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1. QNET VTOL Current Control vi Control the current in the propeller motor QNET VTOL Modeling vi Validate transfer function model and identify system pa rameters QNET_VTOL_Flight_Control vi Control the pitch of the VTOL device using PID Table 5 1 Files supplied with the QNET VTOL Laboratory 5 2 Current Control Laboratory VI The VTOL Current Control VI shown in Figure 5 1 and Figure 5 2 is used to feed an open loop voltage or current to the QNET VTOL Trainer The VI when in current mode is shown in Figure 5 1 In this mode a current controller is used to regulate the current in the motor and the user chooses the reference current In voltage mode shown in Figure 5 2 the voltage chosen is applied directly to the QNET amplifier which in turn drives the motor As a quick VI description Table 5 2 lists and describes the main elements of the QNET VTOL Current Control VI Every element is uniquely identified by an ID number located in Figure 5 1 and Figure 5 2 for both current and voltage mode P 09 QNET_VTOL_Current_Control vi File Edit View Project Operate Tools Window Help QNET VTOL Current Control Lot 5 L Device Sampling Rate Hz NATIONA INSTRUMENTS oei Jesoo 13 14 Pitch deg Digital Scopes 1 eoon M amp S Current 2 Voltage Current Control ON ON Current Setpoint Signal Type a 6 7 Amplitude 3 0 10 peany Josa 40 Offset 92 10 210 A 9 Current Control Para2. 11 Click on the Stop button to stop running the VI 5 GUANSER 4 4 Lab 2 PID Steady State Error Analysis 4 4 1 Pre Lab Exercises 1 Calculate the VTOL Trainer steady state error when using a PID controller Enter the value in Table 4 1 4 4 2 In Lab Experiment 1 Go through steps 1 8 in Section 4 3 2 to run the PD controller 2 In the Position Control Parameters section increment the integral gain until you reach k 4 0 A rad s 3 Capture the VTOL Trainer step response when using a PID controller and measure the steady state error Enter the measured PID steady state error value in Table 4 1 How does it compare with the computed value in Section 4 4 1 4 To stop the control in the Signal Generator section set Amplitude rad to 0 rad and slowly decrement Offset rad to 8 0 rad 5 Click on the Stop button to stop running the VI 4 5 Lab 3 PID Control Design 4 5 1 Pre Lab Exercises 1 Find the natural frequency wn and damping ratio required to meet a peak time of 1 0 seconds and a percent overshoot of 20 Enter the value in Table 4 1 2 Calculate the PID gains kp ki and k needed to meet the VTOL Trainer specifications Enter the value in Table 4 1 4 5 2 In Lab Experiment 1 Open the QNET_VTOL_Flight_Control vi as shown in Section 5 4 Make sure the correct Device is chosen 2 Make sure that the VTOL counter weight is placed as far from the propeller assembly as possible without lifting the
3. Wpolwnd w2 J kp K ki pow J K k B poJ 2wnJ Ki 4 2 Flight Control Virtual Instrument The virtual instrument used to run the flight controller on the QNET VTOL trainer is shown in Figure 4 3 11 QNET_VTOL_Flight_Control vi File Edit View Project Operate Tools Window Help gt am Q QNET VTOL Flight Control NATIONAL _ Device Sampling Rate Hz INSTRUMENTS a7 E Jps0 0 QGUANSER Pitch deg 10 preen Position 42 z Ho Current 2 4 A Voltage 7 0 y Postion Sepo a Signal Type A Amplitude 2 00 deg Frequency Joss He 104 panne r 1 1 1 i Offset 2 00 deg 10 0 110 120 130 140 150 160 Position Control Parameters Current A en kp E 1 50 Ajrad aoo Af tad s kd Joo A sjrad Current Control Parameters kee fo 2s0 wa ke gio vas VTOL Offset deg Jeso lt Figure 4 3 LabVIEW virtual instrument used to run VTOL trainer flight control OS Q QNET VTOL Workbook Student Version QUANSER 4 6 4 7 4 8 v 1 0 4 3 Lab 1 PD Steady State Analysis 4 3 1 Pre Lab Exercises 1 Calculate the theoretical VTOL Trainer steady state error when using a PD control with k 2 and kg 1 and a step amplitude of Ro 4 0 degrees Enter the value in Table 4 1 4 3 2 In Lab Experiment 1 Open the QNET_VTOL_Flight_Control vi as shown in Section 5 4 Make sure the correct Device is chosen 2 Make sure that the VTOL c
