Manual - Lehigh University
Contents
1. 17 O 0 05 17 and the state space matrices A B found previously the control gain 37 67 13 21 11 50 20 95 4 769 16 10 10 00 1 000 18 37 67 13 21 11 50 20 95 4 769 16 10 10 00 1 000 a is calculated by minimizing the cost function T J x TOx u Rudt 19 0 with the Matlab LOR command In terms of the PID control gains described earlier the full control gain is expressed Sat E E MA AS e R S K 20 Gi a 0 Da MOS o Og ag Document Number 644 Revision 2 1 Page 25 3 DOF Helicopter Reference Manual 7 In Lab Procedure 7 1 Controller Simulation 7 1 1 Objectives e Investigate the closed loop position control performance using a linear model of the 3 DOF Helicopter system e Ensure the controller does not saturate the actuator 7 1 2 Procedure Follow these steps to simulate the closed loop response of the 3 DOF Helicopter 1 Open Simulink model s_heli3d mdl shown in Figure 27 s_heli3d Seles File Edit View Simulation Format Tools WinCon Quarc Help Deas Blood Tla e fo Nom MiS Quanser 3 DOF Helicopter Closed loop System Simulation Desired Angle from Program 3 DOF HELI 3 DOF Helicopter Model Scopes LOR I Controller Figure 27 Simulink model s_heli3d mdl used to simulate closed loop response of 3 DOF Helicopter 2 Run the Matlab script setup_lab_heli_3d m to load the state space model matrices and the control gain K 3 To generate a desired elevation step of 7 5 degrees2. System specifications are listsed in Section 4 2 2 4 2 1 3 DOF Helicopter Parameters Table 4 below lists the main parameters associated with the Quanser 3 DOF Helicopter experiment The parameters that are not used in the mathematical model of the system or in the lab files given are shaded Symbol Matlab Description Value Notation Ra Rm Motor armature resistance 0 83 Q K Kt Motor current torque constant 0 0182 N m A Document Number 644 Revision 2 1 Page 8 3 DOF Helicopter Reference Manual Symbol Matlab Notation Kecn t Kec Kec ine Kecr Kecp Kece Description Motor rotor moment of inertia Propeller force thrust constant found experimentally Mass of the helicopter body two propellers assemblies encoders etc Mass of the counterweight Mass of front propeller assembly includes motor shield propeller and half helicopter body Mass of back propeller assembly Distance between travel axis to helicopter body Distance between pitch axis to each motor Distance between travel axis to the counterweight Gravitational constant Travel encoder resolution in quadrature mode Pitch encoder resolution in quadrature mode Elevation encoder resolution in quadrature mode Travel encoder calibration gain Pitch encoder calibration gain Elevation encoder calibration gain Table 4 3 DOF Helicopter system specifications 4 2 2 ADS Parameters Table 5 below
3. actuator sensors the data acquisition card e g Q8 and the power amplifier e g UPM as described in Section 4 Reference 1 and Reference 4 respectively e Wiring the 3 DOF Helicopter plant with the UPM and DAC device as discussed in Section 5 e State feedback control and the Linear Quadratic Regulator i e LQR enough to design a controller e Using QuaRC or another equivalent software to control and monitor a plant in real time and in designing a controller through Simulink See Reference 2 for more detail and in particular ensure a few examples described in the Model Examples section are ran before running any of the 3 DOF Helicopter controllers 3 Experiment Files Overview Table 1 below lists and describes the various files supplied with the 3 DOF Helicopter experiment Document Number 644 Revision 2 1 Page 2 3 DOF Helicopter Reference Manual File Name 3 DOF Helicopter Reference Manual pdf 3 DOF Heli Equations mws 3 DOF Heli Equations html quanser ind and quanser lib setup lab heli 3d m setup_heli3d_configuration m setup ads configuration m HELI3D_ ABCD eqns m s heli3d mdl q_heli3dr_zz mdl Description This manual is both the user and laboratory guide for the Quanser 3 DOF Helicopter specialty aerospace plant It contains information about the hardware components specifications information to setup and configure the hardware system modeling control design as well as the exp
4. a scale leave the mass at marked position 11 The standard setup in the default configuration and starting position for the 3 DOF Helicopter system is depicted in Figure 10 Figure 10 Starting position of the 3 DOF Helicopter system 12 Ensure all obstructions that may interfere with the complete 360 degree axial motion of the helicopter are removed before performing any experiment 5 2 Cable Nomenclature Table 5 below provides a description of the standard cables used in the wiring of the 3 DOF Helicopter system Document Number 644 Revision 2 1 Page 12 3 DOF Helicopter Reference Manual Cable Designation 5 pin DIN to RCA N Figure 11 From Digital To Analog Cable 4 pin DIN to 6 pin DIN Figure 12 To Load Cable Of Gain 5 5 pin stereo DIN to 5 pin stereo DIN Figure 13 Encoder Cable 6 pin mini DIN to 6 pin mini DIN Figure 14 From Analog Sensors Cable Description This cable connects an analog output of the data acquisition terminal board to the power module for proper power amplification This cable connects the output of the power module after amplification to the desired actuator e g propeller motor One end of this cable contains a resistor that sets the amplification gain When carrying a label showing 5 at both ends the cable has that particular amplification gain This cable carries the encoder signals between an encoder connector and
5. at 0 04 Hz frequency open the Desired Angle from Program subsystem and set the Amplitude Elevation deg gain block to 7 5 degrees and Frequency input box in the Signal Generator Elevation block to 0 04 Hz 4 To generate a desired travel step of 30 degrees at 0 03 Hz frequency set the Amplitude Travel deg block to 30 0 degrees and the Frequency input box in the Signal Generator Travel block Document Number 644 Revision 2 1 Page 26 3 DOF Helicopter Reference Manual to 0 03 Hz In the Scopes subsystem open the elevation deg pitch deg travel deg and the Vm V scopes Click on start simulation to simulate the closed loop response The elevation and travel angles purple trace should track the corresponding desired position signals yellow trace in each scope Examine the voltage in the Vm V scope and ensure the front yellow plot and back motor purple plot are not saturated Recall that the maximum peak voltage that can be delivered to the motor by the UPM 2405 is 24 V and that the controller implemented on the actual system includes the operation voltage V The operation voltage is approximately 7 5 V and this will be added to the resulting control output Try changing the desired elevation and travel angles to familiarize yourself with the controller Observe that rate limiters are placed in the desired position signals to eliminate any high frequency changes This makes the control signal smoother which places les
