control matrix beta to de oe oe Copyright c 1998 99 by Penguin Aeronautics NNavionLatA 0 2531035 0 1 0 0 182 16 02 8 40 2 19 0 4 448 0 350 0 760 0 0 1 0 0 1 NNavionLatB 0 0 0704561 28 73202 2 294273 2228004 4 583323 0 1 1 2 WAS 12 NNavionLatC o o o r U o o on o o on o o e oo o NNavionLatD o oo o o oc o o 1 states beta p r phi inputs aileron rudder output sideslip roll rate yaw rate roll angle nLatSy
81. c deltaE k2 dt z index 1 11 2 0 12 dt a z 4 ndex 1 11 2 0 b Theta index 1 k1 2 0 K c deltaE k3 dt z index 1 12 2 0 13 dt a z 4ndex 1 12 2 0 b Theta index 1 k2 2 0 K c deltaE 91 k4 dt z index 1 13 2 0 14 dt a z index 1 13 2 0 b Theta index 1 k3 2 0 K c deltaE Theta index Theta index 1 1 6 0 k1 2 0 k2 2 0 k3 k4 z index z index 1 1 6 0 11 2 0 12 2 0 13 14 t tot at Time index t index index 1 end Outer loop plot Time Theta r xlabel Time sec ylabel Theta grid on 92 RK4 Runge Kutta c class test function rk4 cpp This is a test program to integrate a second order tranfer function Given the transfer function 0 0165 s 2 0 186s 0 0165 solving the differential equation this function returns the values at the next time step In this version we use the fourth order Runge Kutta method to do the integration 3 06 98 Eric Vinande original function Doug Hiranaka modified the code to a c function include lt stdio h gt include lt math h gt include lt dos h gt include lt conio h gt include lt stdlib h gt void main kl n Li function opens input file and reads the data from the file to the shape class FILE fout printf Starting the functio
82. ck define S FUNCTION LEVEL 2 include simstruc h include lt dos h gt include lt bios h gt include lt math h gt include lt stdlib h gt include lt string h gt include lt conio h gt include lt math h gt include lt stdio h gt include sticki h float oldVals 5 struct PCLabCard aToD12 struct ADCChannel rThrottle lThrottle pitchPos rollPos rudderPos Function mdlInitializeSizes Abstract Setup sizes of the various vectors Ef static void mdlInitializeSizes SimStruct S 132 x ssSetNumSFcnParams S 0 if ssGetNumSFcnParams S ssGetSFcnParamsCount S return Parameter mismatch will be reported by Simulink ssSetNumContStates S 0 ssSetNumDiscStates S 0 ssSetNumInputPorts S 0 ssSetInputPortWidth S 0 0 ssSetInputPortDirectFeedThrough S 0 1 if ssSetNumOutputPorts S 1 return ssSetOutputPortWidth S 0 5 Stick rudder and throttles ssSetNumSampleTimes S 1 Take care when specifying exception free code see sfuntmpl doc ssSetOptions S SS OPTION EXCEPTION FREE CODE Function mdlInitializeSampleTimes Abstract Specifiy that we inherit our sample time from the driving block static void mdlInitializeSampleTimes SimStruct S de ssSetSampleTime S 0 INHERITED SAMPLE TIME ssSetOffsetTime S 0 0 0 fine MDL START Change to undef to rem
83. craft h aircraft reaction functions include viewcntl h include fcontrol h event handling include screen h video functions include detect h cpu detect byte huge TESTPTR NULL boolean CPU_386 global flag true if 386 processor AirCraft Snoopy one AirCraft object FControlManager controler one flight controler event manager This block declares world view and image objects Pcx bkground Class instance for bkground image 99 int opMode operating mode flag int oldVmode Save area for previous video mode int checkpt 0 Tracks program progress for use in shutdown const DEBUG 0 operating mode constants const FLIGHT 1 const WALK 2 const HELP 3 const VERSION 4 const MAX_ARGS 1 maximum number of cl parameters const MAJ_VER 2 major and minor version numbers const MIN_VER 1 const VER_LET 0 letter if any to follow minor version num called when program ends or if an error occurs during program execution the systems which are shutdown depend on the value of chekpt which is incremented as the system is set up at program start void ShutDown if checkpt gt 2 ViewShutDown viewcntl cpp if checkpt gt 3 Snoopy Shutdown aircraft cpp setgmode oldVmode screen asm note that the FControlManager will shutdown when the destructor is called
84. ction two forms of IO are being provided that Mathworks didn t supply There was no provision for keyboard input to a real time workshop application so modifying the program as it was running was limited to using the supplied external mode interface which allows one process to run Simulink coupled to another process running the real time application This allows Simulink to be linked with running simulation code providing the ability change control parameters inside the simulation while the program is running The user simply changes the values in the Simulink block and the value is immediately updated in the running program This allows different control gain sets to be used during the simulation or parameters such as time delay to be added to the simulation to demonstrate the resulting deterioration in handling qualities This also allows a separate computer to provide a instructor station to control pilot in the loop simulations Graphics is the second form of output that is not supported by the RTW coder Graphics has been in two forms 1 an interface to the World Up VR viewer was adapted to run through the Simulink environment and 2 PhEagle I graphics are being added through the network capability using the existing TCP IP sockets Since the graphics computers only require a state vector providing position and orientation information the Simulink model can use the 39 existing graphics by creating a TCP IP to graphics S function to plug into t
85. d Rud Rudder to command rad La Rudder rad Temperature F Pressure Ib in 2 Le ait ft Density slug ft 3 gt Rho slu ft 3 Right Throttle a ft sec Atmosphere f Fx Ibf forward Left Throttle throttle thrust Ibs Slick thrust 0 Fy Ibf right fi 0 Fz Ibf down EN L p o L ls M Pitch ft lbf nose up qdot pitchrad sec 2 L Roll ft ibf right wing down udot Forward ft sec 2 N Yaw ft lbf nose right x ft y ft z ft P gt Airspeed 700 knots p gt gt Altimeter 06000 ft Pitch8ball 90 deg P Roll8ball 180 deg Yaw 180 deg Psi yaw rad J39 psi deg Theta Theta pitch rad Theta deg Phi pitch rad g Phi roll rad Phi deg Psi to deg u Forward ft sec j lu v Right ft sec Piv knots w Down ft sec jew p roll rad sec to airspeed q pitch rad sec r vawrad seci gt to ft min Alpha rad 57 3 Beta rad ta deg 57 3 gt ul pdot roll rad sec 2 to deg2 Abs rdot yaw rad sec 2 vdot Right fusec 2 vdot Down ft sec 2 mp ameter 4 9 g s P gt Alpha 10 40 deg gt Beta 1 15 deg gt Lrpm 10 110 Rrpm 10 110 gt k Vert speed 6000 ft min gt gt gt gt Point Mass 6 DOF Non Li Figure 18 PhEagle II 6 DOF Model There is a built in Simulink function which passes the time step to the S function ne
86. d first edition of the manual Douglas Cameron for his assistance in assembling the technical paper that was the basis for this thesis Chad Frost for the continual brainstorming that inspired many new and innovative functions added to the PhEagle II project Dr Dan Biezad for providing the technical background and facilities that allowed the project to be initiated Finally I would like to thank Dr Mark Tischler for the use of NASA Ames facilities to complete parts of the project while similar capabilities were still being created at the California Polytechnic State University simulation laboratory Table of Contents LIST OF TABLES LIST OF FIGURES INTRODUCTION Computer Aided Research Objectives PHEAGLE I PhEagle Hardware Sim Cab Sim Cab F 4 F 15 PHantom EAGLE Siblinc Stick Computer PhEagle Hardware Computers Low cost PC s Analog to Digital Input Digital to Analog Output Graphics Cards Voodoo II Network Parallel Computing PhEagle I Software Development of PhEagle I Existing Simulation Tools General Cal Poly Transfer Function State Space vi XII XIII 12 12 12 14 14 15 15 16 16 17 18 18 21 21 22 23 23 23 27 Basic 6 DOF Nonlinear Rigid Body Steady State Subsonic Aerodynamics PHEAGLE II PhEagle II Introduction and Objectives Simulink Modular Problem Setup Simulink Time block Hardware Setup and Test Real Time Workshop Stand alone Code Hardware in
87. deled and tested by using a simple but known transfer function to determine the effects of the dynamics of the feel system For example if the Nz dE g forces to elevator deflection transfer function is known the pitch feel system can use the output to send to the stick force 6 DOF Non linear Non linear simulations require no modifications to the auto coding process The S function containing the non linear equations of motion are included in the Simulink model and connected to the aerodynamic gear and thrust model The source code is placed in the Matlab search path to allow the code to be included in the final program 53 The 6 degree of freedom 3 translational and 3 rotational degrees non linear rigid body model created for PhEagle II started as a Fortran program demonstrating a very basic nonlinear simulation The code was converted to a Matlab program called Fundamentals of Aircraft Simulation And Nonlinear Dynamics FASAND then debugged before conversion to a Simulink S function FASAND is used in the simulation lab to demonstrate the use of batch simulation and coding of the equations of motion Matlab code is very similar to c code so very little change was required to convert to a C MEX S function The nonlinear S function block allows the PhEagle II to model bare airframe dynamics as well as closed loop control systems for aircraft The original model made two assumptions that produced dynamics that were not satisfactory First th
88. des the wind2body transform function and the Euler and RK4 32 integrators All the upgrades and bugs fixed in the Simulink 6 DOF S function have been included in the FASAND code 33 PhEagle II PhEagle II Introduction and Objectives After adding several simulations to the Cal Poly simulation lab using c it was found that it took months to understand the complete set of classes to perform all of the functions Each new function required intensive planning to include in the class structure that existed The RIPTIDE simulation environment was discovered that provided all of the flexibility of the original c based system at Cal Poly while being function based and graphically oriented Since each function is self contained the system requires much less coordination to develop PhEagle II is a PC based rapid simulation environment which uses the Simulink simulation environment as a base to tie all of the Cal Poly simulation hardware and software into a flight simulation and controls laboratory RTW provides the means to create stand alone programs that include any combination of the hardware and software PhEagle phase II took the existing hardware drivers and software and converted the code to Simulink S functions The conversion and testing revealed that some of the functions didn t provide satisfactory results The functions were modified to include a broader range of inputs and outputs and more complete modeling dynamics Finally several new
89. e programmed automatic paper pilot inputs Ref 29 30 31 Batch simulation requires one or more computers and can include simulated or actual hardware Real time simulation requires one or more computers actual or simulated hardware Piloted simulation also requires an inceptor device possibly with feedback graphical or mechanical instrumentation and one or more graphical displays To simulate an aircraft one must start with a basic set of equations of motion for the aircraft and add complexity to simulate more complex behavior or include simulated or actual systems into the basic system The basic equations of motion for fixed wing aircraft assume a rigid body Actual aircraft are not rigid and most aircraft also contain various complex systems that could be modeled Simulation of a flying vehicle can be done at a variety of levels of complexity from treating the aircraft as a set of simple transfer functions to a complex and coupled state space system to a basic nonlinear 6 degree of freedom 6 DOF rigid body to a complex modeling of all the known components involved Ref 32 With the computing power available with a single Pentium processor models up to a basic 6 DOF rigid body can be included in a real time pilot in the loop simulation Batch simulations of any complexity can be performed with the corresponding increase in processing time for the additional complexity 22 General Using multi processor Silicon Graphics workstation
90. e Matlab prompt will provide text to give the user background on the S function 6 DOF Modular Problem Setup Models in Simulink can be created in small components to allow testing of each component using various types of canned inputs to test the output of the component Since S functions are functions good programming practice of creating and testing small components is encouraged The 6 DOF was created using the function testing methodology The program was broken up into three major functions forces accelerations and transforms Each component was wired up with constants and manual calculations were compared with the results When each function was producing correct results the function was included into the main function Throughout the development flexibility was constantly evaluated Most functions can be built up from the basic 37 Simulink block set however when maximum performance is required compiled c code usually provides increased speed Simulink Time block Two methods are available to allow real time simulation through Simulink Real Time Workshop described earlier and including a S function timing block in Simulink to time each simulation step and release the program when the end of the time frame is reached Using an interrupt driven block of S function code is being investigated to provide real time capability in the Simulink environment using a PC s internal timing chip The amount of delay required is significan
91. e SH 2F were obtained using NASA Ames CONDUIT CONtrol Designers Unified InTerface software CONDUIT isa collection of aircraft handling qualities evaluation Ref 18 and optimization tools CONDUIT works to find a optimal solution satisfying multiple handling qualities metrics specs and all the potentially competing requirements The researchers created the control system architecture and applied the handling qualities spec to constrain the design problem to reach a solution Altering the control system gains to satisfy all the imposed HQ specs at the same time improved handling qualities Usually only a few handling qualities specs can be satisfied for any design because of the time involved in checking the spec for a new gain configuration The X 29A and the SH 2f models used verified state space models from NASA Dryden and Kaman corporation as part of NASA Cal Poly research projects into control system optimization research The researchers started with the control systems used for 68 the actual aircraft as a baseline then modified the architecture to improve the handling qualities optimizing the gains using CONDUIT after each modification Dozens of configurations were tested before the final architecture was achieved The pictures to code model of the SH 2f was used by the researcher to confirm the control behavior and to observe the degradation of the control laws as the trim condition moved away from the baseline used to generate the contr
92. e airframe CIFER is also used to modify and confirm simulation models with the actual aircraft Data Collection The Cal Poly controls group created a flight test data acquisition system to collect in flight data from the University s Cessna 150 aircraft The system is based on solid state sensors and a portable laptop personal computer The data are collected using a PCMCIA analog to digital card using software written by graduate students The states that are currently available for measurement are Barometric airspeed barometric altitude outside air temperature engine rpm intake temperature barometric vertical velocity aircraft attitude rates aircraft linear accelerations there are provisions for gps input as well as control position A means to mount the control position potentiometers on the Cal Poly Cessna 150 that is acceptable to the Federal Aviation Administration has not been determined yet Using the data collection system with CIFER to verify and modify the 6 DOF flight model an accurate model can be created for virtually any aircraft 81 Conclusions Converting existing software code to Simulink S functions has provided a flexible powerful easy to use modular simulation laboratory for the Cal Poly controls group A basic capability has been provided upon which to build a complete computational flight modeling laboratory Using systematic testing of the software a procedure was established to create and verify future si
93. e graphics A fixed time step is required to guarantee a smooth accurate and consistent visual simulation 26 Only simple tests using rules of thumb were used to test the integrators since the functions had been tested in the Matlab environment After brief testing it was observed that the model didn t behave correctly to control inputs The pitch always stayed in the world axis while the roll and yaw were correct The attitude dynamics were removed from the simulator and a function was added to integrate body rates p q r roll pitch yaw into the Euler angles Psi Theta and Phi yaw pitch and roll in the world axis The Euler Transform also integrates the body linear rates u v w to the world positions x y z With all of the original game dynamics removed from the game simulator a basic IO template was available to wrap around various dynamics models Programs using the game IO have been given the suffix snoopy to provide an indication of the IO used for the programs The Euler and RK4 integrators original Matlab code have been incorporated in to the FASAND simulator described later to demonstrate the use of numerical integration to simulate several systems The Euler integrator is being used to model simple actuators The RK4 integrator is being used to model engine dynamics State Space A state space model is being developed to allow a model of any level of cross coupling to be created and run with the PhEagle cab to allow handling