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5. cascade control implemented in the VTOL trainer is depicted in Figure 2 1 below A PI current controller the inner loop is designed to regulate the current inside the motor according to a desired current reference This current reference is generated from the outer loop controller a PID compensator that controls the pitch of the VTOL trainer VTOL Actuator Control Figure 2 1 VTOL trainer cascade control system 2 1 2 Current Control In cases where the actuator has relatively slow dynamics such as an electromagnet with a large inductance it is favorable to design a current controller Typically a proportional integral compensator is used to regulate the current flowing in the load This basically makes the actuator dynamics negligible and simplifies the control design of the outer loop In this case the voltage current relationship of the VTOL trainer motor can be described in the time domain by the equation Um Rm im Lmim and by the transfer function Vin s Sd aa a ar Figure 2 2 shows the VTOL current control system implemented The PI compensator computes the voltage nec essary to reach the desired current Using the PI controller Um t kp cliref t im t kae f inert im t dt Q BUANSER Figure 2 2 VTOL motor PI current control loop we obtain the following closed loop transfer function kp cs T Kine G Treg lm s 82 Lm kpe Rm s lig To match the standard second order
6. is chosen 2 Make sure that the VTOL counter weight is placed as far from the propeller assembly as possible without lifting the propeller itself The base of the propeller assembly should rest lightly on the surface of the QNET board as shown in Figure 3 3 oO Inthe Current Control Parameters section set the PI current gains found in Section 2 5 4 Inthe Current Setpoint section set Amplitude 0 00 A Frequency 0 20 Hz e Offset I equilibrium current found in Section 3 3 o Run the VI O Let the VTOL Trainer stabilizes about the horizontal 7 In the Current Setpoint section set Amplitude 0 10 A 8 In the Transfer Function Simulation Parameters section enter the parameters computed in Section 3 5 1 Is the simulation matching the measured signal Capture the response 9 Click on Stop button to stop the VI 3 6 Lab 4 Using the System Identification Tool 1 Ensure the QNET VTOL Modelling VI is open and configured as described in Section 5 3 Make sure the correct Device is chosen Q GUANSER 2 Make sure that the VTOL counter weight is placed as far from the propeller assembly as possible without lifting the propeller itself The base of the propeller assembly should rest lightly on the surface of the QNET board as shown in Figure 3 3 3 in the Current Setpoint section set Amplitude 0 10 A Frequency 0 20 Hz e Offset Teq equilibrium current found in Section 3 3 which shoul
7. propeller itself The base of the propeller assembly should rest lightly on the surface of the QNET board as shown in Figure 4 4 3 Run the VI 4 Inthe Position Setpoint section set Amplitude 0 0 deg Frequency 0 15 Hz Offset 0 0 deg 5 In the Position Control Parameters section enter the PID gains found in Section 4 5 1 6 Let the VTOL system stabilize about the 0 0 rad setpoint Examine if the VTOL Trainer body is horizontal If not then you can adjust the pitch offset by varying the VTOL Offset control By default this is set to 25 0 degrees 7 Inthe Position Setpoint section set OS Amplitude 2 0 deg Frequency 0 40 Hz e Offset 2 0 deg The VTOL Trainer should be going up and down and tracking the square wave setpoint 8 Capture the response of the VTOL system when using your designed PID controller 9 Measure the peak time and percent overshoot of the measured response Enter the values in Table 4 1 Are the VTOL Trainer response specifications satisfied 10 If the specifications were not given what could be done to improve the response 11 To stop the control in the Signal Generator section set Amplitude rad to 0 rad and slowly decrement Offset rad to 8 0 rad 12 Click on the Stop button to stop running the VI 4 6 Results Parameters Symbol Value Units PD steady state error ss pd deg Measured PD steady state error ess meas pd deg P