6. describes the specifications of 3 DOF Helicopter Active Disturbance System Value 1 91E 006 0 1188 LAS 0 713 0 660 0 178 0 470 9 81 8192 4096 4096 7 67E 04 1 50E 03 1 50E 03 counts rev counts rev counts rev rad counts rad counts rad counts Document Number 644 Revision 2 1 Page 9 3 DOF Helicopter Reference Manual Symbol Matlab Description Value Notation Motor nominal input voltage 6 0 Motor armature resistance 2 6 Motor armature inductance 0 18 Motor current torque constant 0 00767 Motor back emf constant 0 00767 Motor rotor moment of inertia 3 90E 007 Internal gearbox gear ratio 3 71 Lead screw pitch 1 3 in rev Maximum travel limit of disturbance mass 0 264 Vmax Maximum speed of disturbance mass 0 25 m s Kecinx ADS encoder resolution in quadrature 4096 count rev mode Kecx Calibration gain for linear position of 2 067E 006 m count disturbance mass 5 System Setup and Wiring Section 5 1 describes how to assemble and setup the Quanser 3 DOF Helicopter specialty plant The cables used to connect the helicopter system are summarized in Section 5 2 and the standard wiring procedure is given in Section 5 3 Section 5 4 features the additional connections needed if using the Active Disturbance System Lastly the joystick that can be used to control the helicopter is discussed in Section 5 5 5 1 System Setup Follow these steps for the mechanical setup of
7. driving the front motor the UPM driving the back motor the Q8 Terminal Board and the Helicopter base The connections are described in detail in the procedure below and summarized in Table 6 Follow these steps to connect the 3 DOF Helicopter system 1 Itis assumed that the Quanser Q3 Q4 or Q8 board is already installed as discussed in the Reference 1 If another data acquisition device is being used e g NI M Series board then go to its corresponding documentation and ensure it is properly installed 2 Make sure everything is powered off before making any of these connections This includes turning off your PC and the UPMs 3 Connect the 5 pin DIN to RCA cable from the Analog Output Channel 0 on the DAC board to the From D A Connector on a UPM 2405 See cable 1 shown in Figure 16 and Figure 18 This carries the attenuated front motor voltage control signal V K where K is the UPM 2405 amplifier gain 4 Connect the 5 pin DIN to RCA cable from the Analog Output Channel 1 on the DAC board to the From D A Connector on a UPM 2405 See the cable 2 shown in Figure 17 and Figure 18 This carries the attenuated back motor voltage control signal V K 5 Connect the 4 pin stereo DIN to 6 pin stereo DIN that is labeled Gain 5 from To Load on the Document Number 644 Revision 2 1 Page 14 A 3 DOF Helicopter Reference Manual 10 11 12 UPM 2405 to the Front Motor connector See connection 3 shown in Figure 16 and F
8. figures 16 and 17 show respectively the front and back UPM connections The cabling on the UPM used to drive the motor of the ADS is illustrated in Figure 20 See Figure 21 for the Q8 Terminal Board connections and figures 22 and 23 for the wiring on the Helicopter base These connections are described in detail in the procedure below and summarized in Table 6 Follow these steps to connect the 3 DOF Helicopter with the Active Disturbance System experiment 1 Go through the 3 DOF Helicopter wiring as dictated in Section 5 3 2 Connect the 5 pin DIN to RCA cable from the Analog Output Channel 2 on the DAC board to the From D A Connector on the UPM 1503 See cable 11 shown in Figure 20 and Figure 21 This carries the attenuated ADS motor voltage control signal V qs Ka where K is the UPM 1503 amplifier gain Connect the 4 pin stereo DIN to 6 pin stereo DIN that is labeled Gain 3 from To Load on the UPM 1503 to the ADS Motor connector See connection 12 shown in Figure 20 and Figure 23 This cable sets the gain of the amplifier to 3 The connector on the UPM side is black and should be labeled 3 The cable transmits the amplified voltage that is applied to the ADS motor Vds ATTENTION The Quanser UPM 1503 is capable of providing the required power to the 3 DOF Helicopter ADS motor However it should be used in conjunction with a To Load cable of gain 3 i e 4 pin DIN to 6 pin DIN cable as described in Reference 4 4 Connec
9. in the elevation deg scope is the desired elevation angle and the red is the measured elevation angle Set the desired elevation angle to a constant of step wave with an amplitude of 7 5 degrees at a frequency of 0 04 Hz as discussed in Section 7 1 The helicopter body should be going up and down as the controller does the elevation tracking Set the Amplitude Travel deg gain block to 30 degrees and the Frequency input box in the Signal Generator Travel block to 0 03 Hz The helicopter body should not be moving forwards and backwards as it tracks the desired travel angle In the travel deg scope the green trace is the desired travel angle while the red is the measured travel angle In the Vm V scope the green line is the front motor voltage and the red trace is the back motor voltage These should be within 25V and not go negative very often Figure 30 below is a sample closed loop position response of the 3 DOF Helicopter when commanding an elevation step of 7 5 degrees at 0 04 Hz and a travel step 30 degrees at 0 03 Hz Document Number 644 Revision 2 1 Page 30 3 DOF Helicopter Reference Manual 19 20 21 No Oo measured l elevation deg o o a a T amp oa Do 5 gt E o E 0 10 20 30 40 50 60 time s Figure 30 Typical closed loop response of 3 DOF Helicopter system Alternatively the desired angle can be generated using a joystick either the analog or USB descr