94. e model The model demonstrates the flexibility of allowing external forces to be input to the system There is no engine built in to the model To add the ability to change the thrust in the model a force of 200 Ibf is scaled and summed by the simulator cab throttle so that at full throttle there is no added external force added and in the idle position there is a 200 Ibf input to the model to counteract the approximately 200 Ibf of thrust generate by the model at trim This provided a throttlable engine to a model that originaly didn t include one Model Assumptions The model used for the tests used stability derivatives for a single trim point Since the aerodynamic forces are integrated for each time step rather than linearized as the state space model elements are the model is accurate much farther from the trim point than the state space model but still has limitations for departing too far from the original trim condition The model originally assumed that thrust and drag are balanced for the trim condition For trim flight the assumption is true however after testing the model the assumption for thrust equaling drag proved to provide inaccurate dynamics The model was always divergent in the phugoid mode while the actual aircraft is damped in phugoid 75 mode The aircraft was divergent despite commands to the inceptor to correct the oscillations After the base drag was included and the initial thrust was set to a constant value equ
95. e model originally assumed a trim condition were the thrust equals the drag and the rotational moments are all balanced in steady state This was a gross simplification that resulted in an unstable long period phugoid mode Using the assumption simplified the development of the equations of motion since a trimmer did not need to be run before each simulation The simulation was modified to have the base drag for the condition input through the SAD file and the thrust is set to a constant value equaling the trim drag from the SAD file The drag changes with changes in velocity while the thrust remains constant The model still assumes balanced moments as initial conditions Future changes to the model will necessitate determining the trim steady state condition to start the model This can be done manually by varying the parameters until the state desired is achieved or can be automated by the creation and use of a trimmer a program to alternately vary a control then integrate the model a few time steps until the steady state condition desired is achieved The model required manual trimming of the altitude speed and density from the published values in Ref 33 The 54 original published values were sea level 176 4 ft sec and 0 0023769 slugs ft 3 The final values established for trimming the model are 2 153 ft 175 215 ft sec and 0 00237254 slugs ft 3 The atmosphere was trimmed rather than the controls as the model is assumed to have the co
96. eated using the literal factors approximations for natural frequency and damping ratio demonstrated in Ref 33 The transfer functions were built up using the Euler block to allow the model to be flown The three models demonstrate the same aircraft modeled at three levels of complexity and allow the models to be flown side by side to compare the dynamics produced by each set of equations The models will be described from the most simple transfer function to the most complex 6 DOF rather than the order they were created Usually transfer function models are used for batch simulation to obtain time histories or frequency domain plots of the motions to check individual responses of a aircraft configuration to a control input The models are used to get a feel for the basic dynamics of an aircraft during the earliest stages of design Flying the equations provide a connection between the parameters obtained from the equations and how the aircraft response is affected by changes to the parameters State space and full nonlinear simulations are usually done later in the development of aircraft due to the overhead of coding the equations of motion and control systems Autocoding software allow models at any stage in the development of an aircraft to be created and flown 48 Since the transfer functions and state space models only provide perturbation information some modifications need to be made to the simple models in order to be flown Linear
97. ebedinsky Doug Hiranaka DATE February 11 1999 Copyright c ALL RIGHTS RESERVED Cal Poly San Luis Obispo 1998 REVISION HISTORY REV AUTHOR DATE DESCRIPTION This was part of the flight simulator fly8 Author Eyal Lebedinsky eyal ise canberra edu au 40 EL Creation joytest c Y dkh 2 8 99 removed test functions 2 dkh 2 11 99 converted into s mex format S mex See simulink src sfuntmpl doc S mex Copyright c 1990 1998 by The MathWorks Inc Revision 1 3 All Rights Reserved This S function block Reads the commanded stick position from a game joystick and sends out values from 1 kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkxix define S FUNCTION NAME game stk define S FUNCTION LEVEL 2 include simstruc h include lt stdlib h gt include lt string h gt include lt conio h gt include lt stdio h gt This is part of the flight simulator fly8 Author Eyal Lebedinsky eyal ise canberra edu au define JS PORT 0x201 define JS TIMEOUT 32000 define JS READ inp JS PORT typedef unsigned short Ushort typedef unsigned int Uint typedef unsigned long Ulong define READING JS TIMEOUT i struct stick Ushort a 4 Ushort b 4 FI 168 typedef struct stick STICK Function mdlInitializeSizes Abstract d Setup sizes of the various vectors static void mdlInitializeSizes S
98. ed graphics and input output IO to the simulation cab By separating the simulation tasks to processes that are only dependant on input once each integration time step or once every several time steps a flexible computing environment using as many or as few computers as are required for each simulation is possible Since the information is sent over a network the machine acting as the master controlling the simulation could be any computer Substituting a Unix workstation for a PC calculating the equations of motion for a complex simulation such as a helicopter blade element model running in real time would be seamless Low cost PC s Since each task in the system is performed on a separate PC with little special hardware upgrades to the system can be made incrementally spreading the cost of hardware upgrades over as much time as is required Slower machines can be quickly set up to perform the less processor intensive tasks such as IO An additional cost savings is achieved by using a switching box to allow the various computers to be controlled by one monitor keyboard and mouse The Instructor Station Figure 7 is the single point of IO from the operator to the system The graphics computers have separate outputs to the out the window screens Analog to Digital Input The A D card uses variations in voltage as input and converts the signal from a analog voltage to a digital number corresponding to the level of voltage Potentio
99. em All oe the output is being handled with the output blocks to keep the oe number of duplicate functions to a minimum oe o The range and nominal units for the inputs are given any oe conversion is left up to the user Any non standard units oe should be noted to the pilot trying to interpret the instruments oe oe inputs channel gauge range input units output units oe 0 Altitude 0 60 000 feet oe 1 pitch8Ball Pitch angle theta Pi 2 rad deg oe 2 roll8Ball Roll angle phi Pi rad deg oe 3 yaw8Ball Yaw angle psi Pi deg oe 4 dirGyro Yaw angle psi Pi deg oe 5 g meter Nz g s 4 9 g s oe 6 vertDevPoint 4 1 oe 7 rudderball Beta side slip 4 1 oe 8 aoaMeter Alpha angle of attack 10 40 degrees deg oe 9 mach meter 0 6 mach number oe 10 Airspeed 0 700 knots oe 11 sidslipAngle Beta side slip 15 degrees deg oe 12 Left engine rpm 110 10 percent rpm oe 13 Right engine rpm 10 110 percent rpm oe 14 Vertical Speed Indicator 6000 feet min ft min SEPARE 12 bit channels FERRER oe 15 right Nozzel 0 100 oe 16 left Nozzel 0 100 oe 17 internal pressure 1 12 oe 18 Course Deviation indicator 1 1 oe 19 cd Horizontal indicator 1 1 oe 20 cd Vertical Indicator 1 1 oe 21 right Engine Temp 200 1400 deg oe 22 left engine Temp 200 1400 deg
100. eople other than the original programmer To create better simulations changes to the code are continually required and flexibility in the combinations of hardware and software is a must Parallel Capabilities Parallel computing is the strategy used to gain large increases in computing power The nature of simulation of aircraft provides tasks that can be easily separated and run in parallel The components required to create a basic parallel computing system using personal computers have existed for a while Custom software combined with the Simulink RTW programs and a Ethernet network running TCP IP protocol provide the means to rapidly set up and run a parallel computing system Open Code Maintainability The key to software that is maintainable is code that is common and well documented C is a programming language that is familiar and powerful without being complex Students exposed to Fortran have little difficulty maintaining c code Since the real time workshop system requires the original source code to auto code the Simulink diagram despite the fact that Simulink uses dynamically linked libraries to execute the program the source is available to researchers requiring alterations of the functions The documentation is available in four places help files supplied as m functions with the S functions a hardcopy kept with the PhEagle hardware the comments in the source code and a html document on Spiegle 83 Future Work PhEagle II
101. er 4 9 g s L gt rudder rad l toalt lat input Navion itati L Alpha 10 40 deg inpu Archangel 1 0 pes r delata rad beta rad Psi rad i deg Thet gt Beta 1 15 deg StateSpace lat output si rad psi leg Theta gt Lrpm 10 110 p u ft sec gt Rrpm 10 110 Sum Theta rad gt Theta deg Phi gt Vert speed 6000 ft min 0 Py ft sec Constant gt Yaw Force 1 0 wi fuge E hi rad gt Phi deg Psi gt Roll Force 1 Constanti gt Pitch Force 1 Euler Transform to deg Instruments amp Force gt gt ul to deg2 Abs Figure 16 Archangel State Space Model Modifications Required to Fly Flying a linear transfer function and the simple state space models require giving the model a steady state motion to be perturbed from Starting the model from the trim Initial condition and performing a numerical integration on the differential equations allow the student to see the effects of perturbations on the math model The state space model has the speed directly connected to the throttles with the perturbations from the model summed in before the speed is fed to the Euler block To be able to fly the aircraft the equations need a world to fly in and the capability to be oriented in the virtual space In a standard simulator this is done by defining and keeping track of the position and orientation using world coordinates and the Euler angles Psi compass heading Theta pitch angle above or below the horizon and Phi roll ang
102. er p q r alpha beta u v w returns position vectors x y z and euler angles psi theta and phi from open or closed loop flight control models The inputs required are the old position the angular rates to be provided by the flight model alpha and beta can be zero and airspeed which can be a gain block providing constant airspeed The routine stores the position x y z states and angle psi theta phi states for the next integration The initial position and angles are input through the s function block parameters in the order x y z psi theta phi Inputs rotation rates body axis p q r rad sec angle of attack and sideslip alpha beta degrees Linear velocity body axis u v w ft sec Outputs position flat earth x y x ft orientation Euler Psi Theta Phi rad Douglas Hiranaka Cal Poly San Luis Obispo San Luis Obispo CA See simulink src sfuntmpl doc Copyright c 1990 1998 by The MathWorks Inc All Rights Reserved Revision 1 3 Created 9 21 98 fine S FUNCTION NAME to euler fine S FUNCTION LEVEL 2 clude simstruc h clude lt math h gt Number of S function parameters and macros to access from the simstruct de de de de de de de fine NUM_PARAMS 6 fine X POS PARAM ssGetSFcnParam S 0 fine Y POS PARAM ssGetSFcnParam S 1 fine Z POS PARAM ssGetSFcnParam S 2 fine PSI ANGLE PARAM ssGetSFcnParam S 3 fine THETA ANGLE PARAM ssGetSFcnParam S 4 fi
103. f This is a state space used as a template to oe This script loads the oe The A and B matricies oe o o oe o oe oe oe Doug Hiranaka oe oe Created 1 99 oe Aircraft Simulation And Nonlinear Dynamics model of the Navion example aircraft set up a state space model in Simulink matricies to be used in the simulation were obtained from Arcangle 1 0 by inputing the example non dimensional derivatives provided in appendix A of Flight stability and control Robert C Nelson This Script is free to copy and distribute for educational purposes as long as this notice is included Copyright c 1999 by Penguin Aeronautics ANavionLonA 0 0448765 6 297068 32 174 0 0 002097989 2 014955 0 1 0001 0 01899917 6 906006 ANavionLonB 0 0 1593115 0 11 65435 ANavionLonC 1 0 0 0 0100 0010 000 1 ANavionLonD 0 0 0 0 states u alpha inputs elevator 0 2 974 theta q output speed angle of attack pitch angle pitch rate sys ss ANavionLonA ANavionLonB ANavionLonC ANavionLonD statename states outpurname output inputname inputs ANavionLatA 0 2531035 0 1834322 0 0 1 00100 15 86694 0 8 370129 0 2 1844 00001 4 519665 0 0 348499 0 75761 175 ANavionLatB 0 0704561 00 28 73202 2 294273 00 2228004 4 583323 ANavionLatC 10 00 0 01000 001 0 00010 0000 1 AN
104. gging dump mode h H display a command list before starting w W start FOF in world traverse mode v V display program version number void ParseCLP int argc char argv int i if argc lt MAX ARGS 1 for i 1 i lt argc i if argv i d argv i D opMode DEBUG else if argv i opMode HELP else if argv i h argv i H 103 opMode HELP else if argv i w argv i W opMode WALK else if argv i v argv i V opMode VERSION else Terminate invalid command line parameter ParseCLP else if argc gt MAX ARGS 1 Terminate extra command line parameter ParseCLP handles a ground approach by determining from pitch and roll whether the airplane has landed safely or crashed void GroundApproach 1 handle approaching the ground REV 2 1 change debug mode to reset aircraft if opMode FLIGHT opMode DEBUG if Snoopy airborne amp amp Snoopy altitude lt 0 if Snoopy pitch gt 10 Snoopy pitch 10 Snoopy roll 10 Snoopy roll 10 if opMode DEBUG gotoxy 3 1 cprintf CRRAAASSSSHHHHH Go find a real Pilot you Looser else ShowCrash viewcntl cpp Snoopy ResetACState aircraft cpp delay 200 controler ResetControls while controler AnyPress
105. graphics chips The card provides hardware texture mapping z buffering and Gouraud shading The card has a pixel fill rate of 90 million pixels per second at 800 x 600 resolution which translates to 5 to 10 thousand polygons being shaded at 30 Hz The three default views available in PhEagle I are out the cockpit window looking out the front and slightly to the sides The view direction is set on the computer that is doing the graphics for the view through the software The direction that the view is looking is simple to change allowing great flexibility in placement of the side view monitors Placing the side monitor directly to the side allows for close formation flying while placing the monitors close together allows a wider panoramic view out the front The Center Monitor has the additional task of displaying 17 the Heads Up Display HUD While changing the HUD is not a basic task various HUD s can be substituted to test effects of symbology and HUD dynamics Ref 27 28 The graphics are not limited to three views As many views are available as computers that can be connected to the network and supplied with graphics cards Tower views can be processed on a separate computer with the same graphics set up and a graphical model of the aircraft included in the visual database using the position and orientation information to position the aircraft model in the terrain database Since the graphics computers are only receiving position and orient
106. handle special case when aircraft pitch passes the vertical if Theta gt HalfPi Theta lt HalfPi if Phi gt 0 Phi pi else if Phi lt 0 Phi pi if Psi gt 0 Psi pi else if Psi lt 0 Psi pi if Theta gt 0 Theta pi Theta else if Theta lt 0 Theta pi Theta void Wind2Body float FxWind float FyWind float FzWind double AirSpeed float vSquared AlphaSpeed combo 150 vSquared u utw w AlphaSpeed sqrt vSquared combo v AlphaSpeed AirSpeed Fx FxWind u AirSpeed FyWind u combo FzWind w AlphaSpeed Fy FxWind v AirSpeed FyWind AlphaSpeed AirSpeed Fz FxWind w AirSpeed FyWind w combo FzWind u AlphaSpeed RRO RII OOOO ROO ROO OOOO RARA void read_derivs char fname double dp FILE f char c int des if f fopen fname rt free c printf Could Not open file if c char malloc N COLS sizeof char printf Memory not dynamically allocated for i 0 i lt 48 i dp readline c f dp atof c free c fclose f jikkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkixx Function mdlUpdate Abstract perform action at major integration time step EL static void mdlUpdate SimStruct S int_T tid Function mdlTerminate Abstract No termination needed but we are required to have this routine el static void mdl
