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User`s Manual - Alpha Control Lab

1. Azimuth Angle amp Reffrence Azimuth Bi gt i F Angle amp Control m P gt Uy lt Azimuth Angle Fo Sat Azimuth Angle amp Reference Nn al lpr Pitch Angle E PID gt gt t gt A 0 3 iB Sati Azimuth RPM gt Reset gt gt 1 Pitch RPM RPM 0 Lp idi TRAS Normal ee Angle amp Reference une gt Pitch Control Filter gt gt Angie a Conil Fig 5 18 Real time model of the 2 DOF control task Azimuth position and reference signal 0 25 l Te Larra AV MARA RAKA l ets asas HO eae ama que J I j I I I O46 ees NE E eee Ra e on Sucre cte i 0 1 os A pesce cp praeda eds ey ies J 0 05 ey ae Sete Sas O ett ete ae 4 MCG SAO ZULU aaa KRUNE EE TERME NE ENS J l I 0 05 e ENERO ME uisu ere AR ER IES EEN I I 0 1 H 4 4 eode l I I I I I SOG 2e ee a NE MITA A A A Vina i UA i i I ES I kes ey I ud 0 2 i i i I 40 time s Fig 5 19 Results of the 2 DOF control with the simple PID controller azimuth position TRAS User s
2. 1 1 a ThermFlagSource Therm Status gt Pitch Therm Status ThermFlag ThermFlagGain Control PM CE Encoder Convert to rad Azi z PWM EIS 1024 ERR Pit EX l p qua as Saturation PWM PWMGain Azimult 0 PWM Azimuth RPM Convert to RPM Analog Input 4 Pitch RPM Fig 2 10 Interior of the RTWT device driver TRASUsersManual 00 MES 2 5 Simulation Models There are three simulation models available for the TRAS system The first one is a 1 DOF degree of freedom azimuth model This model simulate behaviour of the system in the horizontal plane only Click the DOF Azimuth Simulation Model button to open the model shown in Fig 2 11 Next click the subsystem block to see details of the model TRAS azimuth model m Scope DCP azimuth P lu Abs Fig 2 11 The Azimuth Simulation model and its interior A 1 DOF pitch is the second model It describes behaviour of the system in the vertical plane Click the DOF Pitch Simulation Model button and click the subsystem block to see the 1 DOF pitch model and its interior see Fig 2 12 TRASUsersManual 8 TRAS pitch model rpm vel U pe E pitch pos Scope Fig 2 12 The Pitch Simulation model and its interior The third one is the complete simulation model It describes movements in both planes with an interaction b
3. l oe 1 i eee x eure e I I Ns 4 MEM I s i alle s Ki I MN l m A NL EUR qo I DN OWN Wo mE I EM i o i u M i S i de AL i 775 Rupee Ai I eed i Vy a o La moo i E o 24 j X DO i o i I io E I I E ae I I I A e d I P a X I 1 I V X o I j I i x MEE x l Lo i I U UT uU i ES SSS Pp Reese L Ut SS Ka X ry o I I B Nk o 5 i e e o Ly e e o o x e Q o e e D D O Wd Aio0j9 10104 PWM control value Fig 7 i g 7 1 Static characteristics 69 TRAS User s Manual
4. Two Rotor Aero dynamical System MATLAB R2009a b R2010a b R2011a b R2012a PCI version User s Manual Ww www inteco com pl Table of contents 1 INTRODUCTION ee ccccssssssssssssssssssssscssssssssssssssssssssssssssssssssssssssssssssssssssssssssses 5 1 2 HARDWARE AND SOFTWARE REQUIREMENTS ccccccccessssseecesececeeusseseeceseceeeeuseneeces 7 1 3 BEATURES OETBR AS ettet cut est AR 7 1 4 SOFTWARE INSTALLATION cun 8 2 TRAS CONTROL WINDOW vesscscccseccscccscc sccosssccccoseccaccessscoccssecdacceseccecceseccacceseccscsoaes 9 2 1 STARTING AND TESTING PROCEDURES cccccccccceccccscecscscscsceesescsescscscsesesesessesesseeses 9 2 2 BASIC TESTA huie a a o cin leat Nie a ct 10 2 3 TRAS MANUAL SETUP cut a ds 13 2 4 RTWT DEVICE DRIVER onata ieia bi i e a a i a a aa es 16 2 5 SIMULATION MODELS etc a ect ree ona gt 18 3 MODEL AND PARAMETERS ccccccscscsssssssssscscscscscscscscscsccesssesscesesssesesesesessoes 21 3 2 NONLINEAR MODEL 5 2 eee A ee as 23 3 3 STATE EQUATON Se as E La os fe LI t ts 29 3 4 PHYSICAL PARAMETER Sois 29 3 5 STATIC GHARACTERISTIGCS iia ies 33 3 5 1 Main rotor thrust characteristics o cccccccccccsssscccccccccccssssssscecccesccccssusssescescceees 35 3 5 2 Tail rotor thrust characteristics eee eee eee ete ee nnn 36 4 RIMWTMODEL eese trot osese tec oe Se saob sa esche osoro ga go sae ces oc sa ec eb sa suca dato do a ga oa oa otad sc ad aaoa se 38 4 2 C
5. TRAS User s Manual 47 H Up t Un On DC motor with tail rotor DC Motor with main rotor O i F M u y v G v A R 04 Qn a Fig 5 9 The block diagram of 1 DOF system horizontal plane 5 2 4 Real time 1 DOF azimuth control experiment Fix TRAS in the vertical plane using the special fixing rectangle delivered with TRAS Set it in the zero position and click on the Reset Encoders block in Tras Control Window Click PID Azimuth controller and the model shown in Fig 5 10 opens Set all PID controller coefficients as K 4 9395 K 0 0022 and K 5 1898 Also set saturation of the integral part of the controller to 1 0 Build the model and click on the Simulation Connect to target and Start real time code options H num z TRAS 1 DOF PID Azimuth a Ly Control Fllter Control gt gt Angle amp Reference gt Angle amp Control nann PE gt ced Azimuth Angle Reference Angle PID Controller Gipfieraton Pitch Angle El o Zero Pitch Control Reset 1 Azimuth RPM RPM 0 Normal Reset Encoders Pitch RPM Fig 5 10 Real time model for the PID azimuth control TRAS User s Manual 48 The results of the experiment are shown in Fig 5 11 Notice a high frequency of the control similar to that in the case of the pitch control This phenomena appears due to the quantization effects of the signa
6. 0 05 4 Sg tii Pes een dore ds e e epe ERR Le eis ep e I EM I I I I lie E equilibrum point ee NER RT d Deae AN me E U I I 5e d I I 30105 hen a ENS Lo aa ene Loro I I I I a I 01 b 4 oe ee ee ee e ub abu MEM EP le sme A WAG s M est ttt Io ht oy yee tate Sali Eo 0 2 I L I I I 1 5 1 0 5 0 0 5 1 1 5 vertical position rad Fig 3 7 Returning moment of the gravity forces M The moment of the centrifugal forces is Ms Ma where M 4 2 m m l Q cosa sina 0 0133 Q cosa sina Nm M 7 mJ Q cosa sina 4 0 00037 Q cosa sina Nm M p3 m Q cosa sina 4 0 00052 Q cosa sina Nm M mJ Q cosa sina 0 00057 Q cosa sina Nm M s 7m l Q cosa sina 4 0 0003 Q cosa sina Nm M se m m 1 Q cosa sina 20 0137 Q cosa sina Nm giving finally Fig 3 8 6 M M 002876 O cosa sina Nm TRASUsersManual 32 0 015 caca AA PAC ae a 0 01 J m 0 005 mr E RF SSS SKY DA seen QUA DOS abe POM s WS Of ro el 0 005 azimuth velocity rad s pitch position radi Fig 3 8 Centrifugal returning torque 3 5 Static characteristics It is necessary to identify the following functions e Two nonlinear input characteristics determining dependence of the DC motor rotational speed versus
7. Js M nr L cosa gt Js Mo pe sina ms ms ms m 2 2 2 2 J r m l cosa J pg m Cay m L COSA or in the compact form J E cos a D sina F TRAS User s Manual 27 where D E F are constants m D ad xm m m E m h I Sem m ps m 2 2 F m r ms ms M g A B cosa C sina Using 1 4 we can write the equations describing the motion of the system as follows dA _l F On 9 k g A B cosa C sina dt J 59 A B C sin Za U k U k a Q abs w 6 7 da 9 6 di j 6 dK M _ L F co cosa Q k U k a Q abs o 7 dt J D sin a E cos a F d K Tro Q 8 dt J a and two equations describing the motion of rotors do A do 5 1 U Hi oy and 1 5 U Hio I is moment of inertia of the tail rotor I is moment of inertia of the main rotor The above model of the motor propeller dynamics is obtained by substituting the nonlinear system by a serial connection of a linear dynamic system and static nonlinearity TRAS User s Manual 28 3 3 State equations Finally the mathematical model of TRAS compare Fig 3 2 becomes the set of four nonlinear differential equations with two linear differential equations and four nonlinear functions E RO e p S c u v is the input X is the state and Y is the output vector u lt lt SOS lt
8. lt a A S S lt lt In order to apply the model for control of TRAS the parameters and nonlinear functions should be determined first They can be divided into three groups e physical parameters e nonlinear static characteristics e time constants of the linear part of the model They are described in details in the next section 3 4 Physical parameters To obtain the values of model coefficients it is necessary to perform some measurements First geometrical dimensions and moving masses of TRAS should be measured There are the following results of measurements for a given laboratory TRAS set up m 0 225 kg I 0216 m 0 252 kg m 1 0202 m m 0 0256 kg l 0145 m m 0 032 kg m 1 015 m m 0 03 kg r 0145 i m 001 Tig r 010 m 0 061 kg m 0 083 kg Using the above measurements the moment of inertia about the horizontal axis can be calculated as 8 J MJ 00307 kg m The terms of the sum are calculated from elementary physics laws TRASUsersManual 290 J m l 0 0103 kg m7 J m 1 3 0 00040 kg m7 J m l 0 00057 kg m J m 1 3 0 0007 kg m J m l 0 0105 kg m J mJ2 3 0 00049 kg m J 2m r 2 1 200043 kg m J m r 2 1 00035 kgm The calculated moment of inertia about the vertical axis 1s 8 J y Jas where the terms of the sum are J 7mj l cosa 3 0 00049 cos a J 7m L cosa
9. FigNum figure Visible on A NumberTitle off Name Menubar none tr ctras ret for i l length Ctrl Set control signal s set tr PWM ACtrl i PCtrl i Wait for steady state pause 10 ret 1 1 CEPA Read a number of tacho voltages to calculate the average tacho output AuxVolt 0 0 for j 1 10000 AuxVolt AuxVolt get tr end ret 1 2 3 AuxVolt 10000 Plot results plot ret 1 ret hold on plot ret 1 title RPM vs PWM xlabel PWM control value ylabel Rotor velocity end oe oe RPM 2 9 CX Dy ret 2 3 hold off grid Set return variable ChStat Control ret t l ChStat RPM ret 2 3 ChStat Force ret 4 Switch off the control signals set tr PWM 0 0 The diagram generated by the call tras_pwm2rpm ap r 0 5 0 5 11 Ep Et or LA Ap 1 Rotor velocity vs PWM characteristic RPM is shown below Two curves represent static characteristics of the azimuth and pitch propellers TRAS User s Manual 68 RPM vs PWM 6000 i LO I YI M T I u E I I I E 7 X I I I d I p ni T i ERA x n uc d eo i aaa eee MEM IX ibd b ee IT i co I DXX m NS I AM e I i v MEN I j l NE I I pV i E i X U pol O I x ETT v I U RO
10. Notice that rtwin tmf template makefile is used This file is default one for RTWT building process TRAS User s Manual 4 K Configuration Parameters MySystem Configuration Target selection _ __ _ 2 i System target file twin the Browse Data Import Export Optimization Language E y E Diagnostics Description Real Time Windows Target Select Sample Time Data Integrity Documentation Conversion TT Generate HTML report i Connectivity I bu Compatibility Launch report after code generation completes i Model Referencing Hardware Implementation Build process P Model Referencing TLC options SER eal Time Workshop Make command make rtw i Comments P Symbols Template makefile rewin tmf Custom Code Debug G eed er Generate code only Build B bd Fig 4 5 Configuration parameters Real Time Workshop tab If all the parameters are set properly you can start the real time executable building process For this purpose press the Build push button at the Real Time Workshop tag Fig 4 5 or simply CRTL B Successful compilation and linking processes generate the following message Model MyModel rtd successfully created Successful completion of Real Time Workshop build procedure for model MyModel Otherwise an error message is displayed in the MATLAB Command Window In this case check again yo