10. joystick connections to Analog Inputs 0 3 on the terminal board using the 5 pin DIN to 4xRCA cable as illustrated in Figure 17 and Figure 18 The RCA side of the cable is labeled with the channels Note that the cable with label 1 is goes to Analog Input Channel 0 Ensure UPM and PC are off when making this connection The X and Y signals that are connected to the S3 and S4 terminals on the UPM are read in as Analog Input 2 and Analog Input 3 in QuaRC Document Number 644 Revision 2 1 Page 15 3 DOF Helicopter Reference Manual Universal Power Module i E i Universal Power Module GUANSER INNOVATE EDUCATE WWW quensar com of A K u i y Ome Amplifier i is 5 e To Load FELL p_e 3 UPM 2405 120VACONLY Gpucaaos 120 VAC ONLY Figure 16 Front Universal Power Module Figure 17 Back Universal Power Module UPM 2405 UPM 2405 Document Number 644 Revision 2 1 Page 16 3 DOF Helicopter Reference Manual SAN f Taan cable Colors amp number al board Colors amp ime CABLE 3 ORANGE ABLE 2 GREEN ABLE 1 BROWN Figure 18 Q8 Terminal Board Connections Figure 19 3 DOF Helicopter Connections Signal 1 Terminal Board Front UPM From D A Control signal to the front UPM DAC 0 connector 2 Terminal Board Back UPM From D A Control signal to the back UPM DAC 1 connector 3 Front UPM To 3 DOF Helicopter Power leads to the 3 DOF Helicopter s front Load connecto
11. the Quanser 3 DOF Helicopter device 1 Place the support base component 12 shown in Figure 3 on a table or on the floor 2 Install the elevation encoder frame component 7 in Figure 3 on the top of the base Ensure the white arrow labels on the circuit ID 10 in in Figure 3 and on the frame are aligned Once fitted tighten the two thumb screws 3 Guide the long blue arm ID 6 in Figure 3 through the elevation encoder frame Tighten the cap screw maintaining perpendicularity to the elevation encoder frame wall CAUTION Never apply extreme loads in the vertical direction Document Number 644 Revision 2 1 Page 10 3 DOF Helicopter Reference Manual 4 There are two cables protruding from the main arm the 6 pin DIN to 6 pin DIN motor connector and the 5 pin DIN to 5 pin DIN encoder connector Connect the motor cable to the connector labeled MOTOR on the helicopter circuit component 10 shown in Figure 10 Connect the encoder cable to the connector labeled ENCODER on the helicopter circuit ID 10 in Figure 10 Make sure there is sufficient slack in the wiring harness to accommodate the total travel of the arm CAUTION Never lift the system using the blue arm Always carry from the base with one hand and stabilize the blue arm with the other hand Connect the flat 5 pin encoder connector from the helicopter circuit to the elevation encoder ID 8 in Figure 4 Make sure the GND pin on the cable is wired to the c
12. the data acquisition board to the encoder counter Namely these signals are 5 VDC power supply ground channel A and channel B This cable carries analog signals e g from joystick plant sensor to the UPM where the signals can be either monitored and or used by a controller The cable also carries a 12VDC line from the UPM in order to power a sensor and or signal conditioning circuitry Document Number 644 Revision 2 1 Page 13 3 DOF Helicopter Reference Manual Designation Description This cable carries the analog signals unchanged from the UPM to the Digital To Analog input channels on the data acquisition terminal board L i im Figure 15 To Analog To Digital Cable Table 5 Cable Nomenclature 5 3 Typical Connections For The 3 DOF Helicopter The travel pitch and elevation encoders are connected directly to the data acquisition board This provides the position feedback necessary to control the helicopter The data acquisition board i e DACB outputs a control voltage that is amplified and drives the front and back motors Both motors are driven by a Quanser Universal Power Module 2405 1 e UPM 2405 or equivalent The UPM 2405 is capable of delivering a maximum voltage of 24V to the motors This section describes the typical cabling connections that are used by default for the Quanser 3 DOF Helicopter system Figures 16 17 18 and 19 below illustrate respectively the wiring of the UPM
13. vertical base is equipped with an eight contact slipring Electrical signals to and from the arm and helicopter are channeled through the slipring to eliminate tangled wires reduce friction and allow for unlimited and unhindered travel Figure 1 3 DOF Helicopter when running The objective of this experiment is to design a control system to track and regulate the elevation and travel angles of the 3 DOF Helicopter The system is supplied with a complete mathematical model the system parameters and a sample state feedback controller As shown in Figure 2 the 3 DOF Helicopter can also be fitted with an Active Mass Disturbance System ADS The ADS is comprised of a lead screw a DC motor an encoder and a moving mass The lead screw is wound through the mass such that when lead is rotated the mass moves along the helicopter arm linearly One end of the lead screw is connected to a DC motor and the other end has an Document Number 644 Revision 2 1 Page 1 3 DOF Helicopter Reference Manual encoder As the motor is driven the lead screw rotates and causes the mass to move Using the encoder measurement and a position controller the user can move the mass to a desired position and actively disturb the helicopter Figure 2 Active Disturbance System on the 3 DOF Helicopter 2 Prerequisites In order to successfully carry out this laboratory the user should be familiar with the following e 3 DOF Helicopter main components e g
14. 0 travel Motor Input Voltage Ch 1 pitch Ch 2 elevation HIL Read Cable Gain Encoder Timebase ECLI utelev_O HIL Read Encoder Timebase Initial Elevation rad Encoder Resolution CHIL 1 A Elevation rad count p K_EC_P X eps p lambda eps_dot p_dot lambda_dot Encoder Resolution Pitch rad count LU K_EC_T Encoder Resolution wef 2 s Travel rad count s2 2 zetafwctstwct 2 Derivative Filter Elevatio wer 2 s 2 zetafwefstwct 2 Derivative Filter Pitch wof 2 s 37 2 zetafwefstwct 2 Derivative Filter Travel 100 Figure 29 3 DOF Helicopter subsystem used to interface with hardware 7 The voltage sent to the Analog Output block is amplified by the UPM 2405 and applied to the power amplifier s attached motor Note that the control input is divided by the amplifier gain K_CABLE before being sent to the DACB This way the amplifier gain does not have to be included in the mathematical model as the voltage output from the controller is the voltage being applied to the motor The UPM and DACB saturation blocks limit the amount of voltage that can be fed to the motor In this case since K CABLE 5 the voltage is only saturated by the UPM and not by the DACB The Vm V sink is the effective motor input voltage and shows when the amplifier is being saturated 8 Click on Quarc Build to compile the code from the Simulink diagram 9 Open the elevation deg