107. hannelInit amp rollTrimDef amp aToD12 ADCChannelInit amp rollTrimPos amp aToD12 ADCChannelInit amp rollVelocity amp aToD12 ADCChannel Init amp rudderPos amp aToD12 ADCChannelInit amp rudderForce amp aToD12 ADCChannelInit amp rudderTrimPos amp aToD12 ADCChannelInit amp rudderVelocity amp aToD12 ADCChannelInit amp rThrottle amp aToD12 ADCChannelInit amp lThrottle amp aToD12 endif MDL_START define MDL_INITIALIZE_CONDITIONS Change to undef to remove function tif defined MDL INITIALIZE CONDITIONS Function mdlInitializeConditions Abstract Initialize the state Note that if this S function is placed 119 ki with in an enabled subsvstem which is configured to reset states E this routine will be called during the reset of the states static void mdlInitializeConditions SimStruct S endif MDL INITIALIZE CONDITIONS Function mdlOutputs Abstract gt simply passes states y n x n El static void mdlOutputs SimStruct S int T tid InputRealPtrsType uPtrs ssGetInputPortRealSignalPtrs S 0 real_T y ssGetOutputPortRealSignal S 0 float newVal newVal doConversion amp pitchPos aToD12 newVal 0 4 newVal 0 6 oldVals 0 oldVals 0 newVal y 0 int newVal newVal doConversion amp pitchForce aToD12 newVal 0 4 newVal 0 6 oldVals 1 oldVals 1 newVal y 1 int newVal
108. hat NdelA NdelR airpath axis Note that there is an assumption that the difference between airpath axis the direction the aircraft is going and body axis the direction the aircraft is actually pointed x out the nose y out the right wing and z out the bottom is small small angle approximation This is only valid for small alpha and beta As the small angle approximation is exceeded the alpha starts to be mapped into drag and Beta reduces overall drag causing changes in the aircraft dynamics The control deflections are used to determine additional forces and moments added to the aerodynamic forces and moments Once the total forces and moments are Table 5 Equations of Motion summed the forces and moments are Qwot F m g sin quirv X applied to the mass and inertias of the DVD E Y BITE COSO Ep ow ot F m g cose cos pvtqu airframe to determine the translational Z a dI 1 TI pgyl XL XX YY XZ X and rotational accelerations Table 5 aq at M R2II I FRU EI I XX ZZ XZ XZ Y aplat oP at PQ I 1 FORI INI YY XX XZ shows F ma rearranged to a F m to ZZ obtain the accelerations on the body The equations include the gravity component in 3l each of the linear force terms The body axis accelerations are integrated to body axis velocities and rates Table 6 shows how the body axis velocities are then combined with the previous Euler angles to obtain the world axis velocities Table 6 u out the nose v
109. he forces mapped from the wind axis to the body axis The effect of the mapping is to decrease the natural frequency and increase the damping in the long period dynamics Figure 21 shows the decrease in natural frequency from the Archangel model and the decrease in damping compared to 61 both models The two state space models in the lateral axis provided the same response Impulse Response Pitch Angle T Amplitude State Space 6 DOF l I I I 0 20 40 60 80 100 120 140 160 180 200 Time sec Figure 21 Theta to Elevator Phugoid for a step input The 6 DOF in rudder to beta figure 22 exhibits a similar difference from the state space models as the pitch response Figure 20 shows that the 6 DOF model is less damped and a higher frequency than the state space models The mapping of the forces reduce the drag for a sideslip condition by mapping the drag to a drag and a pure side force The result is a higher frequency than the model without the mapping and less damping than the unmapped model The Roll rate to aileron figure 22 response matched the state space the closest The roll angle response also exhibits the same difference in natural frequency and reduced damping compared to the state space model Both models show the same under damping and the washout of the angle due to the dihedral effect in the wings Figure 23 shows the characteristic washout of the roll angle due to the dihedral effec
110. he graphics TCP IP server socket Hardware in the Loop The ability to provide hardware in the loop code was the feature that initiated the use of real time workshop Since the PhEagle simulation cab uses A D and D A IO the simulator is already hardware in the loop Using back up IO cards the hardware capabilities exist now to include many types of flight hardware into the current system Existing Infrastructure Creating the output to the instruments and the input from the stick has created a infrastructure for doing hardware in the loop simulations The input from the stick is in analog voltage varied through potentiometers located on the stick The instruments are voltage meters that use the output reference voltage to command the position of the needles After all the stick and instruments are hooked up on Spiegel unused channels remain available on both the input and output cards that can be used for hardware in the loop input and output The addition of hardware requires very small changes to the Simulink S functions The Phantom computer has D A cards and software currently being used as a backup system for Spiegel Phantom is available to provide hardware in the loop IO through the Ethernet PhEagle II Software Starting with bits and pieces of simulation and IO program functions created by various Cal Poly alumni in Fortran c and c along with new functions the PhEagle II Simulink RTW library was created tested and verified
111. he input and output connection between the function and Simulink is called a C MEX S function The user code is called through an S function in Simulink with as many input and output channels as required The C MEX API provides a gateway function to the Matlab environment while the C MEX S function is the gateway to the Simulink environment With a couple of restrictions most c code can be placed in the S function template The first restriction is that only basic keyboard input is allowed Mathworks supplies a modified interrupt function for the keyboard which limits escape codes from interrupting the program To get around this restriction a TCP IP communications block was created to allow communications outside the simulation software hardware This allows the user to create a GUI using Matlabs programming language to provide the 35 instructor a graphical interface to control the simulation that runs as a separate process or even on a separate computer The second restriction is that there 1s no direct support for graphical output Users can write their own graphics wrapped in the S function template Keeping in mind the two limitations just about any thing that can be written in c can be used as an S function including reading from and writing to hardware storage TCP IP communications graphics timing functions and custom math functions and models Simulink model code is platform independent as long as only generic c S function code b
112. he reset of the states A static void mdlInitializeConditions SimStruct S float u0 SAD_FILE_NAME read derivs navion tsf dp load the design parameters read derivs fname dp set up physical attributes of the aircraft Mass dp 7 32 2 mass sl Ixx dp 8 Inertia about x axis integral y 24z 2 dm sl ft 2 Iyy dp 9 Inertia about y axis sl ft 2 Izz dp 10 Inertia about z axis sl ft 2 Ixz dp 11 Ixz integral x z dm sl ft 2 Ixy 0 0 Ixy integral x y dm 0 0 in this version sl ft 2 Iyz 0 0 Iyz integral y z dm 0 0 in this version sl ft 2 These are the initial values of the state vector Rho dp 1 u0 dp 2 Velocity component in body x direction ft sec v 0 0 Velocity component in body y direction ft sec w 0 0 velocity component in body z direction ft sec p 0 0 roll rate rad sec q 0 0 pitch rate rad sec cr 0 0 yaw rate rad sec Theta 0 0 body pitch angle rad Phi 0 0 roll angle rad Psi 0 0 Yaw angle rad xx 0 0 absolute x position of the c g tE 7 yy 0 0 zz dp 0 Area dp 4 Reference area s usualy wing area ft Span dp 5 Reference span b ft Chord dp 6 Reference chord c usualy MAC ft Stability derivatives All derivatives are dimensionless
113. here the coherence was at or close to one Given a complete set of control inputs and outputs CIFER can create a full set of dimensional stability derivatives and state space model To demonstrate the procedure for creating converting moving and processing CHIRP data using CIFER a Simulink model was created to produce the time history files and several programs were created to save and convert the output data to a format CIFER uses for input CIFER requires a binary file with a separate file for each control and response Each file contains a column of numbers representing the position of the control or the acceleration or angular rate of the airframe To demonstrate the procedure for collecting 79 the data and converting to the proper format a Simulink model chirp mdl Figure 31 was created to generate a CHIRP and collect the input and output data The chirp went from 0 2 to 12 RAD sec and was sampled over 60 seconds at a sample rate of 0 02 seconds using a Dormand Prince numerical integration technique The data were sent to In Stick Out Airframe 36 3271 __eoe o_o simOut 52 8 29985 36 3271 Chirp Signal dynamics to wrkSpace Transfer Fcn inputCmd Cmd to wrkSpace Figure 31 CIFER Tutoreial Sample Tranfer Function Model the Matlab workspace and a Matlab m file maketext m was created to save the data to ASCII files before txt and after txt A transfer function was used to model the dynamics of a small aircraf
114. igure 18 PhEagle II 6 DOF Model 58 Figure 19 L 17 Navion 60 Figure 20 Theta to Elevator Short Period Longitudial Dynamics 61 Figure 21 Theta to Elevator Phugoid 62 Figure 22 Lateral Beta to Rudder and P to Aileron 63 Figure 23 Roll Angle Response 64 Figure 24 Atmosphere Conversion from SI to English Units 64 Figure 25 NASA X 29A 69 Figure 26 X 29A Block Diagram 71 xiii Figure 27 Figure 28 Figure 29 Figure 30 Figure 31 Kaman SH2 F SH 2F Block Diagram Bode Plot of 36 S 2 8 3S 36 Transfer Function Chirp Time and Frequency Plots from Cessna Transfer Function CIFER Tutorial Sample Transfer Function Model 72 73 78 78 80 Introduction Computer Aided The goals of research and education are very similar to gain a better understanding of the world through the systematic exploration of it Looking at the world using only one tool is as limiting as observing the world using only one sense Understanding differs from knowledge in the scope of information Knowledge is being aware about something while understanding involves being thoroughly familiar with the topic The ability to experiment with and manipulate things allows understanding to begin Ref 1 Theory and equations provide the basis for understanding engineering However there is usually no single tool provided that ties all of the theories and equations together to demonstrate how the topic being studied fits into the complex set of dynamics that m
115. imStruct S ssSetNumSFcnParams S 0 if ssGetNumSFcnParams S ssGetSFcnParamsCount S return Parameter mismatch will be reported by Simulink ssSetNumInputPorts S 0 LE ssSetInputPortWidth S 0 0 ssSetInputPortDirectFeedThrough S 0 1 if ssSetNumOutputPorts S 1 return ssSetOutputPortWidth S 0 2 Stick rudder and throttles ssSetNumSampleTimes S 1 Take care when specifying exception free code see sfuntmpl doc ssSetOptions S SS OPTION EXCEPTION FREE CODE Function mdlInitializeSampleTimes Abstract Specifiy that we inherit our sample time from the driving block el static void mdlInitializeSampleTimes SimStruct S ssSetSampleTime S 0 INHERITED SAMPLE TIME ssSetOffsetTime S 0 0 0 define MDL START Change to undef to remove function tif defined MDL START Function mdlStart Abstract Initialize the da cards static void mdlStart SimStruct S endif MDL_START define MDL_INITIALIZE_CONDITIONS Change to undef to remove function if defined MDL INITIALIZE CONDITIONS Function mdlInitializeConditions Abstract Initialize the state Note that if this S function is placed with in an enabled subsystem which is configured to reset states this routine will be called during the reset of the states 169 El static void mdlInitializeConditions SimStruct S endif
116. in the Y direction Wind axis excluding controls direction wind axis excluding controls Compute the pitching moment excluding controls CL CLAlpha Alpha_Pert CLAlphaDot AlphaDotHat CLq gHat 0S kkkxxj PitchingMoment Cm0 CmAlpha Alpha_Pert CmAlphaDot AlphaDotHat Cmq qHat QS Chord 147 Compute the rolling moment excluding controls RollingMoment ClBeta Beta_Pert Clp pHat Clr rHat 0S Span Compute the yawing moment excluding controls YawingMoment CnBeta Beta_Pert Cnp pHat Cnr rHat 0S Span Compute the forces and moments due to controls deflections and rates This includes throttle setting effects This routine modifies the already computed values of the forces and moments in wind axis Controls done here Cy CyDelR Deflect_Rudder Cz CLDelE Deflect_Elevator Cl C1DelA Deflect_Aileron C1DelR Deflect_Rudder Cm CmDelE Deflect Elevator Cn CnDelA Deflect_Aileron CnDelR Deflect_Rudder Fx Fx Cx 0S dimensionalize and add the control forces FyWind Cy 0S FzWind Cz QS Lift caused by elevator Lift is negative z RollingMoment C1 QS Span PitchingMoment Cm 0S Chord YawingMoment Cn QS Span Wind2Body FxWind FyWind FzWind AirSpeed Fx Fx Thrust Thrust force Body axis void Accelerate load deltaVect struct with delta change values for roll
117. ineering student quickly builds and tests a model of a bare airframe designs the control laws to tailor the response types and flying qualities Ref 7 then performs tests of the resulting augmented aircraft via batch simulation or joy stick inceptor on the desktop PC or electronic force feedback inceptor in a fixed based simulator Using Matlab Simulink on a PC consistent and verifiable real time and batch simulation code can be auto coded from block diagrams representing the equations of the simulation and architecture of the control laws The development of Fly By Wire FBW flight control systems has produced dramatic advances in aircraft handling qualities and performance Ref 10 However this increase in design complexity now requires extensive training and experience for the engineer to be able to analyze these complex systems rapidly and cost effectively This training is based upon fundamental understanding of highly coupled flight mechanics 6 along with the fundamentals in FBW flight control systems This combination of disciplines must be tied together with hands on experience working with control systems dynamics Demonstrating the resulting handling qualities to engineering students of their designs of Fly By Wire flight control systems has been nearly impossible due to the high cost of computer hardware and the long time required for skilled engineers to program the source code for the simulation and the control laws Frequency dom
118. int To provide complete dynamics for a training type simulator would require a complex lookup table that would require one or more dedicated computers doing the interpolation from the look up tables Table 3 summarizes the information contained in a typical SAD file Table 3 SAD File 100 1 Initial Altitude ft 0 002377 2 Starting Density slugs ft 3 175 05 3 initial forward velocity U ft sec 0 4 Starting Altitude ft 184 5 Wing reference area S ft 2 33 4 6 Wing span b ft 5 7 7 Wing mean aerodynamic chord MAC ft 2750 8 Aircraft weight Ibs 1048 9 Moments of inerita Ixx slug ft 2 3000 10 Iyy slug ft 2 3530 11 Izz slug ft 2 0 12 Ixz slug ft 2 0 41 13 CLI Initial total lift coefficient 0 05 14 CDI Initial total drag coefficient 0 05 15 CTXI Initial thrust coefficient 0 16 Cml Initial pitch moment coefficient 0 17 CmTI Initial pitch moment due to thrust 29 0 683 4 36 9 96 4 44 0 0 3 8 0 33 0 0 0 355 0 00 0 923 0 074 0 41 0 107 0 134 0 0107 0 071 0 0575 0 125 0 0035 0 072 0 564 0 0 0 0 0 0 0 0 18 Cmu Pitch moment due to forward velocity 19 Cma Pitch moment due to angle of attack 20 Cmadothat Pitch moment due to rate of alpha 21 Cmqhat Pitch moment due to pitch rate 22 CmTu Pitch moment due to thrust andu 23 CmTa Pitch moment due to thrust and alpha 24 CLu Lift due to forward velocity 25 CLa Lift due to angle of attack 26
119. is required For the responses to control inputs aircraft models can be TI simplified to resemble a spring damper system Analysis of spring damper systems are performed using frequency domain bode plots figure 29 NASA Ames CIFER software provides the tools necessary to process time histories into frequency domain data To get a bode plot the Fa B o o a i i o S o o pes o p S e a motion of the control input and the airframes response to the Frequency rad sec control is required The Figure 29 Bode Plot of 36 S 2 8 3S 36 Transfer maneuver that is used in Function