11. I I I I I I I I I PA I I I I S I I I I I j I I o 2 E I Ss I I I mE CUTE pos Pe ee acia a a AAA DI E SE CE I I I I I I I I i I I I EA I y I I I I I I I I a I I I I T I ot I I I l j I I l T 5 I I I LH 1 o ILL o B hocce A A a A i I i I i I I E in A o i i I aT I I I I I I I I i I He o I I L_ HT I I I I I I I I I I o I T s I I I I I I I I I I I I I gt 04 I I I A A A A bese doe bop be Oe o PA D A O MED E pen aed I I I I I I I Lag A a g i I l I I I I I I I I I IA I I I I I I I I I I I I I 3 I 5 E I I I i I I I I I I MC Si oa I I I I L I L 2 ps o g i 1 A L L N g 9 0o m 5 oO y Oo r w 0 x o9 5689 3 3 S 59 3 O o o o 3 1 3 o uv N wv On Pe as time s 58 Fig 5 26 Comparison the simple to the cross coupled PID control pitch TRAS User s Manual 6 PID controller parameters tuning There are several methods to design closed loop control systems In order to obtain optimal or sub optimal settings of parameters for the PID controllers the so called tuning methods may be used The following tuning methods can be distinguished e Tuning based on the time or frequency responses An experiment is performed with the process and with the model of the process Tuning rules are based on time or frequency responses of the system This method is not used for TRAS e More general method is the minimisation of a objective function The idea of this method for TRAS with a PID controller is
12. Manual 54 Pitch position and reference signal 0 3 NS ZEN NE Lat SUUM UU ney eames ry ar TERMINE MN 1 of N meen n I N I id IN I I V p I A I 0 1 vi sana we A OS 5 NUT RE Pme oru MINE o CX 3 foo j i8 o S caer Gb fe ennt eto Ga intet cien etie AY h fi ERE f I Y og fi I ae Mi i A L Pp 0 1 bene Eee dat eee c I E SERVE HE N E NE T JE sen som JU sm O ce E FU o NE MA REM IE MEET VAM dd 0 10 20 30 40 50 60 70 80 90 time s Fig 5 20 Results of the 2 DOF control with the simple PID controller pitch position 5 3 3 Cross coupled PID controller The cross coupled PID controller steers the system in the pitch and azimuth planes In this control system the influence of one rotor on the motion in the other plane can be compensated by the cross coupled structure of the controller The control system is shown in Fig 5 21 The cross coupled PID controller structure is shown in Fig 5 22 PD 2 DOF cross coupled U SYSTEM Olvd Fig 5 21 The block diagram of the 2 DOF control system with the cross coupled PID controller TRASUsersManual ig Fig 5 22 The block diagram of the cross coupled PID controller 5 3 4 Real time 2 DOF control with the cross coupled PID controller Click the 2 DOF controller button and the model shown in Fig 5 18 opens Set the coefficients of the crossed PID controllers
13. PWMPrescaler Therm ThermFlag Example set tr PWM 0 3 0 0 7 8 PWMPrescaler Purpose Determine the frequency of the PWM waves Synopsis Prescaler get tr PWMPrescaler set tr PWMPrescaler NewAzimuthPrescaler NewPitchPrescaler Description The prescaler values can vary from O to 63 The O value generates the maximal PWM frequency The value 63 generates the minimal frequency The first prescaler value is responsible for the azimuth PWM frequency and the second for the pitch PWM frequency The frequency of the generated PWM wave is given by the formula PWM frequency 40MHz 1023 Prescaler 1 See PWM 7 9 Stop Purpose Sets the control signal to zero Synopsis set tr Stop TRASUsersManual 630 Description This property can be called only by the set method It sets the zero control of the DC motors and is equivalent to the set tr PWM 0 0 call See PWM 7 10 ResetEncoder Purpose Reset the encoder counters Synopsis set tr ResetEncoder ResetFlags Description The property is used to reset the encoder registers The ResetFlags is a 1x2 vector Each element of this vector is responsible for one encoder register the first value controls the reset signal of the azimuth encoder and the second controls the reset of the pitch encoder If the reset flag is equal to the appropriate register is set to zero If the flag is equal to O the appropriate
14. and tail motors work properly e Double click the Open loop control button When Fig 2 6 opens one can to set the control inputs to the main and tail motor The vertical axis corresponds to the main motor and the horizontal axis corresponds to the tail motor When you locate the mouse pointer at 0 0 5 and click then the control equal to 0 5 is set for the main motor And if you click at 0 5 0 the control 0 5 is set for the tail motor Using the mouse click and slowly drug a rectangle The motors rotate with respect to the mouse pointer location the intersection of the green and red lines in Fig 2 6 The red ends of the blue lines show the rotational velocities of the propellers If the rectangle movement of the mouse is finished a picture similar to that given in Fig 2 6 should be visible TRAS User s Manual 12 Use mouse to open loop control E 10 x Color options Click and drag to set new control values Fig 2 6 Motors control and checking of tacho generators Troubleshooting Message or faulty action Board not detected Check mounting of the board Check if the driver is installed Angles measurements failed Check the Enc socket and wiring Propellers do not rotate Check the M socket Mains and ON switch Check the T socket and wiring 2 3 TRAS Manual Setup The TRAS Manual Setup program gives access to the basic parameters of the laboratory Two Rotor Aerodynamical System setup The most important data transferred
15. angular velocity azimuth velocity of TRAS beam rad s U is horizontal DC motor PWM control input 0 is rotational speed of tail rotor rad s nonlinear function H Ut rad s F is aerodynamic force from tail rotor nonlinear function Fr Fr wa N l is effective arm of aerodynamic force from tail rotor Jn I av m J is nonlinear function of moment of inertia with respect to vertical axis Jn Ji as kg m7 M is horizontal turning torque Nm K is horizontal angular momentum Nms f is oment of friction force in vertical axis Nm a is vertical position pitch position of TRAS beam rad Q is angular velocity pitch velocity of TRAS beam rad s U is vertical DC motor PWM voltage control input is rotational speed of main rotor nonlinear function w H U t rad s F is aerodynamic force from main rotor nonlinear function F Fi N l is arm of aerodynamic force from main rotor m J is moment of inertia with respect to horizontal axis kg m TRASUsersManual 220 M is vertical turning moment Nm K is vertical angular momentum Nms f is moment of friction force in horizontal axis Nm R is vertical returning moment R fy f R a Q Nm J is vertical angular momentum from tail rotor Nms J is horizontal angular momentum from main rotor Nms H is differential equation H U st H is differential equation 0 H U st G is aerodynam
16. as follows PID the azimuth controller K n 3 2465 K 0 0367 and K 2 152 Set the integral saturation to 1 0 PID the cross azimuth pitch controller K yy 7 0 9334 K 0 0 and K 0 7845 PID the cross pitch azimuth controller K gt 0 0363 K 0 0 and K 0 0223 pvh ivh Dvh PID the pitch controller K w 70 4978 K 0 4392 and K the controller to 1 43 0 4464 Set the saturation of the integral part of Dvv Also set the reference signals as in the previous experiment the reference azimuth signal as square wave with 0 2 rad amplitude and 1 40 Hz frequency and the reference signal for azimuth as sinusoidal wave with the amplitude and frequency as before Build the model and click on the Simulation Connect to target option and Start real time code option The results of the experiment are shown in Fig 5 23 and Fig 5 24 TRASUsersManual 56 Azimuth position and reference signal a ql e m eti ee 0 25 0 2 0 15 90 80 time s Fig 5 23 Results of the 2 DOF control with the cross coupled PID controller azimuth position Pitch position and reference signal f a f M time s Fig 5 24 Results of the 2 DOF control with the cross coupled PID controller pitch position 57 TRAS User s Manual cross coupled PID red 5 25 and F
17. automatic power down flags of the power amplifiers Read time information TRASUsersManual 66 R read only property S allowed only set operation R S property may be read and set 7 18 CTRAS Example To familiarise a reader with the CTRAS class this section presents an M file example that uses the properties of the CTRAS class to measure the static characteristics of the DC motor The static characteristics is a diagram showing the relation between DC motor control signal and the velocity of the propellers The M file changes the control signal and waits until the system reaches a steady state The velocity of the propeller is proportional to the voltage generated by the tachogenerator The M file is written in the M function form The name of the M function is TRAS_PWM2RPM The body of this function is given below The comments within the function describe the main measurement stages The function requires five parameters SelectRotor Selects the propeller used during the measurements Available values are A for azimuth propeller P for pitch propeller and AP for both propellers CtrlDirection a string that selects how to change the control value The A string causes the control is changed in ascending manner from minimal to maximal control value the D string causes the control is changed in descending order from maximal to minimal value and the R string causes reverse double changes from minimal to max