15. Aerospace Plant 3 DOF Helicopter Position Control 3 DOF Helicopter Reference Manual 3 DOF Helicopter Reference Manual Table of Contents Ae ENT RODUCUION rr io asias 1 ZE REREOUISITES A EIE AREE E EEIE S TEA 2 Di EXPERIMENT FILES OVER A II O RT 2 4 SYSTEM DESCRIPTION dai AA A AAA de 4 AL Components anie niana r E a a a n oelinde bana Soni detunn tee 4 4 1 1 3 DOF Helicopter Components oseta nea a e ae iaa aaa e a r ES 4 4 1 2 Active Disturbance System Compomnents c ccccccccsscesssecesseessnsesseeceeceeseesseeceaecseeeessaeesseeeeeeeneeensees 7 4 2 System AAA OS 8 4 2 1 3 DOF Helicopter Parameters renesans o A R A RARO AGEA AAEL 8 42 2A DS Parameters nenene NO 9 S SYSTEM SETUP AND W RIN ausiesiicaskaeaseae ditusasadteians sactwaven seeaceassidaansivebapasvaceutdaavasavasaseava 10 Sle System SETUD ES e E E ree A 10 2 CS NM a Cadi ii NA Cah O NS 12 5 3 Typical Connections For The 3 DOR Helicoptero a ss 15 5 4 Additional Connections for the 3 DOF Helicopter w ADS cccceccecscceseeeeteeeeeeneeeeesseeeeeseeees 19 HON E DECIA eiie ieii DS ach dh aa a laa a ental laaab aly aatioe 21 6 MODELING AND CONTROL DESIGN scasisseasseadenceaddessiceualencedastensceeatendscdeusthseassaudedadslcxbassetensstsnsnushiaaasssdadaauaene 22 NN 22 6 2 Control Desirs nn a e A a aT a a ML a a N E AAAA 25 Te INLAB PROCEDURE 30 A AA A AAA EEk EEAS A n 27 E Le Controller Simulations A da 27 Document Number 644 Revision 2 1 P
16. Having the controller go across the 0 V line often can cause damage to the amplifiers Ensure the helicopter hardware is setup as discussed in Section 5 1 and all the connections have been made as instructed in Section 5 4 Turn the power of the two Universal Power Amplifiers on The red LED on the upper left corner of the each UPM should be lit In the g_heli3d_ads Simulink diagram make sure the Program Joystick block shown in Figure 31 is set to 1 in order to generate the desired angle from Simulink Click on QuaRC Start to begin running the controller The active disturbance is first calibrated The mass is moved back towards the helicopter base until contact with the spring is made It is then moved to the middle lead screw position i e the home position Once calibrated the front and back motors on the helicopter should begin running The controller can be stopped at any time by clicking on the STOP button located in the Simulink tool bar The helicopter elevation angle is initially 27 5 degrees Set the desired elevation angle to 0 degrees by setting the Constant Elevation deg gain block which is found in the Desired Angle from Program subsystem to 0 degrees The helicopter should now be stabilized above its horizontal Set the ADS Setpoint Amplitude m slider gain block to 0 13 and the Frequency inside the Signal Generator block to 0 05 Hz The disturbance mass will move 0 13 meters at 0 05 Hz about the middle of the slide
17. In the Vm V scope the green line is the front motor voltage and the red trace is the back motor voltage These should be within 25V and not go negative very often The response in the elevation deg scope shows elevation angle as the position of the disturbance mass is varied Recall that the green plot in the elevation deg scope is the desired elevation angle and the red is the measured elevation angle As the mass is brought to the base the elevation increases However the integrators in the position controller begin to compensate for the shifted weight and the elevation begins to drift back to 0 degrees Similarly the elevation goes down when the mass if moved forward towards the helicopter and the controller integration begins to reject the disturbance Figure 32 below depicts the measured closed loop position response of the 3 DOF Helicopter with the ADS when the disturbance mass is moving between 0 13 meters at 0 05 Hz Document Number 644 Revision 2 1 Page 33 3 DOF Helicopter Reference Manual a h measured ads position m o N elevation deg travel deg 0 5 10 15 20 25 30 time s Figure 32 Closed loop response of 3 DOF Helicopter ADS device 15 Alternatively the desired angle can be generated using a joystick either the analog or USB described in Section 5 5 To use the joystick set the Program Joystick switch shown in Figure 31 to 2 The rate at which the desired angle increases or decrea
18. OF Helicopter Terminal Board Active Mass Disturbance lead screw angle ADS Encoder Encoder Channel 3 feedback signal to the data acquisition card ENC 3 connector Table 7 Additional wiring summary for 3 DOF Helicopter with Active Mass Disturbance system 5 5 Joystick Description The Quanser 3 DOF Helicopter experiment is supplied with either an analog joystick shown in Figure 24 or a Logitech Attack 3 USB joystick shown in Figure 25 They are used to generate a desired position instead of commanding it via the Simulink model blocks see lab procedure later Document Number 644 Revision 2 1 Page 20 3 DOF Helicopter Reference Manual Rate Command knob Figure 24 Analog joystick Figure 25 Logitech Attack 3 USB joystick The setup procedure for the analog joystick is described in steps 11 12 in Section 5 3 The setup procedure for the USB joystick is described in step 10 in Section 5 3 The rate command knob shown in Figure 25 changes the rate at which a command is generated by the joystick The rate is at its greatest when the knob is turned fully toward the joystick handle The system requirements for the Logitech Attack 3 USB joystick are e PC with Pentium Processor or compatible e 64MBRAM e USB port e Windows 98 2000 Me or Xp 6 Modeling and Control Design The mathematical model developed for the 3 DOF Helicopter system is summarized in Section 6 1 In Section 6 2 the feedback system used to control