120. it amp rudderPos amp aToD12 endif MDL_START define MDL_INITIALIZE_CONDITIONS Change to undef to remove function tif defined MDL INITIALIZE CONDITIONS Function mdlInitializeConditions Abstract ia Initialize the state Note that if this S function is placed with in an enabled subsystem which is configured to reset states E this routine will be called during the reset of the states static void mdlInitializeConditions SimStruct S 134 endif MDL INITIALIZE CONDITIONS Function mdlOutputs Abstract simply passes states y n x n ky static void mdlOutputs SimStruct S int T tid InputRealPtrsType uPtrs ssGetInputPortRealSignalPtrs S 0 real_T y ssGetOutputPortRealSignal S 0 float newVal newVal doConversion amp pitchPos amp aToD12 newVal 0 4 newVal 0 6 oldVals 0 oldVals 0 newVal y 0 int newVal newVal doConversion amp rollPos amp aToD12 newVal 0 4 newVal 0 6 oldVals 1 oldVals 1 newVal y 1 int newVal newVal doConversion amp rudderPos amp aToD12 newVal 0 4 newVal 0 6 oldVals 2 oldVals 2 newVal y 2 int newVal newVal doConversion amp rThrottle amp aToD12 newVal 0 4 newVal 0 6 oldVals 2 oldVals 3 newVal y 3 int newVal newVal doConversion amp lThrottle amp aToD12 newVal 0 4 newVal 0 6 oldVals 2 oldVals 4 newVal y 4
121. itude s psi euler yaw Keeps angles in RADIANS theta euler pitch phi euler roll 7 static void mdlOutputs SimStruct S int_T tid int T i 162 InputRealPtrsType uPtrs ssGetInputPortRealSignalPtrs S 0 real T y ssGetOutputPortRealSignal S 0 time T stepSize Note this will blow up if aircraft passes through 90 degrees Straight up Inputs float p uPtrs 0 body roll rate per frame float q uPtrs 1 body pitch rate per frame float r uPtrs 2 body yaw rate per frame not including rudder only effects YET float alpha uPtrs 3 float beta uPtrs 4 float u uPtrs 5 Airspeed body x forward float v uPtrs 6 Airspeed body y right float w uPtrs 7 Airspeed body z down float uWind vWind wWind sAlpha cAlpha sBeta cBeta float dt Outputs float xDot yDot zDot psiDot thetaDot phiDot pre calculate all the angle trig functions float STheta SPhi SPsi float CTheta CPhi CPsi float TTheta SecTheta stepSize ssGetStepSize S dt stepSize sec STheta sin Theta SPhi sin Phi SPsi sin Psi CTheta cos Theta CPhi cos Phi CPsi cos Psi TTheta tan Theta SecTheta 1 0 if CTheta 0 0 SecTheta 1 0 CTheta This is the Euler Angle Conversion phiDot p q SPhi r CPhi TTheta thetaDot q CPhi r SPhi psiDot q
122. ixed wing rigid body aircraft the single most computationally intensive task is the out the window graphics Using a Ethernet network and TCP IP sockets for communication the tasks can easily be broken up and run on separate computers with each machine being sent the aricraft states over the network Separating the graphics from the flight model and having separate computers process each view frame rates exceeding 30hz for each view are possible The Cal Poly simulation lab currently has 4 166 MHz Pentium computers Analog a Stick Throttles Computer E Graphics Center Drivers View Instruments HUD Graphics Left Graphics View Right view Phantom Backup AID DIA Drivers Joysick Keyboard FlyBox Stdout Instructor GUI Virual Actual Hardware Figure 10 PhEagle I Distributed Parallel Computing Pheagle Spiegle Eagle and Phantom Figure 10 Ethernet hub and simulation cockpit cab with feedback stick and mechanical instrumentation 3 high resolution graphics cards 19 and monitors and computer code to simulate various aircraft and run and connect the various pieces of hardware and graphics Pheagle is the primary equations of motion EOM engine and will control the flow of data to and from the other computers In addition to the EOM engine the computer has one of the graphics cards to send graphics to the left view the side view requiring less processing not having the Heads up display to process
123. kMax Chan gt minV else checkMax Chan gt maxV checkMin Chan minV if value gt checkMax value lt checkMin if errorChecking printf DACChannel Value 1 3f is out of range n value value value gt Chan gt maxV Chan gt maxV Chan gt minV count unsigned short Chan gt gain value Chan gt offset outpw Chan addr count Function mdlTerminate Abstract No termination needed but we are required to have this routine y static void mdlTerminate SimStruct S ifdef MATLAB MEX FILE Is this file being compiled as a MEX file include simulink c MEX file interface mechanism telse include cg_sfun h Code generation registration function endif 113 Instrument Help File function allinst altitude pitch roll yaw direction fz ball alpha mach aispeed beta l rpm r rpm h dot rnozz lnozz intpre ss CDI CDh CDV ltemp rtemp lfuel rfuel ptot fpitch froll fyaw Sallinst c Simulink RTW s function pheagle Flight sim output block E oe allinst altitude pitch roll yaw direction fz ball alpha mach oe aispeed beta l rpm r rpm h dot rnozz lnozz intpress CDI CDh oe CDV ltemp rtemp lfuel rfuel ptot fpitch froll fyaw oe This function sends commands to the instruments through a A to D oe card This block is a complete set of the outputs for the PhEagle oe cab The block includes outputs for the stick force syst
124. le The definition of the orientation must be in this order or the virtual aircraft will have an orientation other than the one expected The World Up 51 viewer has the end of the runway conveniently located at the 0 0 0 location in the virtual world This makes setups for basic tests rapid and simple The World up viewer uses quaternions to keep track of the world angles but the models do not yet so it is still possible to stop the simulation if the model passes through straight up or straight down In addition to having a space to fly in the model requires commanded input and output to allow the pilot to observe theresponses Euler Block To allow a transfer function model to be flown a Euler S function block was created to give position and orientation to the simple model which supplies rate information The Euler transform was separated from the 6 DOF simulator and converted to a stand alone S functions The block takes in as part of the parameter set up the initial position orientation and velocity The block starts using the initial position and orientation then takes in angle rates in the body coordinates and integrates them to get a change in angle then transforms the body angles to world axis to orient the aircraft The velocities are transformed from the body axis to the wind axis through the angles alpha and beta The transform from body axis to wind axis is the transpose of the transform from wind axis to body axis used in the
125. leTimes SimStruct S ssSetSampleTime S 0 INHERITED SAMPLE TIME ssSetOffsetTime S 0 0 0 define MDL_START if defined MDL_START Function mdlstart el static void mdlStart SimStruct S d16 nBits 16 dl6 baseAddr 0x340 di6 nLimit 5 0 dl6 pLimit 5 0 dl6 nChannels 16 d16 vDefault 0 0 d12 nBits 12 d12 baseAddr 0x300 d12 nLimit 5 0 d12 pLimit 5 0 d12 nChannels 16 d12 vDefault 0 0 errorChecking 0 0 turns off 1 truns on DACChannel 16 bit channels roll8Ball channelNumber 1 roll8Ball minV pi roll8Ball maxV pi yaw8Ball channelNumber 2 yaw8Ball minV pi yaw8Ball maxV pi dirGyro channelNumber 3 dirGyro minV pi dirGyro maxV pi gMeter channelNumber 4 gMeter minV 4 gMeter maxV 9 pitch8Ball channelNumber 5 pitch8Ball minV 0 5 pi pitch8Ball maxV 0 5 pi vertDevPoint channelNumber 6 vertDevPoint minV 10 vertDevPoint maxV 40 108 rudderBall channelNumber 7 rudderBall minV 1 0 rudderBall maxV 1 0 aoaIndicator channelNumber 8 aoalIndicator minV 10 aoalndicator maxV 40 machIndicator channelNumber 9 machIndicator minV 0 machIndicator maxV 6 airspeed channelNumber 10 airspeed minV 0 0 airspeed maxV 700 0 sideslipAngle channelNumber 11 sideslipAngle minV 15 sideslipAngle maxV 15 leftEngRPM channelNumber 12 leftEngRPM minV 110 leftEngRPM maxV 10 rightEngRPM
126. ll levels of flight dynamics analysts Input output I O hardware has matured and evolved from expensive specialty items to mass produced consumer products and the equations of motion for a standard configuration aircraft are well understood The Cal Poly simulation lab has computers equations of motion a simulation cab desktop input inceptors and CAD design packages to analyze and design aircraft and control systems Individual components don t make up a simulator any more than a stack of chips make up a computer After creating several tools to add to the basic simulator a sophisticated and flexible system was developed that could be used by engineers and students with almost any level of preparation Simulink along with Real Time Workshop provide a flexible and powerful environment that separate the hardware drivers and simulation software into individual functions and allow the components to be assembled in any combination The system was verified by creating simulations using several verified models and comparing output from the Simulink model with the output from Real Time Workshop Acknowledgements The author of this paper would like to thank all of the contributors to the Pangloss and PhEagle projects especially Fritz Anderson for the contributions that allowed this work in progress to commence I would also like to thank Eric Vinande for his contribution to the Snoopy simulator project Dee Williams for his work on the FASAND GUI an
127. locks are included in the model This feature has the advantage that a model can be created on a desktop PC then be ported to a Unix based workstation Using a workstation advanced analysis and optimization programs can be made available The speed increase possible using a workstation could allow real time execution if the model is complex enough that real time execution is not possible on a PC Some hardware drivers can be ported between platforms as long as the c code is generic The BG systems FlyBox uses a serial port with generic c code drivers so the S function drivers should function on a PC as well as a Unix workstation The generic nature of the c and S function code was demonstrated by running the Euler S function and the 6 DOF S function blocks on both a PC and a several Silicon Graphics workstations including an Indigo and an Onyx On a Windows 95 system the user can only use 32 bit program code to link into the S functions This caused all of the 16 bit snoopy game IO functions used to test the original desktop simulation functions to be abandoned A new set of 32 bit game joystick 36 functions were found and graphics output were found that uses the World up virtual reality viewer with the CessnaVR output using OpenGL Figure 14 Help files have been provided by creating a Matlab script macro with the same name as the S function Typing in Figure 14 Screen Shot of World Up VR Player gt gt help 6 DOF at th
128. lta change in yaw deg per ms double dRoll delta change in roll deg per ms double Psi double PhiDot double Theta float OldPhiDot float Oldrz float OldTheta float Oldpz float OldPsi float Oldyz the AirCraft class class AirCraft public state vect 97 private void CalcPowerDyn void CalcFlightDyn float CalcTurnRate void CalcROC void ApplvRots protected void DoWalk public inline boolean AnyButton return buttonl button2 start up the aircraft model This must be called at program start up boolean InitAircraft int mode shut down the aircraft model You have to call this one at exit If you don t the very least that will happen is that the sound will stay on after the program terminates void Shutdown void GetZetaOmega subseqent functions are the hooks to the rest of the program RunFModel is called to iterate the flight model one step It is normally called once per frame but will work properly no matter how often you call it per frame up to some theoretical limit at which timer inaccuracy at low microsecond counts screws up the delta rate calculations void RunFModel void ResetACState void LandAC Called from GetControls to remap surface deflection void ReduceIndices change ignition to opposite state off or on void ToggleIgnition void ToggleBrakes ACDump pe
129. ltimeter pitch8Ball 124 roll8Ball yaw8Ball rudderBall airspeed dirGyro gMeter aoalndicator sideslipAngle leftEngRPM rightEngRPM verspeedIndicator yawForceOut rollForceOut pitchForceOut Function mdlInitializeSizes Abstract Setup sizes of the various vectors El static void mdlInitializeSizes SimStruct S ssSetNumSFcnParams S 0 if ssGetNumSFcnParams S ssGetSFcnParamsCount S return Parameter mismatch will be reported by Simulink if ssSetNumInputPorts S 1 return ssSetInputPortWidth S 0 14 ssSetInputPortDirectFeedThrough S 0 1 if ssSetNumOutputPorts S 0 return ssSetOutputPortWidth S 0 1 ssSetNumSampleTimes S 1 Take care when specifying exception free code see sfuntmpl doc ssSetOptions S SS OPTION EXCEPTION FREE CODE Function mdlInitializeSampleTimes Abstract Specifiy that we inherit our sample time from the driving block Py static void mdlInitializeSampleTimes SimStruct S ssSetSampleTime S 0 INHERITED SAMPLE TIME ssSetOffsetTime S 0 0 0 define MDL START if defined MDL START Function mdlstart Abstract Initialize the da cards static void mdlStart SimStruct S 125 d16 nBits 16 dl6 baseAddr 0x340 d16 nLimit AO d16 pLimit 5 0 dl6 nChannels 16 dl6 vDefault 0 0 d12 nBits 12 d12 baseAddr 0x300 d12 nLimit 5 05 d12 pLimit 5
130. ly the stick pedal and throttle position from the cab The forces are set in the instrument block ph inst c ERE EEE IEEE KKK A k k k k k k Ck Ck kCk Ck k Ck CkCk Ck kk kck k ck k k k ck ck ck ck ck ck ck ck ck k ok ck ck ok AA AAA ke ke e x ke e define S FUNCTION NAME al stick define S FUNCTION LEVEL 2 include simstruc h include lt dos h gt include lt bios h gt include lt math h gt include lt stdlib h gt include lt string h gt include lt conio h gt include lt math h gt include lt stdio h gt include sticki h float oldVals 16 struct PCLabCard aToD12 struct ADCChannel rThrottle lThrottle pitchPos pitchForce pitchTrimDef pitchTrimPos pitchVelocity rollPos rollForce rollTrimDef rollTrimPos rollVelocity rudderPos rudderForce rudderTrimPos rudderVelocity Function mdlInitializeSizes Abstract 116 s Setup sizes of the various vectors 7 static void mdlInitializeSizes SimStruct S ssSetNumSFcnParams S 0 if ssGetNumSFcnParams S ssGetSFcnParamsCount S return Parameter mismatch will be reported by Simulink LE ssSetNumContStates S 0 ssSetNumDiscStates S 0 ssSetNumInputPorts S 0 ssSetInputPortWidth S 0 0 jk ssSetInputPortDirectFeedThrough S 0 1 if ssSetNumOutputPorts S 1 return ssSetOutputPortWidth S 0 16 Stick rudder and throttles ssSetNumSampleTimes S 1 T
131. meters are used to vary the Figure 7 Instructor Station reference voltage from the stick and pedals Any device that can be connected to a linear or rotating potentiometer can be used for input to the simulator Digital to Analog Output The instruments Figure 8 and the force feedback are run using a reference voltage sent out from the computer then amplified to run the actuators voltage meters in the instruments and torque motors connected to the stick and pedals Any Figure 8 PhEagle Instruments device that can be controlled using a voltage signal can be used as output from the D A card 16 Graphics Cards Voodoo II Graphics require the greatest amount of processing power in a visual simulation The PhEagle currently has provisions for up to 3 views each view is processed by a single computer providing enough speed for real time high resolution texture mapped graphics Figure 9 Graphics Front View Figure 9 Each computer only requires the position orientation and direction that the view is displaying Each computer gets the information once an integration step The graphics are handled by providing three computers with the same terrain database and software By sending the position and orientation to the three computers the rest of the graphics are processed separately The graphics computers only special pieces of hardware are network cards and Quantum 3D graphics cards based on 3Dfx Voodoo
132. mulations using Simulink RTW and CIFER Taking existing simulation code and creating Simulink blocks provides the fastest way to create simulations Creating Simulink driver blocks for the hardware in the loop inceptor and instrument systems for Cal Poly s fixed base simulator allows rapid creation of basic models or rapid set up of complex configurations Once the basic model functions correctly various configurations can be rapidly created by substituting more complex input output blocks and more complex feedback architectures as well as creating more complete instrument setups from the basic model The engineer creates the block diagrams in Simulink representing the FBW flight control system and bare airframe model then adds the stick and instrument blocks RTW auto codes and compiles the C code representing the block diagrams The compiled auto code is ready for immediate pilot in the loop and or hardware in the loop simulation This system enables rapid design analysis and testing of aircraft and components for various levels of engineering students Innovative and new aircraft can be rapidly loaded and flown in a variety of configurations High level accurate models of fly by wire flight control systems can be created and tested on a desktop 82 Lessons Learned Building a simulation system requires more than a simulation cab and some software To be useful the system must be easy to setup and use and be verifiable and maintainable by p
133. n chan gt channelNumber else chan gt addr Card gt baseAddr chan gt channelNumber lt lt 1 if chan gt min chan gt max min Card gt nLimit max Card gt pLimit chan gt gain float Card gt maxCount max min else chan gt gain float Card maxCount chan maxV chan gt minV chan gt offset chan min TO Ku Bi a a Span GV a ia Bino E o l a l Saq iemel ta di I i i a ln bl Cn e ih cet etl void set struct DACChannel Chan float value unsigned short count float checkMin checkMax if Chan max lt Chan gt minV checkMin Chan gt maxV checkMax Chan gt minV else checkMax Chan gt maxV checkMin Chan minV if value gt checkMax value lt checkMin if errorChecking printf DACChannel Value 1 3f is out of range n value value value gt Chan maxV 7 Chan gt maxV Chan gt minV count unsigned short Chan gt gain value Chan gt offset outpw Chan addr count Function mdlTerminat Abstract No termination needed but we are required to have this routine static void mdlTerminate SimStruct S 129 ifdef MATLAB MEX FILE include simulink c telse include cg_sfun h endif Is this file being compiled as a MEX file MEX file interface mechanism Code generation registration function 130 Abbreviated Instr