18. calculate the angle the encoder counters are multiplied by the values defined as the AngleScaleCoeff property The angles are expressed in radians See Encoder AngleScaleCoeff 7 6 AngleScaleCoeff Purpose Read the coefficients applied to convert the encoder counter values into physical units Synopsis scale_coeff get tr AngleScaleCoeff Description The property returns two digits They are equal to the coefficients applied to convert encoder impulses into radians The incremental encoders generate 4096 pulses per rotation so the coefficients are equal to 2 pi 4096 See Encoder Angle TRASUsersManual 62 7 7 PWM Purpose Set the direction and duty cycle of the PWM control waves Synopsis PWM get tr PWM set tr PWM NewAzimuthPWM NewPitchPWM Description The property determines the duty cycle and direction of the PWM control waves for the azimuth and pitch DC drives The PWM waves and the direction signals are used to control the DC drives so in fact this property is responsible for the DC motor control signals The NewAzimuthPWM and NewPitchPWM variables are scalars in the range from 1 to 1 The value of 1 0 0 and 1 mean respectively the maximum control in a given direction zero control and the maximum control in the opposite direction to that defined by 1 The PWM wave is not generated if the corresponding thermal flag is set and the power amplifier is overheated See
19. cca cho sal Ses ces aie dau Otros eque ERE 63 7 8 PWMPRESCATER osa il ins 63 7 9 STOP SA A A lid 63 TAO AAA ii eget abou testis 64 d bk VOLTAGE da Soe Os RETR nt 64 P MM A TEUER 64 713 ARPMSCALECOEFE eet eere Sos eee ere er e EAE eee ds Sau pedes 65 JAR RER E 65 TAS S EHERMBLDAGs SS A na o lios 65 TAO EIME 3 itis osedede istos tepida tdt apa lan tein EKG 66 WX QUIEN REFERENCE TABLE lt a tasas 66 TAS CTRA S EXAMPER iii tata 67 TRAS User s Manual lt 3 COPYRIGHT NOTICE Inteco Sp z 0 0 All rights reserved No part of this publication may be reproduced stored in a retrieval system or transmitted in any form or by any means electronic mechanical photocopying recording or otherwise without the prior permission of Inteco Sp z 0 0 ACKNOWLEDGEMENTS Inteco acknowledges all trademarks MICROSOFT WINDOWS are registered trademarks of Microsoft Corporation MATLAB Simulink RTWT and RTW are registered trademarks of Mathworks Inc TRAS User s Manual 4 1 Introduction Two Rotor Aero dynamical System TRAS is a laboratory set up designed for control experiments In certain aspects its behaviour resembles that of a helicopter From the control point of view it exemplifies a high order nonlinear MIMO system with significant cross couplings The system is controlled from a PC Therefore it is delivered with hardware and software which can be easily mounted and installed in a laboratory You obtain the mechanical
20. for the azimuth DC drive The second one corresponds to the thermal status of the pitch power amplifier See ThermFlag 7 15 ThermFlag Purpose Control an automatic power down of the power amplifiers Synopsis ThermFlag get tr ThermFlag set tr ThermFlag NewAzimuthThermFlag NewPitchThermFlag Description If the NewAzimuthThermFlag or and NewPitchThermFlag are equal to 1 the azimuth or and DC motors are not excited by the PWM waves when the corresponding power interfaces is overheated TRASUsersManual 650 See Therm 7 16 Time Purpose Return time information Synopsis T get tr Time Description The CTRAS object contains the time counter When a CTRAS object is created the time counter is set to zero Each reference to the Time property updates its value The value is equal to the number of milliseconds which elapsed since the object was created 7 17 Quick reference table BaseAddress Read the base address of the RT DAC PCI board Bitst Versi Read the version of the logic design for the RT itstreamVersion DAC PCI board Encoder R Read the incremental encoder registers Angle R Read the angles of the encoders Read the coefficients applied to convert encoder PWMPrescaler R S R S S S M mw ke Read the coefficients applied to convert coa EN tachogenerator voltages into RPMs Therm Read the thermal flags of the power amplifiers Thermblae Read set the
21. ob o I i i i eo I I I I I sva I I I I m I I I IZ I I I adi o I I I I I SS I I I 1 I I O I I I I I SSS I I I LOG I I I I I I I RRJ I I I LLL ELS I o a I I I I O a o Sb L n Sf ob 3 I L 1 i 4 I I I I I R N I I I I I I i 4 SE x SE SE os oe U P u Gm I I I I I I I I I I I I I I I I I 5 I I I I I I I FR I I I I I I I I I I I I E ere LE ee eee STT e oo ws cui is ruso pedes esl jp p 4 1 igpERRRO I I I I I ri I I I I I I I Ee I I I I I A I I I I I I I I I cat I i I I U I I I La T e I l l I l I a I I I I T sec WR A TA TT 2 je o E o 9 v 0 N T e T m o Lo e N o eo o o o o o o o o o o o o o o time s 46 Fig 5 6 The non filtered control TRAS User s Manual Pitch position and reference signal 0 3 T eee ee f QA eee fett E coi A time s Fig 5 7 Pitch position and the reference signal 5 2 3 Horizontal 1 DOF control In the next experiment we apply stabilising PID controller in the horizontal plane We block the system in one axis so that it cannot move in the vertical plane using the included fixing rectangle A corresponding block diagram of the control system is shown in Fig 5 8 and in a more detailed form in Fig 5 9 Ond desired azimuth Fig 5 8 1 DOF control closed loop system azimuth stabilisation Notice that only the horizontal part of the control system is considered
22. property_name new property value The display method is applied to display the property values when the object name is entered in the MATLAB command window This section describes all the properties of the CTRAS class The description consists of the following fields Provides short description of the property Shows the format of the method calls Description Describes what the property does and the restrictions subjected to the property Describes arguments of the set method Refers to other related properties Provides examples how the property can be used TRASUsersManual 60 7 2 BaseAddress Purpose Read the base address of the RT DAC PCI board Synopsis BaseAddress get tr BaseAddress Description The base address of RT DAC PCI board is determined by the computer Each CTRAS object has to know the base address of the board When a CTRAS object is created the base address is detected automatically The detection procedure detects the base address of the first RT DAC PCI board plugged into the PCI slots Example Create the CTRAS object tr CTRAS Display their properties by typing the command tr Type CTRAS Object BaseAddress 54272 D400 Hex Bitstream ver x40F Encoder 2 65517 bit Reset Encoder Input voltage 0 01 0 02 TIV PWM 0 PWM Prescaler i j M PWM Thermal Flag J Angle 03068 0 029146 rad zu 19 9 RPM 5347 See RPM 0 1 PWM The
23. sample time constraint Unconstrained y Connectivity Fixed step size fundamental sample time fo 01 Compatibility Tasking mode for periodic sample times SingleT asking y Model Referencing Hardware Implementation Higher priority value indicates higher task priority Model Referencing Automatically handle data transfers between tasks Real Time Workshop i Comments Fig 4 4 Solver tab The Solver tab allows you to set the simulation parameters Several parameters and options are available in the window The Fixed step size editable text box is set to 0 01 this is the sampling period in seconds The Start time has to be set to O Fig 4 4 The solver method has to be selected In our example the fifth order integration method ode5 is chosen The Stop time field defines the length of the experiment This value may be set to a large number Each experiment can be terminated by pressing the Stop real time code button The Fixed step solver is obligatory for real time applications If you use an arbitrary block from the discrete Simulink library or a block from the drivers library remember that different sampling periods must have a common divider Third party compiler is not requested The built in Open Watcom compiler is used to create real time executable code for RTWT The RTW tag is shown in Fig 4 5 The system target file name is rtwin tlc It manages the code generation process
24. the main and tail rotors are shown in Fig 3 9 8000 6000 4000 2000 2 L rotor velocity rpm o 2000 F t 17 SUDO odo a aa ee eee eee du PWM control value Fig 3 9 Main and tail rotor static characteristics TRAS User s Manual 34 If the characteristic is measured in Reverse mode the control has been changed from 1 to 1 and reverse there are two slightly different plots e Two nonlinear characteristics determining dependence of the propeller thrust on DC motor rotational speed thrust characteristics F F F F The thrust static characteristics of the propellers should be measured in the case when the propellers were changed by a user In this case a proper electronic balance not delivered with the system is necessary to measure the force created by rotational movements of the propellers The characteristics included in TRAS Toolbox and shown in this section has been obtained by the manufacturer of TRAS 3 5 1 Main rotor thrust characteristics a string electronic balance balance weight L Fig 3 10 Measuring of the main rotor thrust characteristics To perform measurements correctly block the beam so that it could not rotate around the vertical axis place the electronic balance under the beam in such a way that it is pulled by the propeller straight up To balance the beam in the horizontal position attach a weight to t
25. the input voltage RPM characteristics H U and H U To measure the characteristics double click the Static characteristics button in TRAS Control Window The window given in Fig 3 opens In this window one defines the minimal and maximal control values and a number of measured points The control order can be set as Ascending Descending or Reverse Also one can choose the pitch or azimuth static characteristic Note that the control signal is normalised and changes in the range 1 1 what corresponds to the input voltage range 24V 24V TRASUsersManual 33 Measure Velocity vs PWM zi x Minimal control value 1 0 Maximal control value 1 0 Control order No of measured points 11 Axis Azimuth ji Help ELOSE Fig 3 How to collect the points of the static characteristic Block the beam before the experiment is started Choose Azimuth axis tail rotor and click the Run button The constant value of the control activates the DC motor so long as a steady state of the shaft angular velocity is achieved Then the velocity is measured and the control value is changed to the next constant value and DC motor is activated again These steps are repeated to the end of the control range Simultaneously the measurements are displayed in the screen This action should be repeated for pitch axis main rotor to obtained the both characteristics Examples of the measured static characteristic for