8. the VTOL counter weight is placed as far from the propeller assembly as possible without lifting the propeller itself The base of the propeller assembly should rest lightly on the surface of the QNET board as shown in Figure 3 3 QUANSER po O o A O 10 Figure 3 3 VTOL initial position Set the Current Control ON switch to ON Run the VI Inthe Current Control Parameters section set the PI current gains found in the first part of Section 2 5 Inthe Current Setpoint section set Amplitude 0 00 A e Frequency 0 40 Hz Offset 1 00 A Gradually increase the offset current until the VTOL Trainer is horizontal The pitch should read 0 degrees when the VTOL Trainer is horizontal You may need to adjust the pitch offset by varying the VTOL Offset control By default this is set to 25 0 degrees The current required to make the VTOL Trainer horizontal is called the equilibrium current Teq Capture the pitch and current response and record this current Click on Stop button to stop the VI 3 4 Lab 2 Find Natural Frequency 1 Ensure the QNET VTOL Current Control VI is open and configured as described in Section 5 2 Make sure the correct Device is chosen Make sure that the VTOL counter weight is placed as far from the propeller assembly as possible without lifting the propeller itself The base of the propeller assembly should rest lightly on the surface of the QNET board as shown in Fig
9. ID steady state error ss pid deg Measured PID steady state error ess meas pid deg Desired peak time ty 1 0 S Desired percentage overshoot PO 20 0 Desired pole location Po 1 0 rad s Natural frequency Wy rad s Damping ratio Proportional gain kp Alrad Integral gain kp Al rad s Derivative gain kv A s rad Measured peak time tp s Measured percentage overshoot PO Table 4 1 VTOL Trainer control results summary A BUANSER 5 SYSTEM REQUIREMENTS Required Hardware e NI ELVIS II Quanser QNET Vertical Take off and Landing VTOL See QNET VTOL User Manual 1 Required Software NI LabVIEW 2011 or later NI DAQm x 9 3 5 or later NI LabVIEW Control Design and Simulation Module 2011 or later ELVIS II Users ELVISmx 4 3 or later installed from ELVIS II CD E Caution If these are not all installed then the VI will not be able to run Please make sure all the software and hardware components are installed If an issue arises then see the troubleshooting section in the QNET VTOL User Manual 1 5 1 Overview of Files File Name Description QNET VTOL User Manual pdf This manual describes the hardware of the QNET Vertical Take off and Landing system and how to setup the system on the ELVIS QNET VTOL Lab Manual Student pdf This laboratory guide contains pre lab questions and lab experiments demonstrating how to design and implement controllers on the QNET VTOL system LabVIEW
10. NATIONAL IV INSTRUMENTS QUANSER STUDENT WORKBOOK QNET VTOL Trainer for NI ELVIS Developed by Quanser Curriculum designed by Jacob Apkarian Ph D Quanser Paul Karam B A SC Quanser Michel L vis M A SC Quanser Peter Martin M A SC Quanser Curriculum complies with ABET ABET Inc is the recognized accreditor for college and university programs in applied science computing engineering and technology Among the most respected accreditation organizations in the U S ABET has provided leadership and quality assurance in higher education for over 75 years 2011 Quanser Inc All rights reserved Quanser Inc 119 Spy Court Markham Ontario L3R 5H6 Canada info quanser com Phone 1 905 940 3575 Fax 1 905 940 3576 Printed in Markham Ontario For more information on the solutions Quanser Inc offers please visit the web site at http www quanser com This document and the software described in it are provided subject to a license agreement Neither the software nor this document may be used or copied except as specified under the terms of that license agreement All rights are reserved and no part 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 written permission of Quanser Inc Acknowledgements Quanser Inc would like to thank the following contributors Dr Hakan Gu