134. n gt gain float Chan gt adcount Chan gt offset return value me Bi Sl SE iyi dui D A A ls ie ig fen toi ps ace on LE Source code for ADCChannel class m AAA ira iii e A A A A SI A A A ehi void ADCChannelInit struct ADCChannel chan struct PCLabCard card float value chan gt adcount 0 if chan gt minV chan maxV chan gt minV card gt minADVoltage chan gt maxV card gt maxADVoltage chan gt gain chan gt maxV chan gt minV float card maxADCount chan gt offset chan gt minV value chan gt gain float chan gt adcount chan gt offset Function mdlTerminate Abstract No termination needed but we are required to have this routine 136 static void mdlTerminate SimStruct S ifdef MATLAB MEX FILE Is this file being compiled as a MEX file include simulink c MEX file interface mechanism telse include cg_sfun h Code generation registration function tendif 137 Header file for Stick S functions MODULE sticki h AUTHOR S Fritz Anderson Douglas Hiranaka DATE April 1 1997 Copyright c by Systems Technology Incorporated ALL RIGHTS RESERVED The data and methods contained in this document are proprietary to Systems Technology Incorporated REVISION HISTORY REV AUTHOR DATE DESCRIPTION 0 fga 4 1 97 Creation 7 L dh 9 14 98 converted to c A
135. n c Ref 34 The code for the simulator was written in 25 Figure 11 BYOFS Original Screen Figure 12 Snoopy Screen c so the integrators were recoded in c The simulator was modified by removing the original equations of motion as well as all unused game code Two setup files were included to store the calibration for the game joysticks and to store the springing and damping ratios for the numerical integrators The graphics were simplified to increase the screen display area and simulate a simple Heads up Display HUD Figures 11 amp 12 The new integrators were added to the simulators existing classes and the code modified to provide input to the integrators The output from the integrators was sent to the base class while a linear airspeed was hard wired State information was output to the graphics and Heads Up Display A second version of the code was modified by removing the game joystick classes then combining graphics and equations of motion classes into the stick and instrument classes in the PhEagle I c code Modifications were then made to the timing classes to change from a floating time scheme where the integration time step is estimated from the length of the previous computational cycle to a fixed time step were the length of the frame is hard coded and all of the computations must be completed before the end of the frame A fixed time scheme always involves unused CPU time while the program waits to be released to th
136. n n fp fopen fcube dat r if fp printf can not open intput file n exit 1 printf input file open n fscanf fp i i amp number of vertices amp number of lines Read vert lines rintf i i WMn number of vertices number of lines p printf number of lines iWMn number of lines variables dt time increment Theta pitch angle deltaE elevator angle float DegToRad 0 01745329 float Theta 250 z 250 Time 250 K wn zeta begin inputs printf n nEnter K steady state gain Mn scanf S 8K 93 float K 10 0 printf nEnter wn natural frequency rad sec n scanf f amp wn float wn 0 12845 printf nEnter zeta damping Nin scanf f szeta float zeta 0 724 float deltaE 1 0 float dt 0 5 float tFinal 100 float a b c float Rly 11 k2 12 k3 13 k4 14 end of inputs coefficients for Runge Kutta method 2 0 zeta wn b wn wn c wn wn Theta 1 0 z 1 0 float t dt Time 1 0 int index 2 while t lt tFinal kl dt z index 1 11 dt a z index 1 b Theta index 1 K c deltaE k2 dt z index 1 11 2 0 12 dt a z index 1 11 2 0 b Theta index 1 k3 dt z index 1 12 2 0 13 dt a z index 1 12 2 0 b Theta index 1 k4 dt z index 1 13 2 0 14 dt a z index 1 13 2 0 b The
137. nal and is rotated void ForcesMoments 146 u Trim static float OldAlpha AlphaDot Alpha Pert Alpha Trim Beta Pert Beta Trim u Pert Two u pHat qHat rHat AlphaDotHat Alt QS static double TrueSpeed AirSpeed Static float FxWind FyWind FzWind float Cx 0 0 float Cy 0 0 float Cz 0 0 float Cl 0 0 float Cm 0 0 float Cn 0 0 initialize environment OldAlpha Alpha Alpha atan w u Beta atan v sqrt u utw w AlphaDot Alpha OldAlpha dt Alpha_Pert Alpha Beta_Pert Beta ifdef junk Alpha Pert Alpha Alpha Trim Beta Pert Beta Beta Trim u Pert u u Trim tendif Rho rhoSAD TrueSpeed sqrt u utv vtw w AirSpeed sgrt u utv vtw w set up variable to dimensionalize derivvatives Two_u 2 0 AirSpeed pHat p Span Two_u gHat q Chord Two u rHat r Span Two u AlphaDotHat AlphaDot Chord Two u Alt zz FxWind 0 FyWind 0 FzWind 0 QS 0 5 Rho AirSpeed AirSpeed Area Compute the force in the Drag x CD20 FxWind CD CDAlpha Alpha_Pert 0S ekkxx FyWind CyBeta Beta_Pert QS fx Compute the force in the Lift FzWind fx Cm0 0 0 z altitude simple atmospheric model x n f xen change this to read in from the inport dynamic press q area direction Wind axis excluding controls Compute the force
138. nclude simstruc h lt dos h gt lt bios h gt lt math h gt lt stdlib h gt string h lt conio h gt lt stdio h gt cyda h char errorChecking float pi 3 14159 struct DAC d16 d12 106 struct DACChannel altimeter pitch8Ball roll8Ball yaw8Ball rudderBall airspeed dirGyro gMeter vertDevPoint aoalndicator machIndicator airspeed sideslipAngle leftEngRPM rightEngRPM verspeedIndicator rightNozz leftNozz internalPress courseDirIndicator cdHorIndicator cdVerIndicator leftEngTemp rightEngTemp leftEngFuel rightEngFuel pTotGauge yawForceOut rollForceOut pitchForceOut Function mdlInitializeSizes Abstract Setup sizes of the various vectors xy static void mdlInitializeSizes SimStruct S si ssSetNumSFcnParams S 0 if ssGetNumSFcnParams S ssGetSFcnParamsCount S return Parameter mismatch will be reported by Simulink if ssSetNumInputPorts S 1 return ssSetInputPortWidth S 0 29 ssSetInputPortDirectFeedThrough S 0 1 if ssSetNumOutputPorts S 0 return jk ssSetOutputPortWidth S 0 1 ssSetNumSampleTimes S 1 Take care when specifying exception free code see sfuntmpl doc ssSetOptions S SS OPTION EXCEPTION FREE CODE 107 Function mdlInitializeSampleTimes Abstract Specifiy that we inherit our sample time from the driving block static void mdlInitializeSamp
139. nction Testing the function before it was included into the S function template required writing a stand alone program to send signals to the instruments Once the functionality was confirmed the c code was stripped of the test function and placed in the S function template supplied by The Mathworks The function was wired to constant input blocks and a simulation was run The functionality was first confirmed on a static set of inputs and then on a set of dynamic sine function inputs Instruments To simplify the setup of the instruments the offset and gain from the digital counts have been incorporated into the S function code The following instruments table 8 are available through the S function There is also a basic S function with just a basic set of flight instruments and no stick force outputs The calibration of the stick is in progress Basic stick dynamics and force shaping functions are in the process of being created Table 8 Instrument Output Channel Gauge Range input units Output Units I pitch8Ball Pitch angle theta Pi 2 rad deg 2 roll8Ball Roll angle phi Pi rad deg 3 yaw8Ball Yaw angle psi Pi rad deg 4 directinal Gyro Yaw angle psi Pi rad deg 5 g meter Nz g s 4 49 g s 6 vertDevPoint 1 7 rudderball Beta side slip 1 8 aoaMeter Alpha angle of attack 10 40 deg deg 9 mach meter 0 6 mach number 10 alrspeed 0 700 knots 11 sideslip angle
140. nd with the experience of the user Having students gain experience using the same tools and analysis techniques that they will use after completing their education provides insight into the theoretical as well as the practical aspects of the discipline The Cal Poly simulation lab includes computers a basic flight model a full scale aircraft cockpit cab with a force feedback system CAD software to analyze and design flight control systems a desktop FlyBox inceptor an ethernet hub and high resolution graphics monitors and cards The individual tools exist that would provide researchers at any level a complete flight modeling laboratory The challenge is to provide the flexibility of a system that is easy enough to be used by engineering students while providing the power and flexibility required by researchers A simulator in its most basic form consists of a computer equations of motion some form of control input and output of the calculated state information to the user Providing useful prediction of performance and flying qualities requires a method to verify the accuracy of the flight model Until recently a flexible model required expert programming skills To have a model simple enough for students required enough simplification of the model that it was no longer accurate enough for research Since the model was hard coded very little could be done to modify it unless the student had access to the source code a compiler and a programmer 2
141. ne PHI ANGLE PARAM ssGetSFcnParam S 5 160 define INIT_X real T mxGetPr X POS PARAM 0 define INIT Y real T mxGetPr Y POS PARAM 0 define INIT Z real T mxGetPr Z POS PARAM 0 define INIT PSI real T mxGetPr PSI ANGLE PARAM 0 define INIT THETA real T mxGetPr THETA ANGLE PARAM 0 define INIT PHI real T mxGetPr PHI ANGLE PARAM 0 States not using the simstruct to save the states float X Previous locations to update float YY float 2 altitude float Psi euler yaw angle RAD float Theta euler angle float Phi euler angle float OldThetaDot float OldPhiDot float OldPsiDot float OldxDot float OldyDot float OldzDot const float TwicePi 3 1415927 2 0 const float Deg2Rad 0 01745329 const float Rad2Deg 57 2957795 Function mdlInitializeSizes Abstract ke Setup sizes of the various vectors kl static void mdlInitializeSizes SimStruct S ssSetNumSFcnParams S NUM PARAMS if ssGetNumSFcnParams S ssGetSFcnParamsCount S return Parameter mismatch will be reported by Simulink ssSetNumContStates S 0 ssSetNumDiscStates S 0 if ssSetNumInputPorts S 1 return ssSetInputPortWidth S 0 8 ssSetInputPortDirectFeedThrough S 0 1 if ssSetNumOutputPorts S 1 return ssSetOutputPortWidth S 0 6 ssSetNumSampleTimes S 1 Take care when specifying exception free code see sf
142. ngle sys ss NNavionLatA NNavionLatB NNavionLatC NNavionLatD statename states inputname inputs oe outpurname output 180 Navion Transfer Function Setup E Navion transfer function setup SFASAND Fundamentals of Aircraft Simulation And Nonlinear Dynamics El E E oe oo oe o oo oe oo oe oo oo oe oe oe This is a tranfer function model of the Navion example aircraft template file to set up a litteral factors tranfer function model to run in Simulink The litteral factors were calculated using equations in Flight stability and control Robert C Nelson This Script is free to copy and distribute for educational purposes as long as this notice is included Doug Hiranaka Created 1 99 Last Update Copyright c 1998 99 by Penguin Aeronautics pitch q zw qNavionZ 9725 qNavionW 2 55 El roll p zw TauPNavion 8 4036 SpNavionZ 1725 pNavionW 2 8989 E yaw r zw rNavionz 0 254 rNavionW 2 17 c172 m Cessna 172 longitudianl transfer function E oe oo oe oo oe oe oo oe oo oe oe oe oe oe This is a transfer function model of a Cessna 172 aircraft used to demonstrate the CIFER code The values for the coefficients were obtained from appendix of Roscam Stability and Control This Script is free to copy and distribute for educational purposes as long as this notice is included Doug Hiranaka Created 1
143. ntrols trimmed for the condition Before the trim of the model was refined the initial conditions perturbed the model enough to excite the phugoid mode at the start of a simulation For a man in the loop simulation the small perturbation was not distinguishable however the motion was significant in batch simulations during validation of the model The second change from the most basic model is to correct for the assumption that the aircraft body axis is the same as the airpath axis the difference between the direction the aircraft is pointed and the direction it is actually going Originally the model was to only map the lift and drag forces to the body axis Ref 32 After referencing the PhEagle I c code the PhEagle II S function included the side forces Fy to the coordinate transform The transform was done in two stages from airpath axis through the angle beta along the airpath z axis equation 7 Then through the angle alpha along the beta y axis Equation 7 Wind to B to the aircraft body axis equation 8 The cos B sin B 0 DragWind Fxa sin B cos B 0 FyWind Fya 0 0 1 LiftWind Fza transform were multiplied together then multiplied by the force vector to obtain the Equation 8 f to Aircraft Body cos a 0 sin a Fxa FxBodv final transform matrix equation 9 The 0 1 0 Fya FyBody sin 0 cos a Fza FzBody Equation 9 Total Transform cos a 0 sin a cos B sin B 0 cos a cos B cos a sin B sin a Drag
144. o 3 May June 1997 pp 581 587 Hess R A Technique for Predicting Longitudinal Pilot Induced Oscillations J Guid Cont and Dyn vol 14 no 1 1991 pp 198 204 Chalk C R Excessive Roll Damping Can Cause Roll Ratchet J Guid Cont and Dyn vol 6 no 3 1983 pp 218 219 Smith R E Sarrafian S K Effect of Time delay on Flying Qualities An Update J Guid Cont and Dyn vol 9 no 5 1986 pp 578 584 Berry D T In Flight Evaluation of Incremental Time Delays in Pitch and Roll J Guid Cont and Dyn vol 9 no 5 1986 pp 573 577 Hess R A Effects of Time Delay on Systems Subject to Manual Control J Guid Cont and Dyn vol 7 no 4 1984 pp 416 421 Powers B G An Adaptive Stick Gain to reduce Pilot Induced Oscillation Tendncies J Guid Cont and Dyn vol 5 no 2 1983 pp 138 142 Candide by Voltaire Translated by Lowell Bair Bantam Books New York 1981 88 27 28 29 30 31 32 33 34 39 36 37 Bailey R E Effect of Head Up Display Dynamics on Fighter Flying Qualities J Guid Cont and Dyn vol 12 no 4 1983 pp 514 520 Sarrafian S K Simulator Evaluation of a Remotely Piloted Vehical Visual Landing Task J Guid Cont and Dyn vol 9 no 1 1986 pp 80 84 Hess R A Mnich M A Identification of Pilot Vehical Dynamics from In Flight Tracking Data J Guid Cont and Dyn vol 9 no 4 1986 pp 4
145. ol system gains X 29A Pitch axis only State Space Fixed Wing Model With Feedback The first aircraft model used was a thesis project completed at the NASA Ames research center by Mark Morel The aircraft model is a verified pitch axis only state space e Deven Fl ghi Rocemrcn Cancer Goel 4321 OT Pheraraphed 128 25 Lmecke Tot gt model of the X 29A figure 25 provided by NASA Dryden research uc ica center with a quickness pre filter added to the original control system to improve the handling qualities After adding the quickness filter the system gains were optimized using the CONDUIT software The trim speed of the model is 726 feet second Modifications Required to Fly The Simulink model of the X 29a contains outputs for Forward velocity body axis alpha angle of attack q pitch rate theta pitch angle world coordinates Nz g s stick actuator rate flap actuator rate and canard actuator rate The outputs from the state space are all perturbations from a steady state An example is that even though the trim speed of the model is 726 feet second if the speed output from the state space is fed 69 directly to the Euler block the output speed is zero until the system in perturbed then the speed just oscillates until trim is achieved again which is 0 ft sec The output speed was modified so that the output from the model was summed with a constant input block in figure 26 the flight model The pitch rate was ou
146. ontrol law optimization Simulink based CONDUIT uses the same models that can be easily modified to create a real time simulation The model is created on a PC and then ported to a workstation for flying qualities analysis and control gain optimization using CONDUIT After the gain optimization has been completed the gains can be reset in the original model on the PC and new simulation code generated and flown immediately This is the concept behind RIPTIDE Ref 9 Real time Interactive Prototype Technology Integration Development Environment a NASA rapid prototyping project that uses RTW to generate simulations and eventually flight control law code using Silicon Graphics IRIX workstations The Cal Poly flight simulation and controls laboratory duplicates much of the capability of the CONDUIT RIPTIDE system using networked PC s rather than expensive workstations Finally a procedure for performing model identification verification was demonstrated using NASA s CIFER Ref 12 13 15 16 software Handling qualities for many types of aircraft such as helicopters Ref 11 cannot be completely predicted before the aircraft is built For these aircraft NASA s CIFER Comprehensive Identification from FrEquency Response program is used to identify the characteristics 10 of the aircraft The results of the data returned from CIFER can be used to correct a flight simulation Ref 14 for further development of the aircraft and flight control system