26. to rearrange the laboratory set up as shown in Fig 3 13 and the electronic balance should be used The measured by the manufacturer of TRAS thrust static characteristics of the tail motor are given in Fig 3 14 TRASUsersManual 00 6 thrust of tail rotor Fh N tail rotor velocity rpm De T T T T T T T a 6000 4000 2000 D 2000 4000 6000 A A A 42 1 i i i i i i 58000 6000 4000 2000 0 2000 4000 6000 8000 tail rotor velocity rpm control Uh axo i i ao e dodo bod 1 0 8 06 04 02 0 0 2 0 4 06 08 1 Fig 3 14 Thrust characteristics measured for the tail rotor For further applications the characteristics can be replaced by their polynomial approximations For this purposes one can use the MATLAB polyfit m function The obtained polynomials are as follows F 2 6 10 w3 41 10 o 32 100 73 10 w 21 10 0 0091 6 22 100U 17 10 U 45 10 U 3 10 U 98 10 U 92 thrust of tail rotor N tail rotor velocity rpm 1 T T T T T 8000 data1 _ _ 5th degree I I data 1 5th degree 6000 Ug eee ts es ee ee eed H 4000 2000 D 2000 4000 r 6000 He i i i i i i i awi d i i io i i i i 5000 6000 4000 2000 0 2000 4000 6000 8000 1 08 0 6 04 02 0 02 04 06 08 1 tail rotor velocity rpm control Fig 3 15 Polynomial approximation of tail rotor characteristics TRASUse
27. torques are produced by the rotors and that the moment of inertia depends on the pitch angle of the beam the horizontal motion of the beam around the vertical axis can be described in principle as rotative motion of a solid E 4 where M is the sum of moments of forces acting in the horizontal plane J is the sum of moments of inertia relative to the vertical axis Then M YM Ry i l i l To determine the moments of forces applied to the beam and making it rotate around the vertical axis consider the situation shown in Fig 3 5 TRAS User s Manual 26 thrust of tail rotor F O vertical axis of rotation hl Fig 3 5 Moments of forces in horizontal plane as seen from above M L F cosa is angular velocity of tail rotor F o denotes the dependence of the propulsive force on the angular velocity of the tail rotor should be determine experimentally see section 4 5 M Q f M is the moment of friction depending on the angular velocity of the beam around the vertical axis f is constant M is the cross moment from U M U k k is constant M is the damping torque from rotating propeller M a Q abs o a is constant According to Fig 3 5 we can determine components of the moment of inertia relative to vertical axis it depends on pitch position of the beam Ju zu L cosa Ji sl cosa Jig 1 sin a J m I cos a
28. 3 0 0004 cos a J m 1 sina 3 0 0007 sin a J m l cosa 0 0103 cos a J 7 m l cosa y 0 0105 cos a J 7m L sina 0 00057 sina J m r2 2 12c08a 0 0003 0 0028 cos a J m r2 2 I cos a 0 00087 0 0034 cos a giving finally Fig 3 6 kg m kg m kg m 9 J Ju Ecos a Dsin a F 00279 cos a 0 0013 sin a 0 0021 TRAS User s Manual 30 moment of inertia Jh kg m2 0 03 0 025 0 015 I I I I I 4 I I j 0 02 ae I 7 I I I I 1 I I I y I 010 eee eee Cs Ne SEE SEE SR IEEE eee eee Sees eee vertical position rad Fig 3 6 Moment of inertia J The returning torque from gravity forces is expressed by 8 M NM 2 and its components are given by M 9 81m 1 cosa 2 0 0297 cosa N m mm 981m 1 cosa 0 4994 cosa Nm M ma M 981m l cosa 0 1645 cosa N m M 9 81 ml cosa 2 0 0339 cosa N m M 981m l cosa 0 4768 cosa Nm M 981m l cosa 01293 cosa Nm M 981my sina 2 00711 sina Nm M 981ml sina 00377 sina Nm giving finally Fig 3 7 8 M MM 00536 cosa 0 1088 sina N m TRASUsersManual 31 returning moment of gravity forces Nm 0 15 I l I I I Othe da Se Io e eee Al E eee nee A Sa I I I I I mi I I I I Mo
29. 4 controller parameters Saturation blocks introduce four additional 4 parameters Lvvsar Lvnsar Inhsar and Thysat Which are the limits of absolute values of the integrals of errors and two Ujmax and U max parameters which are the limits of absolute value of controls These 18 12 4 2 parameters have their default values 5 2 1 DOF controllers The task of the one degree of freedom 1 DOF controllers is to move TRAS to an arbitrary position in the selected plane and to stabilise it there 5 2 1 Vertical 1 DOF control At the beginning we restrict our control objective to stabilising the system in the vertical plane only We reduce the original system to the 1 DOF system by mechanically fixing using the included clamp its freedom to move in the horizontal plane A corresponding block diagram of the PID control system is shown in Fig 5 1 Qa U Y 1 DOF 9 rm SYSTEM Oa desired pitch Fig 5 1 1 DOF pitch control system TRAS User s Manual 43 The block diagram below shows the system in a more detailed form Fig 5 2 Notice that only the vertical part of the control system is considered Fy Mi Ky On Hy Unst F 01 l s vo Un Qn a Qh DC motor with tail rotor Ri Q Qn PN DC Motor with main rotor H U t Oly Fig 5 2 The block diagram 1 DOF system vertical plane 5 2 2 Real time 1 DOF pitch control experiment Fix TRAS in the horizontal plane using the spec
30. I I I I I I PA E eS PR RER I I L I I I aT I l I he eS ee SOJA PR d HARIAS ST I I I I I I I I I I I I I I I I I I T I I BSS Ee eee Pee Spe pe Pompe I I I I I I I I I I i T T U I I I Y 0o N oO e e e e e 30 time s Fig 5 13 The non filtered control Azimuth position and reference signal 0 5 30 25 20 10 time s Fig 5 14 The azimuth position and reference signal 50 TRAS User s Manual 5 3 2 DOF PID controller The structure of the cross coupled multivariable PID controller is shown in Fig 5 15 a b saturation block U max saturation block J sa Fig 5 15 Structure of the cross coupled PID controller a general b single PID block The controller is described by the equations given bellow Qu TQ O pg 05 where are errors of the vertical pitch and horizontal angle azimuth are the reference values of the vertical and horizontal angles are the vertical and horizontal angles The integrators are described by the following equations I f koled for er s 5 s T ot 0 if I 2 UN then I SE I 3 if E lt E then I x ca MUN Da t m kaled for n Tsai Iy d 0 if I 2 Ts then D re if I lt a then I c od I t lodi for Tissot lt Iry S Tisai 0 TRAS User s Manual 51 if I gt Lasar then I if I lt Li
31. REATING AMODEE teanientiedeieunindmedeiedenmnunigdudcesbrieds 38 4 3 CODE GENERATION AND THE BUILD PROCESS eee eene emen eres es esee 40 5 CONTROLLERS AND REAL TIME EXPERIMENTS eese eese nnnunu 43 5 2 1 DOECONTROLEERS iie cet treten te b eet de Het dus 43 5 2 1 Vertical 1 DOF control eese Ka ev dade va kakaa de ae da aaa irade aka dlana 43 3 2 2 Real time 1 DOF pitch control experiment eese eene 44 5 2 3 Horizontal 1 DOF control eese eene eene hhehet esee nennen nien eee 47 5 2 4 Real time 1 DOF azimuth control experiment eese 46 5 3 2 DOF PID CONTROLLER ii ertet ed deer ever Cete ede ede vies 51 ES Simple PID CONG OW CT rads deve di Aa 52 5 3 2 Real time 2 DOF control with the simple PID controller 53 5 3 3 Cross coupled PID ontroller ue A ena IH 5 3 4 Real time 2 DOF control with the cross coupled PID controller 56 2 9 5 Comparison the simple and cross coupled PID controller 58 6 PID CONTROLLER PARAMETERS TUNING cccccscscscscssssssscssssscscssscecsess 59 7 DESCRIPTION OF THE CTRAS CLASS PROPERTIES eere eene nenne 60 7 2 BXSEADDRESS 24 52 eoe erected eet dt ve a ect lec duse Melek ede ob Tee 61 7 3 BIISTREAMVERSION 2 25 idas 61 7 4 ENCODER E e e de e A U 62 7 5 ANGLE ale iaa 62 7 6 INNGLES CALEC OBER cido ida etes iive i it 62 TRAS User s Manual 27 Dd PNW IN Mech
32. This section explains how to perform the tests One can check if mechanical assembling and wiring has been done correctly The tests have to be performed obligatorily after assembling the system They are also necessary if an incorrect operation of the system happens Due to the tests sources of the system fails can be tracked The tests have been designed to validate the existence and sequence of measurements and controls They do not relate to accuracy of the signals At the beginning one has to be sure that all signals are transmitted and transferred in a proper way The following steps are applied e Double click the Basic Tests button The Basic Test window appears Fig 2 2 TRAS_BasicTest lel ES File Edit View Simulation Format Tools Help Fig 2 2 The Basic Tests window The experiment may be stopped in any time Double click on the Stop block in the TRAS Control Window or somewhere else If you wish to stop the visualisation process click once on the Stop bar in the Simulation menu As well the emergency switch can be used anyway The first step in the TRAS testing is to check if the RT DAC PCI measuring and control board is installed properly TRAS User s Manual 10 e Double click the Detect RT DAC PCI board button One of the messages shown in Fig 2 3 opens If the board has been correctly installed the base address and the number of logic version of the board are displayed BasicTestFunction Step 1 2101 x Bas
33. ar velocity of the main rotor F w denotes the dependence of the propulsive force on the angular velocity of the rotor It should be measured experimentally see section 4 5 m m m M Q gt m a la 2 m m Lm etu sina cosa or in the compact form M 2 A B C sina cosa M is the moment of centrifugal forces corresponding to the motion of the beam around the vertical axis da 2 di 2 Q is the angular velocity of the beam around the vertical axis is the azimuth angle of the beam and Q TRASUsersManual 250 M is the moment of friction depending on the angular velocity of the beam around the horizontal axis where Q aa 3 dt Q is the angular velocity around the horizontal axis f 1s a constant M is the cross moment from U M U k k is constant M is the damping torque from rotating propeller M a Q_abs w a is constant According to Fig 3 4 we can determine components of the moment of inertia relative to the horizontal axis Notice that this moment is independent of the position of the beam Ie Ju M mr li gt J m m gt J Mep l l I b 2 Ju m 3 J s M l gt Js m E m Ja a 5 TU p gt Jg Mo i Mo bp gt m st s r 18 the radius of the main shield r is the radius of the tail shield Similarly we can describe the motion of the beam around the vertical axis Having in mind that the driving