11. PID response plot from Step 8 in Section 4 5 2 4 Provide applicable data collected in this laboratory from Table 4 1 lll ANALYSIS Provide details of your calculations methods used for analysis for each of the following 1 VTOL Trainer response characteristics in Step 9 in Section 4 5 2 2 Improvements to the flight controller in Step 10 in Section 4 5 2 IV CONCLUSIONS Interpret your results to arrive at logical conclusions for the following 1 How does the measured steady state PD error compare to the computed value in 9 in Section 4 3 2 2 How does the measured steady state PID error compare to the computed value in 3 in Section 4 4 2 3 Are the VTOL Trainer response specifications satisfied in Step 9 of Section 4 5 2 5 BUANSER 6 4 Tips for Report Format PROFESSIONAL APPEARANCE Has cover page with all necessary details title course student name s etc Each of the required sections is completed Procedure Results Analysis and Conclusions Typed All grammar spelling correct Report layout is neat Does not exceed specified maximum page limit if any Pages are numbered Equations are consecutively numbered Figures are numbered axes have labels each figure has a descriptive caption Tables are numbered they include labels each table has a descriptive caption Data are presented in a useful format graphs numerical table charts diagrams No hand drawn sketches diagrams References are cited
12. Sampling Rate Wm Sets the sampling rate of the VI Hz 15 Stop Vin Stops the LabVIEW VI from running 16 Scopes Pitch Wm Scope with measured in red VTOL pitch deg position 17 Scope Current Te Scope with reference current in blue A and measured current in red Table 5 2 Components of QNET VTOL Current Control VI 5 3 Modeling Laboratory VI This VI is used for model validation and parameter identification and is shown in Figure 5 3 A transfer function is ran in parallel with the actual system and enables users to confirm whether their derived model is correct Using the LabVIEW System Identification Toolkit the VTOL Trainer transfer function model can be identified automatically by collecting the measured stimulus i e current and response i e measured pitch angle signals and specifying the order of the transfer function process model The main components of the QNET VTOL Modeling VI front panel are listed and described in Table 5 3 Every element is given an ID number which is used to uniquely identify the VI components in Figure 5 3 0 520656 0 106808s 0 03928605 1 ys u s Figure 5 3 QNET VTOL Modeling VI QNET VTOL Workbook Student Version INNOVATE EDUCATE ID Label Symbol Description Unit 1 Position 0 Pitch position numeric display deg 2 Current Im Motor armature
13. Viscous damping B N m s rad Natural frequency Wn rad Stiffness K N m rad Sys ID Torque thrust constant Kiia N m A Sys ID Viscous damping Bia N m s rad Sys ID Stiffness Ki N m rad Table 3 1 VTOL Trainer modeling results summary 4 FLIGHT CONTROL 4 1 Background 4 1 1 Steady state Error Analysis Steady state error is the difference between the reference and output signals after the system response has settled Thus for a time t when the system is in steady state the steady state error equals Ess Tss t _ Yss t 4 1 where rss is the value of the steady state reference and yss is the steady state value of the process output The block diagram shown in Figure 4 1 is a general unity feedback system with a compensator C s and a transfer function representing the plant P s The measured output Y s is supposed to track the reference signal R s and the tracking has to yield to certain specifications Compensator Plant Figure 4 1 Unity feedback system The error of the system shown in Figure 4 1 is and by solving for E s the resulting closed loop transfer function R s KEE C s P s is obtained The error transfer function of the VTOL trainer when subject to a step of and using the PID compensator ki C s kp kas m Q BUANSER Ro ki kp kas Ky s 14 B K 1 824 35 5 If the transfer function is stable then the steady state error can be found
14. characteristic equation s 2Cwns w2 2 1 we need a proportional gain of kp Rm 2lwn Lm 2 2 and an integral gain of bp iin 2 3 These gains can then be designed according to a desired natural frequency wn and damping ratio C 2 2 Current Control Virtual Instrument In this laboratory open loop voltage or current is fed to the VTOL trainer In current mode shown in Figure 2 3 a current controller is used to regulate the current in the motor and the user chooses the reference current In voltage mode shown in Figure 2 4 the voltage chosen is applied directly to the QNET amplifier which in turn drives the motor b 09 QNET_VTOL_Current_Control vi File Edit View Project Operate Tools Window Help QNET VTOL Current Control PONTMars rer jae Pitch deg Digital Scopes Position bs Current bs A Voltage y Current Control ON ON Current Setpoint Signal Type m Amplitude E 0 20 Fremen Afaa He Offset 0 50 SO Current Control Parameters kpe 50 250 VIA ke gfioo was YTOL Offset deg Jeo amp 09 QNET_VTOL_Current_Control vi File Edit View Project Operate Tools Window Help amp n a QNET VTOL Current Control NATIONAL Device Sampling Rate Hz BYINSTRUMENTS Bom m Jesoo Pitch deg GUANSER Digital Scopes Position deg Current 1 7 A Voltage 51 y Current Control ON Open loop Yoltage 40 50 6 0 30 esti ng YTOL Off