147. op and inflight simulations Since the simulations are created on a PC tools used in research and industry become available to anyone with the resources to set up operate and program a PC TCP IP protocols used for network internet based communications can be included as functions in the Simulink environment allowing computing to be distributed to other machines The software developed takes advantage of the fact that personal 5 computers are now fast enough to do a single sophisticated simulation task in real time and inexpensive enough to purchase enough to do each of the tasks required Networking takes care of distributing the information each computer requires to complete its part of the simulation After processing is complete each computer either sends the data out as output such as graphics to a screen or sends the data calculated back over the network to the main computer This technique is known as parallel computing The modular structure of model creation allow students to study the dynamics of various aircraft from basic bare airframe aircraft to advanced artificially stabilized aircraft with closed loop digital flight control laws The aircraft can be simulated in a variety of ways from a batch simulation with canned inputs on the desktop using a single personal computer PC to real time simulation on an easily re configurable fixed based simulator including actual flight hardware driven by multiple PCs and or workstations The eng
148. ove function tif defined MDL START Function mdlStart Abstract T Initialize the da cards static void mdlStart SimStruct S unsigned short int addr addr 0x220 aToD12 addr 0x220 aToD12 maxADCount 4095 aToD12 minADVoltage 5 0 aToD12 maxADVoltage 5 0 aToD12 nADChannels 16 aToD12 nDAChannels 2 aToD12 base addr aToD12 cnt0 addr 0 aToDI2 cntl addr 1 aToD12 cnt2 addr 2 aToD12 cntCtrl addr 3 aToD12 dalLow addr 4 aToD12 dalHigh addr 5 133 aToD12 da2Low addr 6 aToD12 da2High addr 7 aToD12 adLow addr 4 aToD12 adHigh addr 5 aToD12 diLow addr 6 aToD12 diHigh addr 7 aToD12 cli addr 8 aToD12 gainCtrl addr 9 aToD12 muxCtrl addr 10 aToD12 modeCtrl addr 11 aToD12 softAD addr 12 aToD12 doLow addr 13 aToD12 doHigh addr 14 ADCChannel rThrottle cNumber 0 rThrottle minV 0 0 rThrottle maxV 1 0 lThrottle cNumber 1 lThrottle minV 0 0 lThrottle maxV 1 0 pitchPos cNumber 2 pitchPos minV 1 0 pitchPos maxV 1 0 rollPos cNumber 7 rollPos minV 1 0 rollPos maxV 1 0 rudderPos cNumber 12 rudderPos minV 1 0 rudderPos maxV 1 0 Set up for the card and the channels PCLabCardInit amp aToD12 ADCChannelInit amp rThrottle amp aToD12 ADCChannel Init amp lThrottle amp aToD12 ADCChannelInit amp pitchPos amp aToD12 ADCChannelInit amp rollPos amp aToD12 ADCChannel In
149. pabilities of the system Adding new functions to the PhEagle II system only requires that the functions use the S function IO template All other inputs and outputs requirements of the function are labeled in the Simulink environment S block To make the block more intuitive a Mask can be put over the block allowing an icon of the functions use to be applied Including Existing IO Functions All existing IO functions that were available as source code from PhEagle I were converted from c code to c code A new data structure was created that is compatible with c Error trapping that was originally part of a complex set of c classes were incorporated into the functions as stand alone code Only program code that was actively being used was incorporated in the S functions While c code is less powerful than c 42 its similarity to other structured languages students have been exposed to allows less experienced programmers to maintain the code and create new functions Since S functions are functions instead of programs the development and testing process is simplified Expanding the Possible The process of separating the IO and modeling functions into Simulink S functions without adding other functions provides greater flexibility to the researchers The ability to select and set up model components one at a time allows a simulation to be built up and tested systematically to the level required for each kind of data collection Output
150. provides basic flexible simulation capabilities upon which to build a complete simulation laboratory More advanced functions can be added to the basic 6 DOF model to provide more accurate flight dynamics over a greater range of conditions Providing external force and moment inputs to the basic 6 DOF rigid body model allow most advanced dynamics to be added to the existing model by creating new Simulink subsystems or S functions Additions to the system can include but are not limited to some functions require a more complex base model than the existing 6 DOF function Advanced Aerodynamics Ground effects Transonic Supersonic Hypersonic Helicopter Rotor Dynamics Momentum Theory Blade Element Non Rigid Structures Non rigid structure dynamics can be added using a S function sending the forces through the force and moment inputs supplied in the basic 6 DOF rigid body model Propulsions Multiple Engine Model Non Centerline Propulsion Thrust vectoring 84 Complex Modeling of Various Systems Landing Gear Additional Hardware in the Loop Adding software to provide a pulse width modulation command output to provide servo motor command capability Coordinate Transform to Place Eyepoint in Cockpit The current model has the eyepoint of the pilot at the center of gravity A translation will be required to move the eyepoint to the correct position for the pilot in any specific aircraft This is a simple coordinate tranform moving
151. pting language by allowing compiled c language functions to be included in the Matlab workspace Cmex S functions allow users to create custom functions that can be included in Simulink models Since the functions are compiled very complex functionality can be added to the basic Matlab Simulink enviorinment Initially a Borland c compiler was used to generate C MEX and C MEX S functions After discovering that the scripts included with the RTW only supported creation of C MEX functions a Watcom c compiler was configured to create both C MEX and C MEX S functions The supplied scripts were run using the example F 14 Simulink model and a batch mode program was created and the output confirmed with the results published in the user manual Using the numerical integrators created for the F 4 F15 Phantom EAGLE simulator PhEagle linear simulation a procedure for creating a S function was established and verified against the data generated from the original functions Next a procedure for creating real time code was established and verified using the numerical integrator S functions and comparing the run time with an external clock to verify the timing functions The final verification was to compare Simulink s built in integrators with the user created numerical integrators using the same integration techniques After the procedure for creating S function blocks was established existing Cal Poly c code used to access various hardware used for input
152. qDot en Forces Moments y Fx qDot u Airspeed P Fy P Fz m gt rDot x ala M rDot Transform Integrate Unit Delay2 Accelerations Irc z Unit Delay cups 1 le z i Unit Delay4 e nitDekys 1 le 1 z nit Delay3 z 4 E Figure 13 Symbolic Model of 6 DOF Functions where the states are calculated The diagram also shows how the states are used by the other functions to calculate the forces and momentes or positions and orientations It is also easy to see where the final states are output Note that in order avoid algebraic loops a unit delay must be included in the feedback states The aircraft is represented at any time by the states summarized in Table 2 The states include the position and orientation 28 Table 2 State Vector Location of aircraft in inertial coordinates Body axis velocity components Body axis rotation rates of the aircraft in inertial space as well as the body axis velocities and rotational rates The forces and moments function starts with stability derivatives read in from a ASCII based Standard Aircraft Data SAD file The file contains 48 elements describing the physical and aerodynamic characteristics of the modeled aircraft along with some initial conditions for the flight condition The function uses a single sad file at one point in the flight envelope The function is intended to be used as a quick check of the dynamics of a developing aircraft at one po
153. raseScreen fadepalout 0 256 following call doesn t matter since the fadepalout routine does this as part of the fade ClrPalette 0 256 SetGfxBuffer 0 ClearScr 0 displays the title screen and waits for a keypress boolean DoTitleScreen boolean result true HTimer pixTimer REV 2 1 remove timer from title display if bkground load title pcx result false if result putwindow 0 0 320 200 bkground Image fadepalin 0 256 bkground Palette return result called from main at program startup to initialize the control view and flight model systems void StartUp CPU 386 detect386 check for 386 processor if detectvga Terminate No VGA analog color monitor detected main Snoopy GetZetaOmega prompt for springing and dampin for the diff eq controler InitControls input cpp initialize controls checkpt 1 clrscr conio h clear the text screen if opMode FLIGHT opMode WALK if not debugging or walking setgmode 0x13 screen asm set graphics mode ClrPalette 0 256 screenc cpp clear the palette if opMode FLIGHT if DoTitleScreen display the title Terminate error loading title image DoTitleScreen if InitView amp bkground opMode 102 Terminate Graphics View system init failed main checkpt 2 update progress
154. ration function endif 123 Abbreviated Instrument D A Simulink S function jikkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkikkkkkkkkkkix MODULE ph_inst c AUTHOR S Friz Anderson Douglas Hiranaka DATE September 25 1998 Copyright c ALL RIGHTS RESERVED REVISION HISTORY REV AUTHOR DATE DESCRIPTION 0 crt 11 5 97 Creation cabtest cpp 1 dkh 6 11 98 reduced to instruments only 2 dkh 7 11 98 put into s mex format S mex See simulink src sfuntmpl doc Copyright c 1990 1998 by The MathWorks Inc All Rights Reserved Revision 1 3 This S function block sends values to the instruments from the computer to the PhEagle flight sim cab This is the a basic version of the outputs to the Sim cab sending out only the altitude airspeed attitude direction g s angle of attack side slip L rpm R rpm Vertical speed and the forces back to the sim cab stick The stick positions are read in the stick block ph stick c kkkkkkkkkkkkikkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkxix define S FUNCTION NAME ph inst define S FUNCTION LEVEL 2 include simstruc h include lt dos h gt include lt bios h gt include lt math h gt include lt stdlib h gt include lt string h gt include lt conio h gt include lt stdio h gt include cyda h char errorChecking float pi 3 14159 struct DAC d16 d12 struct DACChannel a
155. rforms a text mode screen dump of the flight model s internal data It is only called when the program is running in debugging mode void ACDump int x int amp y ReportFrameRate reports the average of the last 500 elapsed frame times Called once at program termination void ReportFrameRate endif 98 Modified Main c class Snoopy l quos a a eto Ho 5 Bim Copyright 1991 1992 Betz Associates All rights reserved File Name FSMAIN CPP Project Snoopy linear simulation Creation January 21 1992 Author Mark Betz MB Machine IBM PC and Compatibles Change History Joc ee Date Rev Author Purpose Lh Mm dont QUEUE T RSS 1 21 1992 14 0 MB Initial development 8 29 1992 1 1b MB first beta 9 26 1992 Ly MB publication release o 9 12 1995 Vu mracky update for C rename dele Project Building Your Own Flight Sim in C 10 22 95 gue mracky fix title display DEBUG mode 1 04 22 98 2 2 DKH convert to Snoopy project Description TA nmn Main module for the Snoopv Group Flight Simulator l Ho Ho Ho Ho include lt dos h gt include lt stdlib h gt include lt bios h gt include lt math h gt include lt conio h gt include lt mem h gt include types h generic data types include htimer h hi res timer class include pcx h include air
156. rintf yaw gotoxy 3 i oe th cprintf speed H gotoxy 3 i oe th cprintf speed V gotoxy 3 i de Fh cprintf rate of climb gotoxy 3 i oe m cprintf altitude char msg int exit code ShutDown REV 2 0 rename program Ts ESVA tu GSMs ti SENS MS tSV My CESVE SV tSV Mir ZENONE y SV V BOVA tSV tSV Tp SENS MSS tSV tSV tSV a ESV char loc rudder pos throttle pos ignition on engine on rpm fuel X pos y_pos z_pos pitch efAOF roll yaw h speed v speed climbRate altitude Based on the value of checkpt it and prints the leadin accordingly but this shouldn t be hardcoded anyway this whole checkpt thing should be made into a throw from the various points where the program has failed cprintf FSIM EXE gt r n if checkpt lt 4 cprintf A critical error occured in function cprintf s r n loc cprintf Error cprintf s causing exit code 1 else cprintf s in msg cprintf s r n loc controlled termination r n msg 101 exit_code 0 if opMode DEBUG ReportFrameRate exit exit code REV 2 1 separate screen fade from draw title screen this wav the world can be loaded while the title is displaved void E
157. rs 9 set amp verspeedIndicator uPtrs 10 set amp yawForceOut uPtrs 11 set amp rollForceOut uPtrs 12 set amp pitchForceOut uPtrs 13 Source code for DACCard setup for d a void DACCardInit struct DAC card si short channel unsigned short count unsigned short addrl float voltage voltage 0 if card gt nBits gt 16 card gt nBits lt 2 printf DAC error Cannot set for d bits n card gt nBits card gt maxCount unsigned short 1 lt lt card gt nBits 1 card gt gainVtoCounts float card maxCount card pLimit card gt nLimit card gt vOffset card nLimit for channel 0 channel lt card nChannels channel if channel gt card gt nChannels printf DACCard channel d is out of range n channel if card gt vDefault gt card gt pLimit card gt vDefault lt card nLimit if errorChecking printf DACCard Voltage 1 3f is out of range n card vDefault voltage voltage gt card gt pLimit card gt pLimit card gt nLimit count unsigned short card gt gainVtoCounts voltage card vOffset addrl card gt baseAddr channel lt lt 1 outpw addrl count 128 Setup for Dac channel void DACChannelInit struct DACChannel chan struct DAC Card float min max if chan gt channelNumber gt Card gt nChannels printf DACCard channel d is out of range
158. s ss NNavionLatA NNavionLatB NNavionLatC NNavionLatD statename states inputname inputs outpurname output 177 Navion Longitudinal State Space Setup Nelson Navion longitudinal state space setup SFASAND Fundamentals of Aircraft Simulation And Nonlinear Dynamics This is a state space model of the Navion example aircraft used to validate the FASAND code The A and B matricies were oe obtained from dimensional derivatives provided in appendix A oe of Flight stability and control Robert C Nelson oe oe This Script is free to copy and distribute for educational purposes as long oe as this notice is included oe oe Doug Hiranaka oe oe Created 8 98 oe Last Modified 1 25 99 DH corrected state and control ref McRuer matrices oe Copyright c 1998 99 by Penguin Aeronautics NNavionLonA 0 0448765 0 036 0 32 174 0 369 2 014955 168 8 0 0 0019 0 0396 2 948 0 0 0 1 0 1 3 2 was 2 948 NNavionLonB 0 28 2856 11 65435 0 1 2 was 27 94324 NNavionLonC 10 0 0 0100 0010 00011 NNavionLonD 0 0 0 0 states u w q theta inputs elevator output speed heave pitch rate pitch angle nLonSys ss NNavionLonA NNavionLonB NNavionLonC NNavionLonD statename states inputname inputs outpurname output 178 Navion Complete State Space Setup Nelson 9 navion state
159. s and the built in TCP IP and shared memory capabilities native to Unix simulations can be performed on a single machine doing complex rotor state calculations using a joystick and one or more screens Simulator cab motion more complex graphics complex simulation of components such as powerplants or navigation aids e g inertial navigation all require multiple computers Cal Poly The software available for the PhEagle I lab include a three axis transfer function model a state space model and a basic nonlinear 6 DOF rigid body model Transfer Function A stand alone three axis transfer function model was created to demonstrate transfer function models as a means of describing a dynamic system The model was also to be used for handling qualities research Ref 16 to provide a simple model with known dynamics to vary control stick force shaping and processing time delay The transfer function model uses first and second order differential equations transformed through a Laplace transform to the frequency domain Ref 33 A transfer function is a ratio of output to the input of a system over a range of frequencies Using literal factors approximations for the pitch roll and yaw axes a simple model of the dynamics of an aircraft can be rapidly synthesized Ref 32 The first order system models an over damped spring damper system that provides a variable delay to the system A first order function models the roll axis of a conventional aircraft
160. se gains The final configuration with a quickness pre filter added and all of the control gains optimized using CONDUIT was much more responsive in pitch with good damping The model showed some tendency toward pilot induced oscillations PIO in the roll direction as the roll was set up to be a transfer 71 function and the dynamics were very simple It is believed that the roll channel included excessive time delay resulting in the reported PIO Several engineers tested the model and observed similar tendencies in the roll channel Kaman SH 2 3 Axis Non Linear State Space Helicopter Model with Feedback A verified full state F A state space model of the a Kaman SH 2f helicopter Figure 27 was obtained from a NASA Cal Polv research project The model was created using a model following architecture with the trim conditions at 35 KA A knots in transitional forward flight A model following control svstem uses dvnamics identified using programs like NASA s CIFER Model following control svstems use a low order 1 or 2 order fit of the high order dynamics identified The low order transfer functions are inverted and combined with feedbacks and cross feeds to remove undesired cross coupling of the controls and to wash out the dynamics of the original plant A model that the control system is designed to follow is placed in the forward path Part of the original research task was to attempt to satisfy as many of the helicopter