34. contains a single entry for each RT DAC PCI board installed in the computer A new selection at the list automatically changes values of the remaining parameters Bus number Displays the number of the PCI bus where the current RT DAC PCI board is plugged in If more then one board is used this parameter may be useful to distinguish the boards Slot number The number of the PCI slot in which the current RT DAC PCI board is plugged in If more then one board is used this parameter may be useful to distinguish the boards Base address The base address of the current RT DAC PCI board The RT DAC PCI board occupies 256 bytes of the I O address space of the microprocessor The base address is equal to the beginning of the occupied I O range The I O space is assigned to the board by the computer operating system and may be different for various computers TRAS User s Manual 14 The base address is given in the decimal and hexadecimal forms Logic version The number of the configuration logic of the on board FPGA chip A logic version corresponds to the configuration of the RT DAC PCI boards defined by this logic Application The name of the application the board is dedicated for The name contains four characters I O driver status The status of the driver that allows the access to the I O address space of the microprocessor The status has to be OK string In the other case the driver HAS TO BE INSTALLED Encoders frame The state of th
35. e encoder channels is given in the Encoder frame The encoders are applied to measure the azimuth and pitch angles Azimuth Pitch The values of the encoder counters the angles expressed in radians and the encoder reset flags are listed in the Azimuth and Pitch rows Value The values of the encoder counters are given in the respective columns The values are 16 bit integer numbers When an encoder remains in the reset state the corresponding value is equal to zero Angle rad The angular positions of the encoders expressed in radians are given in the respective columns If the encoder remains in the reset state the corresponding angle is equal to zero Reset When the checkbox is selected the corresponding encoder remains in the reset state The checkbox has to be unchecked to allow the encoder to count the position Control frame The Control frame allows to change the control signals DC drives are controlled by PWM signals Azimuth and Pitch edit fields and sliders The control edit boxes and the sliders are applied to set a new control values of the corresponding DC drives The control value may vary from 1 0 to 1 0 STOP The pushbutton is applied to switch off the control signals If it is pressed then both the azimuth and pitch control values are set to zero Azimuth and Pitch PWM prescaler TRASUsersManual 00 MS The divider of the PWM reference signal is given The frequency of the corresponding PWM control is equal t
36. e the moments of forces applied to the beam and making it rotate around the horizontal axis consider the situation shown in Fig 3 3 TRASUsersManual 230 horizontal axis of rotation Mmg Fig 3 3 Gravity forces in TRAS corresponding to the return torque which determines the equilibrium position of the system M ales m n 6 tm Ma cosa E l Mala sin a 2 2 i 2 M gl 4 B cosa C sina where tr A om m L m B 35 M Ma la Ce a 2 where M is the return torque corresponding to the forces of gravity m is the mass of the main DC motor with main rotor m is the mass of the main part of the beam m is the mass of the tail motor with tail rotor m is the mass of the tail part of the beam m is the mass of the counter weight m is the mass of the counter weight beam mM is the mass of the main shield m is the mass of the tail shield L is the length of the main part of the beam L is the length of the tail part of the beam t TRAS User s Manual 24 l is the length of the counter weight beam lis the distance between the counter weight and the joint g is the gravitational acceleration vertical axis of rotation horizontal axis of rotation thrust of main i di rotor Fig 3 4 Propulsive force moment and friction moment in TRAS M Ln F lon M is the moment of the propulsive force produced by the main rotor is angul
37. e the original driver They can be introduced only gt inside its copy Make a copy of the installation CD The device driver has two inputs control u t c 1 1 and signal Reset If the Reset signal changes to one the encoders are reset and do not work If the Reset signal is equal to zero encoders work in the standard way It means when switching occurs encoders reset and start measure when the switch returns to the zero normal position It is important that the Reset switch works only when the real time code is executed Block Parameters TRAS x The mask of this block shown Subsystem mask Fig 2 9 contains base address of the RT DAC PCI board m Parameters automatically detected with the Base Address help RTDACPCIBaseAddress RTDACAPCIBaseAddress function and the sampling period Sampling Period which default value is set to 0 002 0 004 sec If one wants to change the Cancel Help Apply default sampling time he must do Fig 2 9 Mask of the device driver it in this mask also The details of the device driver are depicted in Fig 2 10 The driver uses functions which communicates directly with a logic stored at the RT DAC PCI board Parameters Measurements gt ResetEncoder ResetEncoderGain Reset Encoder 0 0 Hd PWNMPrescalerSource Bitstream Version PWMPrescaler PWMPrescalerGain Azimuth Therm Statu
38. etween the pitch and azimuth axes Click the 2 DOF Simulation Model button and the subsystem block to see the model and its interior see Fig 2 13 TRAS 2_dof model azimuth pos pitch rpm AZIMUTH pitch pos PITCH TRASUsersManual S M9 DCP azimuth pos_a pos_p DCP_pith Fig 2 13 The 2 DOF simulation model and its interior TRASUsersManual gg 3 Model and parameters Modern methods of design and adaptation of real time controllers require high quality mathematical models of the system For high order nonlinear cross coupled systems classical modelling methods based on Lagrange equations are often very complicated That is why a simpler approach is often used which is based on block diagram representation of the system which is very suitable for the SIMULINK environment The relations between the block diagram and mathematical model of the TRAS are explained in sections 4 2 4 5 Fig 3 1 shows an aero dynamical system considered in this manual At both ends of a beam joined to its base with an articulation there are two propellers driven by DC motors The articulated joint allows the beam to rotate in such a way that its ends move on spherical surfaces There is a counter weight fixed to the beam and it determines a stable equilibrium position The system is balanced in such a way that when the motors are switched off the main rotor end of beam is lowered The controls of the sy
39. from the RT DAC PCI board and the measurements of the TRAS may be shown Moreover the control signals may be set The application contains four frames see Fig 2 7 e RT DAC PCI board e Encoders e Control and e Tacho TRASUsersManual 00 M vs TRAS Manual Setup 2 0 xj r RT DAC4 PCI board No of detected boards 1 p Azimuth q Pitch Control 305 305 Board Board1 gt H Bus number 0 Base address Azimuth 34 r Pitch Logic version 40 PWM prescaler 2 Application HEL Micra ox Thermal flag status M TO Met r Encoders r Tacho Value Angle rad Reset Voltage V Velocity RPM Azimuth 9 oo T Azimuth oo Lea Pitch Ps Se Pitch 000 m o Help Close Fig 2 7 View of the TRAS Manual Setup window All the data accessible from the TRAS Manual Setup program are updated 10 times per second RT DAC PCI board frame The RT DAC PCI board frame presents the main parameters of the PCI board No of detected boards Reads the number of detected RT DAC PCI boards If the number is equal to zero it means that the software has not detected none of the RT DAC PCI board When more then one board is detected the Board list must be used to select the board that communicates with the program 2 3 1 1 Board Contains the list applied to the selected board currently used by the program The list
40. gnal amp Triggering Signal selection Block Path X Angle amp Control MySystem Angle amp Control M Select all XT Display MySystem TRAS Display Glearal X RPM MySystem RPM on C off Trigger signal zi Go to block Trigger Source manual y Mode normal y Trigger signal Part E Element any MySystem TRAS Displa a Duration 12000 Delay 0 2d j El M Arm when connect to target Direction prising Level 0 4 Hold aff 0 Fig 4 3 The External Signal amp Triggering window 4 3 Code generation and the build process Once a model of the system has been created the code for the real time mode can be generated compiled linked and downloaded into the target processor TRAS User s Manual 40 The code is generated by the use of Target Language Compiler TLC see description of the Simulink Target Language The makefile is used to build and download object files to the target hardware automatically First you have to specify the simulation parameters of your Simulink model in the Simulation parameters dialog box Fig 4 4 The Real Time Workshop and Solver tabs contain critical parameters i Configuration Parameters MySystem Configuration x Simulation time Start time fo o Stop time 30 Data Import E port Optimization i Solver options Diagnostics Sample Time Type Fixed step y Solver ode5 Dormand Prince y Data Integrity Conversion Periodic
41. he beam as in Fig 3 10 thrust of main rotor Fv N E i 4000 3000 2000 1000 0 8 4000 3000 2000 1000 0 1000 2000 3000 4000 main rotor velocity rpm control Uv Fig 3 11 Measured static thrust characteristics of the main rotor TRASUsersManual 35 For further applications the measured characteristics should be replaced by their polynomial approximations For this purposes one can use the MATLAB polyfit m function An example is given in Fig 3 6 The obtained polynomials have the form F 1 8 10 7 8 10 w c 4 1 10 0 2 7 10 c 3 5 10 c 0 014 5 2 10 U7 1 1 10 US 1 1 10 U 1 3 10 Uf 9 2 10 U 31U 6 1 10 U 4 5 thrust of main rotor N main rotor velocity rpm 4000 i data 1 Ly iia pt Ea E E 3000 0 8 2000 0 6 04 1000 0 2 o 1000 02 2000 DA 3000 06 ogi i i i i i i awli i i o 4 do o ho E 4001 3000 2000 1000 1000 2000 3000 4000 08 06 04 02 02 04 06 08 main rotor velocity rpm control 25 Fig 3 12 Polynomial approximation of the main rotor characteristics 3 5 2 Tail rotor thrust characteristics Fig 3 13 shows laboratory set up for measuring thrust of the tail rotor rope balance D di weight electronic m ad balance Fig 3 13 Laboratory set up for the tail rotor thrust characteristics To measure the static thrust characteristics one should