19. ag kas be is the proportional derivative control gain xyT Eg Pg ta O 0 12 1s the desired state x 1s the state defined in Equation 4 rea 17 x1 dt or x3 dt V 13 l fisca 17 x1 att astas x3 dt Is the integral control and Vo is the operation point voltage defined in Equation 1 The variables a Pa and a are the elevation pitch and travel setpoints i e the desired angles of the helicopter In the control the pitch command is set to zero thus pa 0 The gains k through k 3 are the front motor control proportional gains and the gains kz through k2 are the back motor control proportional gains Similarly k through ki are the front motor control derivative gains and k24 through ko are the back motor control derivative gains The integral control gains used in the front motor control are k and k s and the integral gains k and k28 are used in the back motor regulator The PID control gains are computed using the Linear Quadratic Regular scheme The system state is first augmented to include the integrals of the elevation and travel states T EZ 2 a fe anfa ar Xi pP a 9 gt 14 Using the feedback law Document Number 644 Revision 2 1 Page 24 3 DOF Helicopter Reference Manual ua Kx 15 the weighting matrices 10 0 0000 0 0 01 000 0 0 0 0 0 10 0 0 0 0 0 00 000 0 0 0 Q 16 00 0000 0 0 00 0002 0 0 00 0 0 0 0 10 0 00 0 0 0 0 0 0 1 and 0 05 0
20. age i 3 DOF Helicopter Reference Manual Edel OBJEC Ve Sion tatexesi dvs A AS hans Sake 27 ES NS RN 27 T2 Controller apli A ii Rica acadonetias aN RE 28 O A NT 28 7 2 2 Procedure 3 DOF Helicopter iaa aa 28 7 2 3 Procedure 3 DOF Helicopter with ADS ooooonoccnnocononcnconnncnonncnonocnonnnnonnononnrnoncncan nn ron rn rn rn cnn n rro nrnccnannnnrs 32 Se REFERENCES anaes vausnskslusiepecssousseeuanencDececaaeeans 35 Document Number 644 Revision 2 1 Page ii 3 DOF Helicopter Reference Manual 1 Introduction The 3 DOF Helicopter plant is depicted in Figure 1 Two DC motors are mounted at the two ends of a rectangular frame and drive two propellers The motors axes are parallel and the thrust vector is normal to the frame The helicopter frame is suspended from in instrumented joint mounted at the end of a long arm and is free to pitch about its centre The arm is gimbaled on a 2 DOF instrumented joint and is free to pitch and yaw The other end of the arm carries a counterweight such that the effective mass of the helicopter is light enough for it to be lifted using the thrust from the motors A positive voltage applied to the front motor causes a positive pitch while a positive voltage applied to the back motor causes a negative pitch A positive voltage to either motor also causes an elevation of the body i e pitch of the arm If the body pitches the thrust vectors result in a travel of the body 1 e yaw of the arm as well The
21. disturbance is not being used 4 Execute the setup _lab_heli_3d m Matlab script to setup the workspace before compiling the diagram and running it in real time with QuaRC This file sets the state space model of the 3 DOF Helicopter system calculates the feedback gain vector K and sets various other parameters that are used such as the filter cutoff frequencies amplifier gain and the UPM and DACB limits 5 Open the 3 DOF Helicopter subsystem shown in Figure 29 It contains the QuaRC blocks that interface with the hardware of the actual plant The Analog Output block outputs the voltage computed by the controller to the DACB and the Encoder Input block reads the encoder measurements 6 Configure DAQ Double click on the HIL Initialize block in the Simulink diagram and ensure it is configured for the DAQ device that is installed in your system By default the block shown in Figure 29 is setup for the Quanser Q8 hardware in the loop board Document Number 644 Revision 2 1 Page 28 3 DOF Helicopter Reference Manual a q_heli3d 3 DOF Helicopter File Edit View Simulation Format Tools WinCon QuaRC Help k oe E 3 f AS t x eS lint Extemal y R 2 3 DOF Helicopter Reads angles from encoder and applied voltage to motors AO 0 front motor A0 1 back motor u u_front u_back HIL Initialize HIL 1 q8 0 HIL Write Analog UPM Voltage DACB Limit W Limit 4 Cable Gain HIL Write Analog Pre Compensation CHIL 1 Ch
22. erimental procedure to simulate and implement the controller Maple worksheet used to analytically derive the state space model involved in the experiment Waterloo Maple 9 or a later release is required to open modify and execute this file HTML presentation of the Maple Worksheet It allows users to view the content of the Maple file without having Maple 9 installed No modifications to the equations can be performed when in this format The Quanser_Tools module defines the generic procedures used in Lagrangian mechanics and resulting in the determination of a given system s equations of motion and state space representation It also contains data processing routines to save the obtained state space matrices into a Matlab readable file The main Matlab script that sets the model control and configuration parameters Run this file only to setup the laboratory Returns the 3 DOF Helicopter model parameters Kf m_h m_w m_f m_b Lh La Lw and g the encoder calibration constants K_EC_T K_EC_P and K_EC E Returns the various parameters associated with the Active Disturbance System ADS Matlab script file generated using the Maple worksheet 3 DOF Heli Equations mws It sets the A B C and D matrices for the state space representation of the 3 DOF Helicopter open loop system which is used in s_heli3d mdl and to design an LQR based controller Simulink file that simulates the closed loop 3 DOF Helicopter system using i
23. ibed in Section 5 5 To use the joystick set the Program Joystick switch shown in Figure 28 to 2 The rate at which the desired angle increases or decreases given a joystick position can be changed using the K JOYSTICK X andK JOYSTICK Y variables that are set in the setup lab heli 3d m script file CAUTION Do not switch from the Program to the Joystick from 1 to 2 when the controller is running Set the program joystick switch to 2 before starting QuaRC if the joystick is to be used Click on the Stop button on the Simulink diagram tool bar or select Quarc Stop from the menu to stop running the code Power off the two UPMs 7 2 3 Procedure 3 DOF Helicopter with ADS Follow the steps described below to implement the designed controller in real time and observe its effect on the 3 DOF Helicopter with Active Disturbance System ADS plant l Open Simulink model g_heli3d_w_ads mdl shown in Figure 31 that implements a sample LQR controller on the 3 DOF Helicopter with ADS plant The model runs your actual 3 DOF Helicopter w ADS plant by directly interfacing with your hardware through the QuaRC blocks Document Number 644 Revision 2 1 Page 31 3 DOF Helicopter Reference Manual as discussed in Reference 2 The 3 DOF Helicopter System subsystem is basically the Simulink model described in Figure 28 The helicopter is not engaged until the Active Disturbance is calibrated q_heli3d_w_ads File Edit View Simulation Format T