161. sea level temperature and pressure This allows the user to set up non standard conditions to match flight test data that has not been normalized The input is in Kelvin and Newtons meter 2 Input Creating the 6 DOF model as a S function allowed the model to use any of the canned inputs available from Simulink as well as the new PhEagle stick input block The ability to use the standard Simulink Matlab functions allowed the analysis of the aircraft to be done all using a single CAD CAE package Access to a workstation allows CONDUIT to be used to analyze a bare airframe or optimize a control system A paper pilot would be a matter of creating Simulink subsystems or S functions to model piloted inputs Output The output has been expanded from basic text screen output and basic graphics to the Simulink scope to workspace function to file as well as numerical output and advanced graphics of the World up viewer and PhEagle I out the window graphics The ability to produce ASCII file output of the control inputs and airframe dynamics allow the use of the NASA program CIFER for simulation model verification A function has been created to convert ASCII files to Fortran unformatted binary files CIFER requires a Fortran binary file of the input and output for each channel desired for identification Feel With all of the states being written out actual aircraft control feel as well as artificial state feedback feel can be incorporated with the 6 DOF model
162. st 1995 Tischler MB Fletcher J W Diekmann V L Williams R A Cason R W Demonstration of Frequency Sweep Testing Technique Using a Bell 214 ST Helicopter NASA TM 89422 USAATCOM Technical Memorandum 87 A 1 April 1987 87 20 21 22 23 24 25 26 Tischler M B Chen R T N The role of Modeling and Flight Testing in Rotorcraft Parameter Identification vol 11 no 4 1987 pp 619 647 Tischler M B Leung J G M Dugan D C Identification and Verification of Frequency Domain Models for XV 15 Tilt Rotor Aircraft Dynamics in Cruising Flight J Guid Cont and Dyn vol 9 no 4 1986 pp 446 453 Wigdorowitz B Application of Linearization Analysis to Aircraft Dynamics J Guid Cont and Dyn vol 15 no 3 1992 pp 746 750 Sarrafian S K Powers B G Application of Frequency Domain Handlig Qualities Criteria to the Longitudinal Landing Task J Guid Cont and Dyn vol 11 no 4 1988 pp 291 292 Shafer M F Low Order Equivalent Models of Highly Augumented Aircraft Determined from Flight Data J Guid Cont and Dyn vol 5 no 5 1982 pp 504 511 Tischler M B Flying Quality Analysis and Flight Evaluation of a Highly Augumented Combat Rotrocraft J Guid Cont and Dyn vol 14 no 5 1991 pp 954 963 Duda H Prediction of Pilot in the Loop Oscillations Due to Rate Saturation J Guid Cont and Dyn vol 20 n
163. stem transfer function used a Runge Kutta 4 RK4 scheme equation 5 The frequency and magnitude matched exactly with the Equation 5 1 Y 7 f tg 2k 2k k k hf x y h k k hf x y 2 if n 2 Va 2 h k k hf x y 3 if n 2 Ya 3 k hf x h y k Mathworks supplied integrator At 01 sec the difference was less than 0 25 To verify that 0 25 was within the range acceptable for accurate modeling a study was conducted to compare the fixed step numerical integrators available form Mathworks as well as the ones available from ISI in the System Build modeling software At a dt of 0 05 using the RKA integrators and the same three transfer functions there was a 0 55 difference between the maximum overshoots for the transfer functions For a time step of 0 05 the Mathworks integrators Dormand Prince Runge Kutta4 Bogacki Shampine Heun varied less than 0 5 The Euler integrator response error was 100 using a 0 05 sec dt compared with the other methods The time step was reduced to 0 001 sec where the error between the Euler method was reduced to less than 1 The results of the study indicate that caution should be taken to verify that a fine enough time increment is being used when relying on the Euler technique To provide input and output for the integrators code for a joystick and basic software VGA graphics were obtained from a public domain simulator Build Your Own Flight Simulator BYOFS i
164. t The model used a natural frequency of 6 0272 RAD sec and a damping ratio of 0 68852 The natural frequency and damping ratio were derived from a small general aviation aircraft a Cessna 172 Ref 36 Two Fortran programs atobin f atobout f were created to convert the ASCII data files to unformatted Fortran binary format files which CIFER uses for input The output files before bin after bin were copied to the CIFER directory structure and processed in CIFER to bode plots then to a low order equivalent system transfer function The CIFER software and html tutorial reside on a Silicon Graphics Indigo workstation Daniel located in the Cal Poly controls lab The web page contains everything required to create and process a chirp to a bode plot and low order equivalent 80 transfer function The ability to verify that a math model is valid with documentation to show where the model is valid is crucial to publishing the results obtained using the Cal Poly simulation lab Access to tools industry and research is using is vital to the training of future engineers Stability information for a fixed wing standard configuration aircraft are well known and can be predicted accurately However rotorcraft and aircraft with unusual configurations cannot always have the stability information predicted accurately industry and research identify the aircraft after construction using CIFER to refine the control laws to conform with the actual behavior of th
165. t Without flight test data further refinement of the model is not possible The model has demonstrated the correct behavior that an conventional airplane would display to the control inputs with the time constants approximately correct and damping close to a linear model The final verification used the World up viewer to display an external view of the model to view the coupled responses The same step input was 62 Impulse Response Beta o e cS State Space 3 ce 6DOF 4 E E lt 1 1 1 J 15 20 25 30 Time sec Impulse Response Roll Rate T T T T T al 20 7 5 15r 7 o ES tol State Space B aa 6 DOF 57 i ok L RE 1 1 l 1 1 0 5 10 15 20 25 30 Time sec Figure 22 Lateral Beta to Rudder and P to Aileron applied to the model and the graphical output was observed For pitch both the short period and phugoid were observed in the correct magnitudes A step input to the roll control resulted in adverse yaw yaw away from the roll input and finished with a roll angle in the direction of the control input The roll angle washed out and a spiral divergence was initiated A pulse to the rudder displayed the charateristic rotation of the tail of the airplane in the dutch roll mode with a entry into the spiral mode from the induced roll angle once the dutch roll died out Tools described in the CIFER section provide the information that will
166. t as the 6 DOF model finishes 10 seconds of integration using a 10 millisecond integration step in less that a second Hardware Setup and Test The hardware S functions created to work with RTW were compiled to dll s to determine if the functions would work in the regular Simulink environment The driver functions for the stick and the instruments function normally in the standard Simulink batch mode A delay function was required as a batch simulation finish time of 100 000 seconds finished in seconds Since the drivers function properly in the standard Simulink environment Simulink can be used to perform force setup without a timing block on the stick and pedals To slow down the simulation an extremely small time step for the integration or including a delay loop to slow down the processing to close to real time is required Since the force stick hardware drivers do not require a specific time step setup of the stick forces is done without having to generate executable code which takes several minutes each time 38 Real Time Workshop To generate the final executable program a Simulink model must include the source code for all of the user supplied S functions Any custom functions that will run in the Simulink environment can be included in the auto coding to run in a stand alone application Stand alone Code The real time workshop code generator creates an executable that runs in the 32 bit DOS window of Windows 98 Using the TCP IP conne
167. ta index 1 Theta index k1 2 0 K c deltaE k2 2 0 K c deltaE k3 2 0 K c deltaE Theta index 1 1 6 0 k1 2 0 k2 2 0 k3 k4 z index zlindex 1 1 6 0 11 2 0 12 2 0 13 14 Time index t t t dt index while loop output write to a file fout fopen rk4out m w if lfout printf can not open output file n exit 1 printf output file open n fprintf fout t for int j 1 j index j 94 write array to file fprintf fout 1f Time j if feof fout printf End of file n fprintf fout n fprintf fout theta for int l 1 l index 1 write array to file fprintf fout 1f Theta l if feof fout printf End of file n fprintf fout An fprintf fout printf Done writing to file fclose fout printf number of lines i n j printf Done writing to file GAME OVER Have a nice day n end of main 95 Snoopy 2nd order RK4 Class a i Fe e d R pea A Hime Copyright c 1991 1992 Betz Associates All rights reserved File Name AIRCRAFT H Project Flights of Fantasy Creation August 2 1992 Author Mark Betz MB Machine IBM PC and Compatibles Change History Ml Festo OU Date Rev Author Purpose Dur Tonm LESSE FRETTA 8 2 1992 1 0 MB initial development 8 29 1992
168. ta was selected for integration To verify the process and accuracy of the code generated by RTW the RK4 numerical integrators created to test the S functions were placed in a new model and auto coded in batch mode The program was run and the results were automatically saved to a text file for analysis The results from the output file were compared with the output from the PhEagle I numerical integrators the original output from the S function run in the 4l Simulink environment and Mathworks versions of the RK4 integrator The output from the RTW generated code matched all of the other versions of the same code with the same 0 5 variation between the new RK4 integrator and the Mathworks RK4 integrator verifying the batch mode Modular Structure Conversion of the various functions required to create a simulation has reduced the total number of lines of code that require maintenance There is one copy of each of the input output hardware graphics and flight models to keep track of RTW creates a simulation using the same S function code tied to the icon in the Simulink diagram rather than having a separate copy for each simulator as would be the case with stand alone simulations Since the RTW autocoder requires c source code for any of the S functions the functions are provided as open code to allow future researchers at Cal Poly to update and modify the existing functions or use them as templates to create new functions to expand the ca
169. tandard Flying Qualities of Piloted Aircraft However little information is available about which states to feed back and how to cue the pilot through the controls The MIL STD 1797 provides only basic guidelines for the force gradients and one state in each control axis to be fed back Table 1 Table 1 Aircraft control Stick and Pedal Feedbacks Axis Feedback state Force Gradient Maximum Force Pitch Nz 8 Ibf g 50 Ibf Roll Roll Rate p 1 Ibf deg sec 25 lbf Yaw Side Slip Beta 1 Ibf deg 100 Ibf The MIL STD 1797 was used to set up the basic feedback for the PhEagle I Two types of pilot induced oscillation PIO can be predicted using batch and fixed base pilot in the loop simulation Ref 5 A PIO is a phenomena where the pilot sends commands to the plane in a cyclical fashion where his input ends up sending exactly the wrong command to the airframe from the desired response An example of this is trying to 13 highlight some text on a word processing document and over shooting the desired sentence and then correcting up the page and overshooting again etc Cal Poly s basic simulation lab provides many capabilities that are available to anyone with access to personal computers The programmable PhEagle handling qualities force stick and pedals allow Cal Poly to expand the knowledge base on pilot feedback Siblinc The PhEagle s dial instruments are run through an analog computer called the
170. ter noticed that the model was still flying much faster than the actual helicopter would Despite the error in timing with the model a great deal was learned about the flying qualities and dynamics of the flight and control models The control gains were tested to confirm decoupling of the axis then doublets were performed to confirm damping ratio No force feedback was available on the version of RIPTIDE used for the evaluation so actual handling qualities information was limited No actual piloted evaluations of the model were conducted All flights were 73 made by handling qualities engineers However much insight to the nature of a linearized model and limitations of the control system and airframe were obtained from the exercise Since the SH 2f model was a state space model with the trim condition in forward flight interesting things happened when the helicopter was flown too far from the trim conditions Since the dynamics are linearized slowing to hover speeds did not model the correct thrust available from the rotor as well as not modeling ground effects so the model could barely maintain a hover The control laws were optimized for forward flight so the rate command attitude hold made hover tasks a challenge The decoupling of the axis did reduce pilot workload considerably even with a less than optimal command system for the task Control Laws and Trim In forward flight as the model exceeded trim conditions and flew faster the con
171. the Loop Existing Infrastructure PhEagle II Software Modular Structure Including Existing IO Functions Expanding the Possible Output D to A Instruments Input A toD Stick Feedback Force Active Sick Cueing Graphics Network TCP IP Key Features of Simulations Linear Modifications Required to Fly Euler Block Trim Attitude and Speed Feel 6 DOF Non linear 6 DOF Model Verification 28 34 34 34 37 38 38 39 39 40 40 40 42 42 43 43 44 45 45 46 46 46 47 47 48 49 51 52 53 53 53 60 Standard Atmosphere Input Output Feel Control System Closed Loop User manual Intranet Internet Verification of Concept CONDUIT X 29A Pitch axis only State Space Fixed Wing Model With Feedback Modifications Required to Fly Observations of Flight Model Kaman SH 2 3 Axis Non Linear State Space Helicopter Model with Feedback Modifications Required to Fly Observations of Flight Model Control Laws and Trim Insight into Control Laws North American Aviation Navion Fixed Wing 6 DOF Non linear Model Assumptions Portability SAD Files Test Setup for Feedback Portability of Simulations Unix to PC Analysis Tools Matlab Analysis Tools CIFER Data Collection CONCLUSIONS LESSONS LEARNED Parallel Capabilities Open Code Maintainability viii 64 65 65 65 67 67 67 68 69 69 70 72 73 73 74 74 75 75 76 76 77 77 77 77 77 81 82 83 83 83 FUTUR
172. the inputs that are available from the stick through the stick computer 45 Table 9 Cab Inputs Input from cab output range pitch command angle 1 pitch force 1 ptich trim def 1 pitch velocity 1 pritch trim position 1 roll command angle 1 roll force 1 roll trim def 1 roll trim position 1 roll velocity 1 yaw comand angle 1 yaw force 1 yaw trim position 1 yaw control velocity 1 right throttle 1 left throttle 1 Feedback Originally the feedback of the stick forces was done in the simulation code The S function provides only a force input Any feedback architecture is done in the Simulink block diagram Force The force at the stick is controlled by the gain input to the S function By feeding back a state to the force input of the stick cueing of the states is possible Active Sick Cueing Creating canned responses to certain airframe or power plant states allows a pilot to be cued actively that he is approaching a limit or a limit is changing The most common form of active stick cueing is a stick shaker to inform the pilot that stall of the 46 wing is imminent A sine wave input with a frequency of about 5 hz would provide the input for a stick shaker Graphics Graphics is currently being provided by the World Up VR viewer The graphics for PhEagle I are still being developed and will be incorporated as soon as they are av