42. he pivot and two corresponding angular velocities Two additional state variables are the angular velocities of the rotors measured by tacho generators coupled with the driving DC motors TRAS User s Manual 5 In a casual helicopter the aerodynamic force is controlled by changing the angle of attack of the rotors The laboratory set up from Fig 1 1 is so constructed that the angle of attack is fixed The aerodynamic force is controlled by varying the speed of rotors Therefore the control inputs are the supply voltages of the DC motors A change in the voltage value results in a change of the rotation speed of the propeller which results in a change of the corresponding position of the beam Significant cross couplings are observed between the actions of the rotors each rotor influences both position angles Designing of stabilising controllers for such a system is based on decoupling For a decoupled system an independent control input can be applied for each coordinate of the system An IBM PC compatible computer can be used for real time control of TRAS The computer must be supplied with an interface board RT DAC PCI Fig 1 2 shows details of the hardware configuration of the control system for TRAS power interface physical model Fig 1 2 Hardware configuration of TRAS The control software for TRAS is included in the TRAS toolbox This toolbox uses the RTWT and RTW toolboxes from MATLAB TRAS Toolbox is a collection of M func
43. ial plastic clamps delivered with TRAS Set it in the neutral vertical position and wait until the all oscillations are damped In Tras Control Window double click the Reset Encoders block Click the PID Pitch controller button and the model shown in Fig 5 3 opens Set all PID controller coefficients as K 0 6784 K 20 4415 and K 1 31196 Also set saturation of the integral part of the controller to 1 43 Build the model and click on the Simulation Connect to target option and Start real time code option TRAS User s Manual 44 TRAS 1 DOF PID Pitch num z gt den z Filtered Control Fliter Control gt Ld Angle amp Reference gt Angle amp Control Azimuth Ange E 0 gt Zero Azimuth Control T Pitch Angle 0000 A oo PC P PID Control gt gt Reference Angle PID Controller Azimuth mw Generator 0 3 i Pitch Offset y nd gt Reset Y Pitch RPM MS TRAS RPM oo Normal Reset Fig 5 3 Real time model for the pitch control The results of the experiment are shown in Fig 5 4 Notice that control changes with high frequency This phenomena appears due to the quantization effects of the signal caused by the differential part of the controller For this reason the control signal is filtered to obtaining an average value
44. icTestFunction Step 1 n xl Detected RT DACA PCI board Base address 54272 D400 Hex Can not detect any RT DAC4 PCI board t Version 40F Hex Lx ER Fig 2 3 Result of the step 1 If the board is not detected then check whether the board has been mounted correctly into a slot of the computer The boards are checked very precisely before sending to a customer In principle a wrong assembling is the only reason of failure in detecting the board The next step consists in resetting the encoders It means that the initial position of the beam is stored in the interface board e Double click the Reset Angles button When Fig 2 4 opens move the TRAS system to the origin position and then click the Yes option The encoders reset and zero positions of the beam are going to be remembered BasicTestFunction Step 2 x ED Move the TRAS system to the origin position y Do you want to set the origin angles of the load Yes No Cancel Fig 2 4 The Reset Angles window e Double click the Check Angles button When the window opens click Yes then move by hand the beam of TRAS in all directions and observe measurements on the screen see Fig 2 5 TRAS User s Manual MEE TI a File Edit View Insert Tools Window Help osuel rRar 922 Close this figure to terminate the test Pitch Angle Azimuth Angle Fig 2 5 Measurements of the beam motion In the next step one checks if the main
45. ical damping torque from main rotor G o Q G is aerodynamical damping torque from tail rotor G w Q Controlling the system consists in stabilising the TRAS beam in an arbitrary within practical limits desired position pith and azimuth or making it to track a desired trajectory Both goals may be achieved by means of appropriately chosen controllers The user can select between two types of PID controllers and a state feedback controller see section 6 3 2 Nonlinear model The mathematical model is developed with some simplifying assumptions First it is assumed that the dynamics of the propeller subsystem can be described by the first order differential equations Further it is assumed that friction in the system is of the viscous type It is assumed also that the propeller air subsystem could be described in accord with postulates of the flow theory The above assumptions allow us to define the problem clearly First consider the rotation of the beam in the vertical plane i e around the horizontal axis Having in mind that the driving torques are produced by the propellers the rotation can be described in principle as the motion of a pendulum From the second dynamics law of Newton we obtain d a M 1 s 1 dt where M total moment of forces in the vertical plane J the sum of moments of inertia relative to the horizontal axis a the pitch angle of the beam Then M EX p 2x i l i l i To determin
46. ig 5 26 It can be seen that compensating action of the coupling controller Azimuth positions simple PID black Results of experiments for the simple and cross coupled controllers are compared in Fig improves the control quality especially for the pitch angle 5 3 5 Comparison the simple and cross coupled PID controller 0 25 5 E 3 e T I I I T T I eo o I I DT T T I I I I I I I I LA far I I I T I PA lt I I I I I I I I 2 I I I Mm m I I I I I I I I LL ESAS I I I I pa oe I L pee O LLO oy ede La hee ele eee A ee en Ai I I I I I I i I o 3 I I I LS I I KI I I I I I I I I Aa I I LA I I gi I I I I I I I I a I IN end I I I P I I I I I I i I A I i I i AAA A aa ee e Mato Se A A NR x a I I I I I I I I i I I I I I I I I I I I I 2 TU I I I I I I I I I I I I 2 aw I I I in I I I I I I I cu o t i j I I i L a SSS a SL a 2 48g 5 mise NUNC AN PA I I I I I I I I ES o I I I SN I I I I I I I I I I 4 o o I I I wA I i I I I I I I I Yi I o I i I I EP i I I I I I I I I Pi A T ke J a A ER I I I LA I PPS SS RIS Se pa a EGE ee iia Ere o o Amp pS SS a JE erede I I I I I I I gt C O I I pa LI I I I I I I I I Poe d o amp I St I I I I I I I I LE e o 2 SS I I I I I I I I I I gt E Eee I I I I p a rg a A TR Eum ert ee u I I I I I I I I O a K I I I I I 2 I I I I I I I I x2 2 Pd I I I I e
47. imal and after that from maximal to minimal control values MinControl MaxControl minimal and maximal control values The control values must be set within the 1 0 to 1 0 range NoOfPoints number of characteristic points within the range where changes the control signal The exact number of points of the characteristics declared by this parameter is enlarged to two points namely at the ends of the control range function ChStat Sel CUL NoO c Ste swi c c Cc o end TRAS PWM2RPM SelectRotor CtrlDirection inControl MaxControl NoOfPoints ectRotor lower SelectRotor lDirection lower CtrlDirection fPoints max 1 NoOfPoints l alculate control signal step p MaxControl MinControl NoOfPoints tch CtrlDirection ase a Ctrl MinControl Step MaxControl ase d Ctrl MaxControl Step MinControl ase r Ctrl MinControl Step MaxControl MaxControl Step MinControl therwise This should not happen error The CtrlDirection must be A D or R TRASUsersManual 67 Select the rotor s used during the experiment Switch SelectRotor case a ACtrl Ctrl PCtrl O Ctrl case p ACtrl O Ctr1 PCtrl Ctrl case ap pa ACUtr l Ctri PCtrl Ctrl otherwise This should not happen error The SelectRotor must be A end Create figure that presents the current measurements
48. it View Simulation Format Tools Help Dic des S amp B cz E Estemal Jaen Bo T TRAS 1 DOF Controller Angle amp Control Reference Angle PID Controller Generator Zero Pitch Control Reset Reset Encoders 100 Fig 4 1 The MySystem Simulink model Now you can modify the model You have absolute freedom to develop your own controller Remember to leave the TRAS device driver block in the window This is necessary to work in RTWT environment Though it is not obligatory we recommend you to leave the scope You need a scope to watch how the system runs The saturation blocks are built in the Tras driver block They limit the currents to the DC motors for safety reasons However they are not visible for the user who may amaze at the saturation of controls Other blocks remaining in the window are not necessary for our new project Creating your own model on the basis of an old example ensures that all internal options of the model are set properly These options are required to proceed with compiling and linking in a proper way To put the Tras Device Driver into the real time code a special make file is required This file is included to the TRAS software You can apply most of the blocks from the Simulink library However some of them cannot be used see RTW or RTWT references manual The scope block properties are important for an appropriate data acquisition and watching how the system runs The Scope block p
49. l caused by the differential part of the controller For this reason the control signal is filtered It is shown in the upper part of Fig 5 11 iol BB BA sg Filtered Control Fig 5 11 Results of the PID azimuth control The details of the above experiment are shown in Fig 5 12 Fig 5 13and Fig 5 14 PID controller for azimuth position Filtered control P Ih a DN F p midi SG ZE I A E E I I 0 5 10 15 20 25 30 time s Fig 5 12 The filtered control TRAS User s Manual 49 PID controller for azimuth position control T T T I I I I I I I I I I I I I I I l I I T I I t I gt gt gt D A I I I I I I I T I I PA t A Caren acre pom jo mome esce S I I I I I I I I I I I I I I I
50. lboxes not included Control Toolbox from MathWorks Inc to develop the project The TRAS toolbox which includes specialised drivers for the TRAS System These drivers are responsible for communication between MATLAB and the RT DAC PCI measuring and control board The built in Open Watcom compiler is applied Manuals Installation Manual User s Manual The experiments and corresponding to them measurements have been conducted by the use of the standard INTECO system Every new system manufactured and developed by INTECO can be slightly different to those standard devices It explains why a user can obtain results maybe slightly different to these given in the manual 1 3 FEATURES of TRAS A highly nonlinear MIMO system ideal for illustrating complex control algorithms The set up is fully integrated with MATLAB Simulink and operates in real time in MS Windows Real time control algorithms can be rapidly prototyped No C code programming is required The software includes complete dynamic models TRAS User s Manual 27 e The User s Manual library of basic controllers and a number of pre programmed experiments familiarise the user with the system in a fast way Application note The documentation assumes that the user has a basic experience with MATLAB Simulink RTW and RTWT toolboxes from MathWorks Inc 1 4 Software installation Insert the installation CD and proceed step b