24. igure 19 This cable sets the gain of the amplifier to 5 and the connector on the UPM side is gray in colour The cable transmits the amplified voltage that is applied to the front motor denoted Vp ATTENTION The Quanser UPM 2405 is capable of providing the required power to the 3 DOF Helicopter motors However it should be used in conjunction with a To Load cable of gain 5 i e 4 pin DIN to 6 pin DIN cable as described in Table 5 above See Reference 4 for more detail Connect the 4 pin stereo DIN to 6 pin stereo DIN that is labeled Gain 5 from To Load on the UPM 2405 to the Back Motor connector See connection 4 shown in Figure 17 and Figure 19 The cable carries the amplified back motor voltage and is represented by the variable V Connect the 5 pin stereo DIN to 5 pin stereo DIN cable from the Travel Encoder connector on the 3 DOF Helicopter base to Encoder Input 0 on the terminal board as depicted by connection 5 in Figure 18 and Figure 19 This carries the travel angle measurement and is denoted by the variable CAUTION Any encoder should be directly connected to the Quanser terminal board or equivalent using a standard 5 pin DIN cable DO NOT connect the encoder cable to the UPM Connect the 5 pin stereo DIN to 5 pin stereo DIN cable from the Pitch Encoder connector on the 3 DOF Helicopter base to Encoder Input 1 on the terminal board See connection 6 in Figure 18 and Figure 19 This carries the pitch angle measu
25. ler assembly Travel encoder Pitch encoder Front motor connector Arm Back motor connector Elevation encoder frame Travel encoder connector Elevation encoder Pitch encoder connector 1 2 3 4 5 6 l 8 9 Counterweight Elevation encoder connector a Encoder motor circuit Table 2 3 DOF Helicopter component nomenclature Document Number 644 Revision 2 1 Page 4 3 DOF Helicopter Reference Manual Figure 4 Components on 3 DOF Helicopter base Document Number 644 Revision 2 1 Page 5 3 DOF Helicopter Reference Manual Figure 5 Components on the helicopter body of the 3 DOF Helicopter system 4 1 1 1 DC Motors Component 2 The 3 DOF Helicopter has two DC motors the front and back motors Each DC motor is a Pittman Model 9234 It has an electrical resistance of 0 83 Q and a current torque constant of 0 0182 N m A The rated voltage of the motor is 12 V but its peak voltage can be brought up to 22 V without damage See Reference 5 for the full specifications of this motor 4 1 1 2 Propeller Assemblies Component 3 and 4 The front and back propeller assemblies are composed of the actual propeller which is directly mounted to the motor shaft and the aluminum propeller shield The propellers used for both the front and rear motors are Graupner 20 15 cm or 8 6 They have an identified thrust force constant of 0 119 N V 4 1 1 3 Encoders Components 5 8 and 14 The 3 DOF Helicopter expe
26. onnector labeled GND on the elevation encoder Attach the helicopter body ID 1 in Figure 5 to the T fitting of the pitch encoder ID 5 in Figure 5 Ensure the white arrow labels on the helicopter body and the T Fitting are both aligned and tighten the screw from the bottom of the helicopter body Adjust the helicopter body such that it is perpendicular to the arm As illustrated in Figure 9 attach the secondary arm to the end of the main arm ID 6 in Figure 3 and tighten two screws through the nuts The angle of the secondary arm relative to the main arm has been selected such that the effective mass at the helicopter end is relatively constant Once the secondary arm is securely fastenned attach the counterweight to the hole marked 71 g and tighten the thumb screw to secure the weight NOTE When using the Active Disturbance System set the counterweight to the 0 g position as depicted in Figure 9 pii Figure 9 Counterweight and secondary arm setup 10 Using a weigh scale measure the weight of the helicopter body with the counterweight attached at the other end The desired mass differential is approximately 70 g If the body does not weigh Document Number 644 Revision 2 1 Page 11 3 DOF Helicopter Reference Manual 70 g adjust the position of the counterweight i e forward or backward until the body weighs approximately 70 g Once in place the weight adjustment does not have to be repeated If you do not have
27. ools WinCon QuaRC Help D eee gt B EST RZ b Y int Extemal y Ss 0h Quanser 3 DOF Helicopter with Active Mass Disturbance ADS Closed loop Actual System Signal ADS Setpoint Generator Amplitude m Active Disturbance System Q8 Program 1 Joystick 2 Desired Angle from Program Des Position Multiport Rate Limiter Desired Position Switch from Joystick 3 DOF Helicopter System Scopes Figure 31 Simulink model q_heli3d_w_ads_q8 implements an LOR controller on the 3 DOF Helicopter with Active Disturbance system 2 Open the design file setup lab_heli_3d m and ensure everything is configured correctly NOTE Make sure the WITH_ADS parameter in the setup_lab_heli_3d m file is set to YES This indicates to the automatically designed controller that the active disturbance is being used 3 Execute the setup lab_heli_3d m script to setup the workspace before compiling the diagram and running it in real time with QuaRC 4 Click on QuaRC Build to compiled the Simulink diagram 5 Open the elevation deg travel deg and Vm V scopes from the Scopes folder These scopes display both the desired and measured angles of the Helicopter as well as the voltages being applied to the front and back motors CAUTION Make sure the motor input voltage does not go between negative and positive Document Number 644 Revision 2 1 Page 32 3 DOF Helicopter Reference Manual 10 11 12 13 14 very often