173. the viewpoint in the body axis system Simulink Blocks Real time Timing Block for use on a PC Simulink runs in batch mode integrating the equations of motion as fast as the processor will allow Including the stick instrument or hardware blocks allows the simulation to get data from outside the Simulink environment Including a timing block in the Simulink diagram to delay the next iteration of the differential equations to the actual amount of time as the dt used for the numerical integration s provides actual real time data input to a simulation without having to autocode the simulation The process of auto coding takes about 10 minutes for a average size simulation diagram The timing block would provide a means to do setup of the feel system and other IO hardware through the regular Simulink environment Flybox Cal Poly has a BG systems Flybox serial port inceptor The c source code is available providing the opportunity to add desktop input to a Silicon Graphics 85 workstation or PC for function testing without having a test pilot or having to jump in and out of the sim cab Graphics PhEagle I has advanced graphics with several channels available through a TCP IP link with the simulation computer The TCP IP protocol for the information was not complete at the time when the PhEagle II project was initiated however all that is required to add the graphics is to include a TCP IP block in the Simulink block configured to output to
174. this routine 7 static void mdlTerminate SimStruct S ifdef MATLAB MEX FILE Is this file being compiled as a MEX file include simulink c MEX file interface mechanism telse include cg_sfun h Code generation registration function endif 172 Navion Lateral State Space Setup Archangel amp navion lateral state space setup SFASAND Fundamentals of Aircraft Simulation And Nonlinear Dynamics This is a state space model of the Navion example aircraft used to validate the FASAND code The A and B matricies were oe obtained from Arcangle 1 0 by inputing the example non dimensional oe derivatives provided in appendix A of Flight stability and oe control Robert C Nelson oe oe This Script is free to copy and distribute for educational purposes as long oe as this notice is included oe oe Doug Hiranaka oe oe Created 8 98 kud Copyright c 1996 98 by Penguin Aeronautics ANavionLatA 0 2531035 0 1834322 0 g i 0 0 1 0 0 15 86694 0 8 370129 0 2 1844 0 0 0 0 1 4 519665 0 0 348499 0 0 75761 ANavionLatB 0 0 0704561 0 0 28 73202 2 294273 0 0 0 2228004 4 583323 ANavionLatC 10000 01000 00100 00010 0 0 040 L 12 ANavionLatD oO oO o o e a 1 states beta phi p psi r inputs aileron rudder output sideslip bank angle bank rate yaw angle yaw rate aLatSys ss AN
175. tomatic c language code generator RTW generates compilable c code to create a stand alone executable program that runs in DOS or Unix Ref 5 Second RTW creates real time 4 code To process simple equations of motion takes about a millisecond RTW uses a hardware timer driven interrupt to delay the program to equal the integration time step If a integration time step of 10 milliseconds 0 010 sec is selected in the model RTW delays the program 0 009 seconds more so that the code is running at the same rate as the integration step size Third RTW combines hardware drivers into the program to drive any device Ref 6 that can be connected to a computer An inceptor device input device eg Joystick such as the BG Systems FlyBox represented in Figure 2 is included by wrapping the S function IO code around the software drivers supplied by the device manufacturer The RTW software includes any custom S functions as well as built in Simulink blocks allowing applications of any level of complexity In theory anything that can be represented by a Simulink diagram can be simulated in real time Aircraft are complex dynamic systems which are ideal for Figure 2 FlyBox Inceptor the Simulink Real Time Workshop pair Real time or batch simulation and flight control law code is generated from a Simulink model of an aircraft subsystem or component The ability to include hardware drivers allows pilot in the loop as well as hardware in the lo
176. tput from the model so it was fed straight into the Euler block The model was pitch axis only so a yaw position attitude hold and roll rate command attitude hold was added using simple transfer functions The input was from a Flybox inceptor with the input passed through shared memory to the flight model The graphics was set up on its own processor with the input from shared memory from the flight model The connection of the inceptor to the flight model then to the graphics output was created through the Simulink diagram and the whole model was held to real time with a timing S function block included in the flight model Observations of Flight Model 70 Integrator_2 0125841 integral oedtorwara deg de PF gt gt IL J y Time del WT ime delay v o3 07 aproxZOH Canard actuator 00584 Proportional feedforward deg degisec Integrator t ZE gt Y 04 4 gt eB ne 100 visi E gt tela body bo y y apioiZoH Time dey e atr wil gaan ad KST 98765 High Pass U gt phi body command x feedback see For XE swap bi i x gt psi body 7 100 100 Pa 01275 1 0124 DE LowPass Fiter DEI 54100 51
177. trol laws attempted to maintain a zero sideslip angle where the actual helicopter trims to a greater and greater sideslip angle When the tail rotor ran out of control power to maintain the desired sideslip the model simply produced a uncorrectable yaw which rapidly increased to the limit of the integrator and the simulation had to be aborted Insight into Control Laws Using automatic tools like CONDUIT that tune the control gains from the originals require checking the various responses to control inputs to verify that something unexpected did not occur during the optimization process The ability to rapidly create a flyable model allows spot checks on the responses of the model Substituting the full nonlinear model for the linearized plant allow the control laws to be tested in a complex environment close to the final aircraft 74 North American Aviation Navion Fixed Wing 6 DOF Non linear The 6 DOF nonlinear equation of motion model was tested using a SAD file created using the stability derivatives of a North American Aviation Navion in the appendix of Ref 33 The process of creating the model and debugging the program code uncovered several sign and magnitude errors in the derivatives and the state space model of the Navion The errors in the stability derivatives illustrates the requirement for verified flight data to be used to confirm the validity of a flight model Several other modeling deficiencies were observed during testing of th
178. uct PCLabCard Card float value unsigned short bHigh bLow flag 1 if Chan gt cNumber gt Card gt nADChannels printf PCLabCard Analog channel d is out of range n Chan cNumber outportb Card muxCtrl Chan cNumber outportb Card gt softAD Oxff delay 1 while flag bHigh inportb Card adHigh bLow inportb Card gt adLow flag bHigh amp 0x10 Chan gt adcount bHigh lt lt 8 bLow amp 0x00ff value Chan gt gain float Chan gt adcount Chan gt offset return value i IS Po I dn a ht St Cn l du ely ASA AER LE Source code for ADCChannel class A AAA SAA E ws ma st fk aan i hah a CE ee esl A RM ES void ADCChannelInit struct ADCChannel chan struct PCLabCard card float value chan gt adcount 0 if chan gt minV chan maxV chan gt minV card gt minADVoltage chan gt maxV card gt maxADVoltage chan gt gain chan gt maxV chan gt minV float card maxADCount chan gt offset chan gt minV value chan gt gain float chan gt adcount chan gt offset 122 Function mdlTerminate Abstract No termination needed but we are required to have this routine ui static void mdlTerminate SimStruct S ifdef MATLAB MEX FILE Is this file being compiled as a MEX file include simulink c MEX file interface mechanism else include cg_sfun h Code generation regist
179. uire changes to include the trim alpha and initial moments to determine the trim elevator position The point mass model can model fixed wing aircraft spacecraft and basic dynamics of rotorcraft without the rotor dynamics The atmosphere model extends high enough to allow aircraft that require reaction controls to be tested The input for the model is a ASCII text file in the format of the Standard Aircraft Data SAD file The filename is set by double clicking on the 6 DOF block and changing the name in the parameter block for the function The block was initially tested outputting only the position and orientation states After working with the model it was found that it is desirable to output all the states available and to separate some of the inputs to separate functions Figure 18 The density of the atmosphere was sent in as a input from a separate function to allow more simple or more complex models of the atmosphere to be added Additional forces and moment inputs Figure 18 have been added to allow for more complex components to be added such as landing gear The additional force and moment inputs allow for turbulence transonic and supersonic aerodynamics non rigid body dynamics as well as rotorcraft blade element dynamics to be included 57 ni Unit Delay elevator ly elev Elev Up Elevator rad ail Ail Aileron Up Aileron rad Pru
180. ument Help File function ph_inst airspeed altitude pitch roll yaw fz alpha beta l1_rpm r_rpm h_dot fpitch froll fyaw ph inst c Simulink RTW s function pheagle Flight sim output block ph_inst airspeed altitude pitch roll yaw fz alpha beta 1_rpm r_rpm h_dot fpitch froll fyaw This function sends commands to the instruments through a A to D oe card This block is a basic set of the outputs for the PhEagle oe cab The block includes outputs for the stick force system All oe the out put is being handled with the output blocks to keep the oe number of duplicat functions to a minimum oe oe The range and nominal units for the inputs are given any oe conversion is left up to the user Any non standard units oe should be noted to the pilot trying to interpret the instruments oe oe inputs channel gauge range input units output units oe 0 Airspeed 0 700 knots oe 1 Altitude 0 60 000 feet oe 2 pitch8Ball Pitch angle theta Pi 2 rad deg oe roll8Ball Roll angle phi Pi rad deg yaw8Ball Yaw angle psi Pi deg oe dirGyro Yaw angle psi Pi deg oe a B mw oe g meter Nz g s 4 9 g s oe 6 aoaMeter Alpha angle of attack 10 40 degrees deg oe 7 sidslipAngle Beta side slip 15 degrees deg oe 8 Left engine rpm 110 10 percent rpm oe 9 Right engine rpm 10 110 percent rpm
181. unt S return Parameter mismatch will be reported by Simulink if ssSetNumInputPorts S 1 return ssSetInputPortWidth S 0 1 ssSetInputPortDirectFeedThrough S 0 1 if ssSetNumOutputPorts S 1 return ssSetOutputPortWidth S 0 4 ssSetNumSampleTimes S 1 Take care when specifying exception free code see sfuntmpl doc ssSetOptions S SS OPTION EXCEPTION FREE CODE Function mdlInitializeSampleTimes Abstract Specifiy that we inherit our sample time from the driving block kl static void mdlInitializeSampleTimes SimStruct S ssSetSampleTime S 0 INHERITED SAMPLE TIME ssSetOffsetTime S 0 0 0 define MDL START if defined MDL START Function mdlstart Initialize the state variables ef static void mdlStart SimStruct S Value for sea level TEMPERATURE in K TO BASE TEMP T0 288 16 Value for sea level PRESSURE in N m 2 PO BASE PRESS P0 101325 0 Alt 1 0 endif MDL START Function mdlOutputs Abstract Using this the function as a gateway Lookup is 157 in estimate Alt uPtrs 0 meters y 0 y 1 y 2 y 3 TempK Kelvin Press N m 3 Density N kg 3 VSound m sec static void mdlOutputs SimStruct S int T tid InputRealPtrsType uPtrs real_T y Alt uPtrs 0 estimate y 0 y 1 y 2 y 3 TempK Press Density
182. untmpl doc ssSetOptions S SS OPTION EXCEPTION FREE CODE Function mdlInitializeSampleTimes Abstract Specifiy that we inherit our sample time from the driving block ef static void mdlInitializeSampleTimes SimStruct S ssSetSampleTime S 0 INHERITED SAMPLE TIME ssSetOffsetTime S 0 0 0 define MDL START tif defined MDL START Function mdlstart Initialize the state variables static void mdlStart SimStruct S X INIT_X initial locations feet YY INIT_Y Z INIT_Z negative altitude Psi INIT PSI Deg2Rad euler yaw angle input degs Theta INIT THETA Deg2Rad euler angle Phi INIT PHI Deg2Rad euler angle endif MDL START Function mdlOutputs Abstract inputs p uPtrs 0 body roll rate Input in Deg Sec q uPtrs 1 body pitch rate r uPtrs 2 body yaw rate d alpha uPtrs 3 angle of attack set to 0 if supplying v amp W beta uPtrs 4 side slip set to 0 if supplying v amp W m u uPtrs 5 If letting this routine do alpha and beta v uPtrs 6 then v and w whould be 0 Wis uPtrs 7 Fetes PELS AEREA outputs y 0 x position FEET y 1 y position y 2 z altitude y 3 psi euler yaw OUTput in degrees y 4 theta euler pitch id y 5 phi euler roll states not using s function states x position FEET y position z alt
183. up for Feedback Two models for the PhEagle were set up to test the force feedback system and the S function code The first uses the 6 DOF model with Nz and p fed back to the stick The second model has no dynamics in the model so feed back can be set up and tested independently of the flight model Portability of Simulations Unix to PC The Simulink model code is completely portable between a PC and a Unix workstation and the X 29a and the 6 DOF have been run on both The SH 2f has been checked to confirm enough processing speed to run in real time on a PC Analysis Tools Simulink is a graphical front end that runs in the Matlab environment Several blocks are included to provide an interface to the Matlab workspace The ability to send data from a simulation to the Matlab workspace allows immediate analysis of a simulation or control system Matlab Analysis Tools The data that can be passed to the Matlab includes time histories as well as frequency domain data This allows plots of multiple configurations as well as comparisons between a model and data collected from the actual aircraft CIFER The time domain provides a reasonable first cut confirmation of a math model Time domain analysis is performed by perturbing the system with a step or impulse then collecting the response of the airframe as a plot of the magnitude of the motion To validate the model over the complete range of input and output frequencies a frequency domain analysis
184. ut x 0 to 255 double yaw rotation about y 0 to 255 96 double roll rotation about z 0 to 255 float h_speed horizontal speed airspeed true float v_speed vertical speed during last time slice float delta_z z distance travelled in last pass float efAOF effective angle of flight float climbRate rate of climb in feet per minute int altitude altitude in feet boolean airborne true if the plane has taken off boolean stall true if stall condition boolean brake true if brake on byte view_state which way is the view pointing byte sound_chng boolean true if sound on off state chngd float pK p itch axis steady state gain float pzeta p itch axis damping coefficient float pwn plitch axis natural frequency rad sec float rK r oll axis steady state gain float rzeta r oll axis damping coefficient float rwn r oll axis natural frequency rad sec float yK y aw axis steady state gain float yzeta y aw axis damping coefficient float ywn y aw axis natural frequency rad sec double p double q double r double psidot double phidot double thetadot int order 1 for first order 2 for second order struct delta vect is used by the aircraft modeling functions in aircraft cpp as a container for the current delta values for the aircraft rotations struct delta vect double dPitch delta change in pitch deg per ms double dYaw de
185. utput are done in the same blocks oe oe The limits for the stick output are set at 4 1 so oe any other limits can be set using a gain block to alter the oe control signal comming out oe oe outputs oe pitch command angle 1 oe roll command angle 1 oe yaw command angle 1 oe right throttle 0 to 1 oe left throttle 0 to 1 oe oe NOTE this is a help block only there is no function oe attached to this m file oe oe Doug Hiranaka 9 27 98 oe Copyright c 1998 by Penguin Aeronautics 140 Six Degree of Freedom Point mass Non Linear Simulink S function File sixdofl c Abstract This C file S function is the basis for a 6 degree of freedom non linear equation of motion point mass simulator This program is free to copy and distribute for educational purposes as long as this notice is included Doug Hiranaka 7 96 Original coding 9 98 Converted to S function 11 05 98 Added SAD file input 11 21 98 Added drag thrust 12 20 98 Added full state output force and moment input 12 30 98 Added Wind2Body Copyright c 1996 98 Cal Poly State University See simulink src sfuntmpl doc Copyright c 1990 1998 by The MathWorks Inc All Rights Reserved Revision 1 3 define S FUNCTION NAME sixdofl define S FUNCTION LEVEL 2 include simstruc h include lt stdio h gt include lt string h gt
186. wVal 0 6 oldVals 12 oldVals 12 newVal y 12 int newVal newVal doConversion amp rudderVelocity amp aToD12 newVal 0 4 newVal 0 6 oldVals 13 oldVals 13 newVal y 13 int newVal newVal doConversion amp rThrottle amp aToD12 newVal 0 4 newVal 0 6 oldVals 14 oldVals 14 newVal y 14 int newVal newVal doConversion amp lThrottle amp aToD12 newVal 0 4 newVal 0 6 oldVals 15 oldVals 15 newVal y 15 int newVal define MDL UPDATE Change to undef to remove function tif defined MDL UPDATE Function mdlUpdate Abstract A This function is called once for every major integration time step E Discrete states are typically updated here but this function is useful for performing any tasks that should only take place once per x integration step UA Static void mdlUpdate SimStruct S int T tid tendif MDL UPDATE 121 define MDL DERIVATIVES Change to undef to remove function tif defined MDL DERIVATIVES Function mdlDerivatives static void mdlDerivatives SimStruct S endif MDL DERIVATIVES void PCLabCardInit struct PCLabCard card at LE dCard new DACCard 12 card gt dalLow 0 0 5 0 2 0 0 if dCard printf PCLabCard Unable to allocate memory for DAC n outportb card gainCtrl 0x00 outportb card modeCtrl 0x01 float doConversion struct ADCChannel Chan str

An Integrated, Modular Simulation System for Education and

Contents

Download Pdf Manuals

Related Search

Related Contents