51. ler 5 3 2 Real time 2 DOF control with the simple PID controller The control task in this case is the same as in the previous sections but TRAS is not mechanically blocked and therefore it is free to move in both planes Click the 2 DOF controller button and the model shown in Fig 5 18 opens Set all coefficients of the crossed PID controllers to zero In this way the simple PID controller is obtained Set coefficients of the azimuth controller as follows K 3 1352 K 0 0 and K 2 2094 The integral saturation set to 1 0 Set the coefficients of the pitch PID controllers as K 1 2627 K 1 4014 and K 1 2074 Set saturation of the ae integral part of the controller to 1 43 Set the reference azimuth signal as square wave with 0 2 rad amplitude and 1 40 Hz frequency Set the reference signal for pitch as sinusoidal wave with the amplitude and frequency as 1 30 Hz Build the model and click on the Simulation Connect to target option and Start real time code option The results of the experiment are shown in Fig 5 19 and Fig 5 20 The azimuth position does not reach the desired position and the pitch position is weakly damped when disturbances from the rapid motions of the azimuth axis occur TRASUsersManual 53 TRAS 2 DOF PID Crosscoupled num z Azimuth Control Fliter den z gt Filtered 0000 lr OO o000 oo
52. o Fpyy 40000 1023 1 PWMPrescaler kHz Azimuth and Pitch Thermal flag status The thermal flags and the thermal statuses of the power amplifiers If the thermal status box is checked the corresponding power interface is overheated If the power interface is overheated and the corresponding thermal flag is set the RT DAC PCI board switches off the PWM control signal corresponded to the overheated power amplifier Tacho frame The Tacho frame displays two measured analog signals generated by the tachogenerators The voltages and the corresponding velocities of the propellers are displayed Azimuth and Pitch Voltage V Displays the voltage at the outputs of the tacho generators Azimuth and Pitch Velocity RPM Displays the velocity of the propellers The velocities are calculated based on the corresponding voltages and are given in RPM 2 4 RTWT Device Driver The driver is a software go between for the real time MATLAB environment and the RT DAC PCI VO board The control and measurements are transferred Click the TRAS Device Driver button and the driver window opens Fig 2 8 TRAS_DevDriv ni x File Edit View Simulation Format Tools Help O E amp d Bm e 2 es Y extemal ig 8 Mi ES TRAS Device Driver Reset Encoders 10094 Fig 2 8 RTWT Device Driver When one wants to build his own application one can copy this driver to a new model TRASUsersManual 16 Do not do any changes insid
53. of the control signal It is shown in the upper part of Fig 5 4 loxi BB 2S ABB gs Filtered Jit y PA Control ze Fig 5 4 Results of the PID pitch control TRAS User s Manual 45 PID controller for pitch position Filtered control The details of the above experiment are shown in Fig 5 5 Fig 5 6 and Fig 5 7 e o I I I I I I I I I I I I I I I I I I I I I I I I I I ST I I I I I 3 EL I pepsi A xs KE gt I I I I I I I i I I I I I I I I I I I I I I I I d I I I I I I I I JO Po O an a oU N _ i I I I l I I I I I I I m m I I I I I I I eem I I I I I I I a d I 5 I I I I I a I I AAA in 2 5 U t I I I I I I I I I I I I I I I I I 5 c I I I I I I I I I I Kej I I I I I I l Oo I I I I I o 2 I I I I I I I I I O I I I PS iem RG VE i RT LO 7 a I I I I I I I LO I I I I I I I O pan c I I I I I I I I I I I I I I oO O I I I I I I I I I I I I I I DV I I I I I I I I I I I LOA I E de o I I I I I I I I I I I E e I I I I I I I Lees eee eese lo SOSA lo or o O r 4 r d4 I k 2 V O I I I I E I I vt Em I I I I I I Y I I I I a I I ER gt I I I I I l E I I I o E I I I I I SRJ I I I cmEEI I I uv I I I I I I I I gl I I v o I I I I A A A IMS COME a a o Sl os RENE i AE o0 I i i Age I i eo
54. presented in Fig 6 1 Yma simulation model of CONTROLLER TRAS CRITERION O E Un Fig 6 1 Schematic diagram of the PID parameters tuning PROCEDURE min yog Q nUn In the case of TRAS the following criterion is used to tune the PID parameters for all experiments described in the previous section Q lee e u 01 Jar where T 80 s is the simulation time is the azimuth position error is the pitch position error u is the pitch control The 0 1 coefficient is the value of the pitch control which keeps the beam in the horizontal position The TRAS Toolbox includes the m files to perform optimisation procedures of the PID controller parameters These m files are as follows e pid azimuth m e pid pitch m e pid cross m e pid simple m These files use their own simulation models and the criterions m file in optimisation process See the body of these files to learn how the optimisation procedure is performed TRASUsersManual gg 7 Description of the CTRAS class properties The CTRAS is a MATLAB class which gives the access to all the features of the RT DAC PCI board equipped with the logic for TRAS The RT DAC PCI board is an interface between the control software executed by a PC computer and the power interface electronic of TRAS The logic on the board contains the following blocks e incremental encoder registers two 16 bit registers to measure the positions of the incremen
55. register counts encoder impulses See Encoder Example To reset only the first encoder register execute the command set tr ResetEncoder 1 0 7 11 Voltage Purpose Read two voltage values Synopsis Volt get tr Voltage Description Returns the voltage of two analog inputs The analog inputs are applied to measure the output of the tachogenerators See RPM 7 12 RPM Purpose Read velocity of the propelers Synopsis RPM get tr RPM TRAS User s Manual 64 Description Returns the velocities of the propellers The property contains two values The first one is equal to the azimuth propeller velocity The second one is equal to the pitch propeller velocity See Voltage RPMScaleCoeff 7 13 RPMScaleCoeff Purpose Read the coefficients applied to convert the tachgenerator voltage values into physical units Synopsis scale_coeff get tr RPMScaleCoeff Description The property returns two digits They are equal to the coefficients applied to convert tachogenerator voltages into RPMs See Voltage RPM 7 14 Therm Purpose Read thermal status flags of the power amplifiers Synopsis Therm get tr Therm Description Returns the thermal flag of the power amplifier When the temperature of a power amplifier is too high the corresponding flag is set to 1 The property contains two flags The first one corresponds to the thermal status of the power interface
56. rmal Status O ft ab 0 Time 7 Read the base address BA get tr BaseAddress 7 3 BitstreamVersion Purpose Read the version of the logic stored in the RT DAC PCI board Synopsis Version get tr BitstreamVersion Description The property determines the version of the logic design for the RT DAC PCI board TRAS may vary and the detection of the logic design version makes it possible to check if the logic design is compatible with the physical model TRASUsersManual 61 7 4 Encoder Purpose Read the incremental encoder registers Synopsis enc get tr Encoder Description The property returns two digits They are equal to the number of impulses generated by the corresponding encoders The encoder counters are 16 bit numbers so the values of this property is from 32768 to 32767 When an encoder counter is reset the value is set to zero The first encoder register corresponds to the azimuth position and the second register corresponds to the pitch position The incremental encoders generate 4096 pulses per rotation The values of the Encoder property should be converted into physical units See ResetEncoder Angle AngleScaleCoeff 7 5 Angle Purpose Read the angle of the encoders Synopsis angle_rad get tr Angle Description The property returns two angles of the corresponding encoders The first value corresponds to the azimuth and the second to the pitch position To
57. roperties are defined in the Scope property window see Fig 4 2 This window opens after the selection of the Scope Properties tab You can gather measurement data to the Matlab Workspace marking the Save data to workspace checkbox The data is placed under Variable name The variable format can be set as structure or matrix The default Sampling Decimation parameter value is set to 1 This means that each measured point is plotted and saved Often we select the Decimation parameter value equal to 5 or 10 This is a good choice to get enough points to describe the signal behaviour and to save the computer memory TRASUsersManual gg Angle amp Control parameters al x Angle amp Control parameters S x General Data history Tip try right clicking on axes General Data history Tip try right clicking on axes Axes Number of axes 3 floating scope Time range 30 v Save data to workspace Tick labels bottom axis only y Variable name AngleCtrl Sampling Format Structure with time Decimation y 1 12000 Fig 4 2 Setting the parameters of the Scope block When the Simulink model is ready click the Tools External Mode Control Panel option and next click the Signal Triggering button The window presented in Fig 4 3 opens Select Select All check button set Source as manual set Duration equal to the number of samples you intend to collect and close the window MySystem External Si