28. osition dynamics of the system is found Given the state space representation Document Number 644 Revision 2 1 Page 22 3 DOF Helicopter Reference Manual d Ta Ax Bu 2 and d F Cy Du 3 the state vector for the 3 DOF Helicopter is defined T 9 0 9 4 x gt gt Es a gt E 3 Em eee Mer ay 4 and the output vector is y esp 5 where the variables p and are the elevation pitch and travel angles The corresponding helicopter state space matrices as derived in the Maple worksheet are 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 de 0 0 0 000 0 0 0000 6 L m 2L m amp 0 5 gt 5 0000 mL 2m L 2m L ie 0 0 0 0 0 0 L K L K a 2m L m L 2m L m L 7 1 To 2m L 2m L 0 0 fl 0 0 0 0 0 C 0 1 0 0 0 0 8 0 0 1 0 0 0 and ro 0 D 0 0 9 0 0 Document Number 644 Revision 2 1 Page 23 3 DOF Helicopter Reference Manual The model parameters used in the A B matrices are defined in Table 4 6 2 Control Design In this section a linear proportional integral derivative i e PID controller is designed to regulate the elevation and travel angles of the 3 DOF Helicopter to desired positions The PID control gains are computed using the Linear Quadratic Regular algorithm The state feedback controller entering the front motor Vr and the back motor V is defined si op y Kpp Xq x Vos 10 b op where kia Aya 3 Aa fis 6 Gane 11 PD ky 1 kaa ka3 k
29. r Front Motor D A 0 DC motor propeller Cable of gain 5 connector 4 Back UPM To 3 DOF Helicopter Power leads to the 3 DOF Helicopter s back Load connector Back Motor D A 1 DC motor propeller Cable of gain 5 connector 5 3 DOF Helicopter Terminal Board 3 DOF Helicopter s travel angle feedback Travel Encoder Encoder Channel 0 signal to the data acquisition card ENC 0 connector 6 3 DOF Helicopter Terminal Board 3 DOF Helicopter s pitch angle feedback Pitch Encoder Encoder Channel 1 signal to the data acquisition card ENC 1 connector Document Number 644 Revision 2 1 Page 17 A 3 DOF Helicopter Reference Manual Cable From Signal 3 DOF Helicopter Terminal Board 3 DOF Helicopter s elevation angle Elevation Encoder Channel 2 feedback signal to the data acquisition card Encoder ENC 2 connector Joystick X cable Back UPM S3 Joystick voltage signal along the X axis to connector the UPM Joystick Y cable Back UPM S4 Joystick voltage signal along the Y axis to connector the UPM Back UPM To A Terminal Board Joystick voltage signals along both X and D connector S1 to ADC 0 Y axes to the data acquisition terminal S2 to ADC 1 board through the UPM S3 to ADC 2 S4 to ADC 3 Table 6 3 DOF Helicopter system wiring summary 5 4 Additional Connections for the 3 DOF Helicopter w ADS The additional wiring needed to operate the Active Disturbance System is detailed in the section As before
30. rement which is represented by the variable p Connect the 5 pin stereo DIN to 5 pin stereo DIN cable from the Elevation Encoder connector on the 3 DOF Helicopter base to Encoder Input 2 on the terminal board This connection is illustrated in Figure 18 and Figure 19 by ID 7 It carries the elevation angle measurement If you are using the analog joystick shown in Figure 24 go to Step 11 If you are using are using the Logitech Attack 3 USB joystick shown in Figure 25 then connect the USB cable from the joystick to a USB port on the PC while it is running The system should detect the joystick and automatically install the driver you will be prompted See the Logitech Installation Manual for more information on the setup procedure Note that if the USB joystick is used then the analog connections shown in Figure 17 and the 5 pin DIN to 4xRCA cable connection shown in Figure 17 and Figure 18 are not needed and these cables would not be supplied Also the shaded connections listed in Table 6 can be ignored See Section 5 5 for more information on system requirements of the Logitech joystick and how to use the Rate Command knob To setup an analog joystick shown in Figure 24 connect its X analog cable to the S3 socket and its Y analog cable to the S4 socket on a UPM 2405 as shown in Figure 17 with cable 8 for X and cable 9 for Y Ensure the UPM is not powered when making this connection Connect the To A D socket on the UPM 2405 with the
31. riment has three encoders the encoder measuring the pitch of the helicopter body the encoder measuring the elevation of the body and the encoder measuring the travel of the body In quadrature mode the pitch and elevation encoders have a resolution of 4096 counts per revolution and the travel encoder has a resolution of 8192 counter per revolution Thus the effective position resolution is 0 0879 degrees about the pitch and elevation axes and 0 0439 degrees about the travel axis Document Number 644 Revision 2 1 Page 6 3 DOF Helicopter Reference Manual 4 1 2 Active Disturbance System Components The components of the Active Disturbance System ADS on the 3 DOF Helicopter system is labeled in figures 6 7 and 8 and the described in Table 2 and Table 3 Description Description ADS Motor 23 ADS Encoder Active Disturbance Mass 24 ADS Motor Connector Lead screw 25 ADS Encoder Connector Table 3 Additional components on the 3 DOF Helicopter ADS experiment Figure 6 Connectors on base of 3 DOF Helicopter ADS Figure 7 t DOF Helicopter ADS experiment ADS motor connector side view a e di experiment ADS encoder side view Document Number 644 Revision 2 1 Page 7 3 DOF Helicopter Reference Manual Figure 8 Components of the Active Disturbance System ADS on the 3 DOF Helicopter 4 2 System Specifications The 3 DOF Helicopter system specifications are given in Section 4 2 1 and the Active Disturbance
32. s strain on the actuator 7 2 Controller Implementation 7 2 1 Objectives e Implement the controller designed in Section 6 2 using QuaRC to control the position 3 DOF Helicopter 7 2 2 Procedure 3 DOF Helicopter Follow the steps described below to implement the designed controller in real time and observe its effect on the actual 3 DOF Helicopter plant l 2 Load Matlab Open Simulink model g_heli3d mdl shown in Figure 28 that implements a sample LQR controller The model runs your actual 3 DOF Helicopter plant by directly interfacing with your hardware through the QuaRC blocks described in Reference 2 Document Number 644 Revision 2 1 Page 27 3 DOF Helicopter Reference Manual q_heli3d File Edit View Simulation Format Tools WinCon QuaRC Help D e Hg P gt Be lint External y e Quanser 3 DOF Helicopter Progam Ed Closed loop Actual System Joystick 2 Desired Angle from Program Des Position Multiport Rate Limiter Desired Position Switch trom Joystick 3 DOF HELI 3 DOF Helicopter Scopes Wop LQR Controller 100 Figure 28 Simulink model q_heli3d_q8 implements the LOR controller on actual 3 DOF Helicopter system 3 Configure setup script Open the design file setup lab_heli_3d m and ensure everything is configured properly NOTE Make sure the WITH_ADS parameter in the setup_lab_heli_3d m file is set to NO This indicates to the automatically designed controller that the active
33. ses given a joystick position can be changed using the K JOYSTICK X andK JOYSTICK Y variables that are set in the setup lab heli 3d m script file A CAUTION Do not switch from the Program to the Joystick from 1 to 2 when the controller is running Set the program joystick switch to 2 before starting QuaRC if the joystick is to be used 16 Click on the Stop button on the Simulink diagram tool bar or select Quarc Stop from the menu to stop running the code 17 Power off the two UPMs 8 References 1 Quanser 03 04 08 User Manual 2 Quanser QuaRC Help Files 3 Quanser QuaRC Installation Manual Document Number 644 Revision 2 1 Page 34 3 DOF Helicopter Reference Manual 4 Quanser UPM User Manual 5 Pittman Pittman LO COG DC Servo Motor Series 8000 9000 and 14000 Document Number 644 Revision 2 1 Page 35
34. t the 5 pin stereo DIN to 5 pin stereo DIN cable from the 4DS Encoder connector on Document Number 644 Revision 2 1 Page 18 3 DOF Helicopter Reference Manual the 3 DOF Helicopter base to Encoder Input 3 on the terminal board as depicted by connection 13 in Figure 21 and Figure 22 This carries the angular measurement of the ADS lead screw This measurement is then translated to give the linear position of the disturbance mass and is denoted by the variable x o Test Points E A S1 8 s2 rom A gt a Analg oo o oe o Sensors gt a C AAA UPM 1503 120 VAC ON Figure 20 Connections on UPM 1503 used for N ADS motor Figure 21 Q8 Terminal Board connections when using ADS Document Number 644 Revision 2 1 Page 19 3 DOF Helicopter Reference Manual Figure 22 Connections on base of 3 DOF Helicopter Figure 23 Connections on base of 3 DOF Helicopter ADS ADS encoder side view ADS ADS motor connector sidie view Signal 11 Terminal Board ADS UPM From D A Control signal to the ADS Analog Output 3 connector 12 ADS UPM To 3 DOF Helicopter Power leads to the 3 DOF Helicopter s ADS Load connector ADS Motor D A 3 DC motor Cable of gain 3 connector 13 3 D
35. the position of the helicopter is described 6 1 Modeling The free body diagram of the 3 DOF Helicopter is illustrated in Figure 26 and accompanies the Maple worksheet named 3 DOF Helicopter Equations mws or its HTML equivalent 3 DOF Helicopter Equations html The equations can be edited and re calculated by executing the worksheet using Maple 9 Document Number 644 Revision 2 1 Page 21 3 DOF Helicopter Reference Manual Pitch axis F b p gt 0 Back Motor Fr Front Motor Travel axis Counterweight y Elevation y axis Mw g Figure 26 Free body diagram of 3 DOF Helicopter The worksheet goes through the kinematics of the system Thus describing the front motor back motor helicopter body and counterweight relative to the base coordinate system shown in Figure 26 These resulting equations are used to find the potential energy and translational kinetic energy of the front motor back motor and counterweight of the system The thrust forces acting on the elevation pitch and travel axes from the front and back motors are defined and made relative to the quiescent voltage or operating point 1 8 L my L ia L m op 2 LK A a f where all these parameters are defined in Table 4 Using the Euler Lagrange formula the nonlinear equations of motion of the 3 DOF Helicopter system are derived These equations are linearized about zero and the linear state space model A B C D describing the voltage to angular joint p
36. travel deg and Vm V scopes in the Scopes folder These scopes display both the desired and measured angles of the Helicopter as well as the voltages being applied to the front and back motors CAUTION Make sure the motor voltages do not switch between negative and positive often Having the controller go across the 0 V line often can cause damage to the amplifiers Document Number 644 Revision 2 1 Page 29 3 DOF Helicopter Reference Manual 10 11 12 13 14 15 16 17 18 Ensure the helicopter has been setup and all the connections have been made as instructed in Section 5 Turn the power of the two Universal Power Amplifiers on The red LED on the upper left corner of the each UPM should be lit In the g_heli3d Simulink diagram make sure the Program Joystick block shown in Figure 28 is set to 1 in order to generate the desired angle from Simulink Select Quarc Start to begin running the controller The motors should begin running and the two propellers should start turning lightly NOTE Click on the STOP button on the Simulink tool bar at any time to stop running the controller Initially the helicopter elevation angle is 27 5 degrees Set the desired elevation angle to 10 degrees by setting the Constant Elevation deg slider gain block which is found in the Desired Angle from Program subsystem to 10 degrees The helicopter should now be stabilized slightly above its horizontal The green plot
37. ts linear equations of motion model and a position controller Simulink file that implements the real time state feedback LQR controller for the 3 DOF Helicopter system The zz suffix denotes the data acquisition board used for example the q4 or q8 Table 1 Files supplied with the 3 DOF Helicopter experiment Document Number 644 Revision 2 1 Page 3 3 DOF Helicopter Reference Manual 4 System Description The following is a listing of the major hardware components used for this experiment e Power Amplifier Two Quanser UPM 2405 or equivalent e Data Acquisition Board Quanser Q3 Q4 Q8 or equivalent e Helicopter Plant Quanser 3 DOF Helicopter aerospace experiment with or without the Active Disturbance System ADS e Real time control software PC equipped with QuaRC Simulink configuration See the references listed in Section 8 for more information on these components 4 1 Components Section 4 1 1 lists the components on the 3 DOF Helicopter plant and Section 4 1 2 describes the components on the 3 DOF Helicopter device with the Active Disturbance System ADS 4 1 1 3 DOF Helicopter Components The components comprising the 3 DOF Helicopter system are labeled in figures 3 4 and 5 are described in Table 2 The motors propeller assemblies and encoders are described in more detail below S Description Description Helicopter body Slip ring Motor Base Front propeller assembly Ball bearing block Back propel
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