58. rsManual 00 0000000000000 T 4 RTWT model In this section the process of building your own control system is described The Real time Windows Target RTWT toolbox is used An example how to use the TRAS software is shown later in section 5 3 In this section we give indications how to proceed in the RTWT environment Before start test your MATLAB configuration by building and running an example of a real time application Real time Windows Target Toolbox includes the rtvdp mdl model Running this model will test the installation of the Real Time Workshop Real Time Windows Target toolboxes and the Real Time Windows Target Kernel In the MATLAB window type rtvdp Next build and run the real time model To build the system that operates in the real time mode the user has to e create a Simulink model of the control system which consists of TRAS Device Driver and other blocks chosen from the Simulink library e build the executable file under RTWT e start the real time code from the Simulation Start real time code pull down menu In this way the system runs in real time 4 2 Creating a model The simplest way to create a Simulink model of the control system is to use one of the models included in the Tras Control Window as a template For example click on the PID Azimuth button and save it as MySystem mdl name The MySystem Simulink model is shown in Fig 4 1 TRASUsersManual 380 CI MySystem iol xj File Ed
59. stem are the motor supply voltages The measured signals are position of the beam in the space that is two position angles and angular velocities of the rotors Angular velocities of the beam are software reconstructed by differentiating and filtering measured position angles of the beam a tail rotor main rotor U main shield DC motor KG tacho DC motor tacho free free beam articulation Counter balance Fig 3 1 Aero dynamical model of TRAS The block diagram of the TRAS model is shown in Fig 3 2 The control voltages U and U are inputs to the DC motors which drive the rotors PWM mode A rotation of the propeller generates an angular momentum which according to the law of conservation of angular momentum must be compensated by the remaining body of the TRAS beam This results in the interaction between two transfer functions represented by the moment of inertia of the motors with propellers kn and kw see Fig 3 2 This interaction directly influences the velocities of the beam in both planes The forces F and F multiplied by the arm lengths and l are equal to the torques acting on the arm TRASUsersManual gg DC motor with tail rotor 9 EI Em Su On ep E DC Motor with main rotor R 0 Qn gt Gy y Qu Fig 3 2 Block diagram of the TRAS model The following notation is used in Fig 3 2 a is horizontal position azimuth position of TRAS beam rad Q is
60. tal encoders There are two identical encoder inputs that are applied to measure the azimuth and pitch angles e incremental encoder resets logic The incremental encoders generate different output waves when the encoder rotates clockwise and counter clockwise The encoders are not able to detect the reference zero position To determine the zero position the incremental encoder registers have to be set to zero by a computer program e PWM generation blocks generates the Pulse Width Modulation output signals applied to control the azimuth and pitch DC drives Simultaneously the direction signals and the brake signals are generated to control the power interface module The PWM prescalers determines the frequencies of the PWM wave e power interface thermal flags the thermal flags can be used to disable the operation of the overheated DC motors e interface to the on board analog to digital converter The A D converter is applied to measure the output voltages from the tachogenerator All the parameters and measured variables from the RT DAC PCI board are accessible by appropriate properties of the CTRAS class In the MATLAB environment the object of the CTRAS class is created by the command object_name CTRAS The get method is called to read a value of the property of the object property_value get object_name property_name The set method is called to set a new value of the given property set object name
61. tions MDL models and C code MEX files that extends the MATLAB environment in order to solve TRAS modelling design and control problems The integrated software supports all phases of a control system development e on line process identification e control system modelling design and simulation e real time implementation of control algorithms TRAS Toolbox is intended to provide a user with a variety of software tools enabling e on line information flow between the process and the MATLAB environment e real time control experiments using demo algorithms e development simulation and application of user defined control algorithms TRAS User s Manual 6 1 2 Hardware and software requirements TRAS Toolbox is distributed on a CD ROM It contains the software and TRAS User s Manual The Installation Manual is distributed in a printed form Hardware Hardware installation is described in the Installation manual It consists of TRAS Mechanical Unit Power interface and wiring allowing electrical connections to the TRAS set up RT DAC PCI I O board The board contains FPGA equipped with dedicated logic design Pentium or AMD based personal computer Software For development of the project and automatic building of the real time program the following software has to be properly installed on the PC Microsoft Windows XP W7 MATLAB version R2009a b R2010a b R201 lab or R2012a with appropriate versions of Simulink RTW and RTWT too
62. unit with power supply and interface to a PC and the dedicated RT DAC PCI I O board configured in the Xilinx technology The software operates in real time under MS Windows XP W7 using MATLAB R2009a b R2010a b R201 1a b and R201a with RTW and RTWT toolboxes Control experiments are programmed and executed in real time in the MATLAB Simulink environment Thus it is strongly recommended to a user to be familiar with the RTW and RTWT toolboxes One has to know how to use the attached models and how to create his own models The approach to control problems corresponding to the TRAS proposed in this manual involves some theoretical knowledge of laws of physics and some heuristic dependencies difficult to be expressed in analytical form DC motor tachogenerator tail rotor counterbalance DC motor tachogenerator main rotor articulation with measurement encoders power interface Fig 1 1 The laboratory set up helicopter like system A schematic diagram of the laboratory set up is shown in Fig 1 1 The TRAS consists of a beam pivoted on its base in such a way that it can rotate freely both in the horizontal and vertical planes At both ends of the beam there are rotors the main and tail rotors driven by DC motors A counterbalance arm with a weight at its end is fixed to the beam at the pivot The state of the beam is described by four process variables horizontal and vertical angles measured by position sensors fitted at t
63. ur MATLAB configuration and simulation parameters TRAS User s Manual 42 5 Controllers and real time experiments In the following section we propose three PID controllers It is possible to tune the parameters of the controllers without analytical design Such approach to the control problem seems to be reasonable if a well identified model of TRAS is not available The effectiveness of the PID controllers discussed here is illustrated by control experiments PID controllers One degree of freedom 1 DOF control problem is the following Design a controller that will stabilise the system or make it follow a desired trajectory in one plane one degree of freedom while motion in the other plane is blocked mechanically or being controlled by another controller If TRAS is free to move in both axes we refer to the control as two degree of freedom 2 DOF The four PID controllers for TRAS PID PID yn PID and PID h horizontal azimuth v vertical pitch are considered The subscripts indicates the source sink relation for the controller Each control signal U and U is the sum of two controller outputs For example vertical control denoted later as U is the sum of two output signals PID and PID The internal structure of each PID controller is shown in Fig 5 15b There are three parameters to be set for every controller Kp K and Kg The TRAS control in the vertical and horizontal planes requires setting altogether 12 3x
64. vsar then I 1 hvsat hy Toss hvsat hv hvsat Lp 2 Ky edt Sor Lara Lnn S Tisa 0 if Lin gt To then Lin Tis if Iy lt ree then Lin I hhsat gt where K K ivv ivh I I I vvsat gt vhsat K ihv K are gains of the I parts I are saturation s of the integrators hvsat gt hhsat Finally vertical and horizontal controls are d U K 1 K k pv dvv dt pvhEh It EA gt for U ymax s U A if U gt U oss then U U one if U lt git then U U one d de n Uy Ky Ep I f Kaw a Kymn n Fu Kann at for U pmax S Un S U max if U gt U max then U U max if U lt U max then U U max where K pwo KK Ky Ki Kan K pv Ky are parameters of the controllers U max Uy max are the saturation limits of the vertical and horizontal controls 5 3 1 Simple PID controller The simple PID controller controls the vertical and horizontal movements separately In this control system influence of one rotor on the motion in the other plane is not compensated by the controller structure The system is not de coupled The control system of this kind is shown in Fig 5 16 The controller structure is shown in Fig 5 17 2 DOF SYSTEM Fig 5 16 The block diagram of 2 DOF control system with a simple PID controller TRASUsersManual ig Fig 5 17 The block diagram of the simple PID control
65. y step following displayed commands TRAS User s Manual 2 TRAS Control Window 2 1 Starting and testing procedures The TRAS system is an open type It means that a user can design and solve any TRAS control problem on the basis of the attached hardware and software The software includes device drivers compatible with RTWT toolbox It is assumed that a user is familiarised with MATLAB tools especially with RTWT toolbox Therefore we do not include the detailed description of this tool The user has a rapid access to all basic functions of the TRAS System from the TRAS Control Window It includes identification drivers simulation model and application examples In the Matlab command window type tras and then the TRAS Control Window opens see Fig 2 1 cl Tras File Edit View Simulation Format Tools Help Fig 2 1 TRAS Control Window TRAS Control Window contains testing tools drivers models and demo applications The user has a rapid access to all basic functions of the TRAS control system from TRAS Control Window TRAS Control Window shown in Fig 2 1 contains four groups of the menu items TRAS User s Manual 9 Tools Basic Test Manual Setup Reset Encoders and Stop Experiment Drivers RTWT Device Driver Simulation Models Pitch Azimuth and 2 DOF model Identification Steady State Characteristics Demo Controllers PID azimuth PID pitch and cross coupled PID controller 2 2 Basic test

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