15. current numeric display A 3 Voltage Vin Motor input voltage numeric display V 4 Signal Type Type of signal generated for the current reference 5 Amplitude Current setpoint input box A 6 Frequency Current setpoint frequency input box Hz 7 Offset Current setpoint offset input box A 8 kp_c kpc Current control proportional gain V A 9 ki_c kig Current control integral gain Vcdots A 10 VTOL Offset Pitch calibration deg 11 Transfer Func Transfer function used for simulation tion Simulation Parameters 12 Simulation Trans Displays the transfer function begin sim fer Function ulated 13 Order of Estimated Order of transfer function to be estimated Model using the System Identification Toolkit 14 Estimated Transfer Transfer function estimated using the Function System Identification Toolkit 15 Device Selects the NI DAQ device 16 Sampling Rate Sets the sampling rate of the VI Hz 17 Stop Stops the LabVIEW VI from running 18 Scope Pitch 0 Scope with simulated position in blue deg and measured VTOL pitch position in red 19 Scope Current Im Scope with reference current in blue A and measured current in red Table 5 3 QNET VTOL Modeling VI Components 5 4 Flight Control Laboratory VI The QNET VTOL Flight Control VI runs the PID based cascade control system which is described in Section 2 1 1 to control the position of the VTOL pitch Table 5 4 lists and describes the main elements of the QNET VTOL Flight Control VI and every elemen
16. d perturb the VTOL Trainer is about its horizontal equilibrium point with a current amplitude of 0 10 A as described by steps 4 10 in Section 3 5 4 Let the VI run for at least 20 seconds 5 Click on Stop button to stop the VI When the VI is stopped the Estimated Transfer Function displays a newly identified transfer function of the VTOL system based on the last 20 seconds of current i e stimulus signal and pitch angle i e response signal data Enter the identified transfer function Enter the identified TF parameters into the Transfer Function Simulation Parameters section Go through steps 7 10 in Section 3 5 That is bring the VTOL Trainer up to 0 degrees and then feed 0 1 A oO ao N Q In the Transfer Function Simulation Parameters section enter the parameters computed using the System Identification Tool How is the simulation matching the measured signal compared to the transfer function with the manually estimated parameters Capture the response 10 Click on Stop button to stop the VI 11 Assume the moment of inertia is as calculated in Section 3 5 Then from the identified transfer function find the stiffness K d the viscous damping B d and the current torque constant K 4 How do they compare with the parameters you estimated manually 3 7 Results Parameters Symbol Value Units Equilibrium current Leq A Torque thrust constant Ki N m A Moment of inertia J kg m
17. e laboratory the parameters are first found man ually by performing a few experiments and taking measurements Thereafter the LabVIEW System Identification Toolkit is used to automatically find the model This demonstrates how to use software tools to identify parameters or even entire models especially important for higher order systems The modeling is then validated by running the obtained model in parallel with the actual system 3 1 1 Torques Acting on the VTOL The free body diagram of a 1 DOF Vertical Take Off and Landing device that pivots about the pitch axis is shown in Figure 3 1 Propeller Actuator Counter Weight Figure 3 1 Free body diagram of 1 DOF VTOL As shown in Figure 3 1 the torques acting on the rigid body system can be described by the equation 1 Te M2 g l2 cos A t m gl cos O t 5 mn g Ln cos O t 0 3 1 The thrust force F is generated by the propeller and acts perpendicular to the fan assembly The thrust torque is given by Tt Fi ly 3 2 Q ABUANSER where l is the length between the pivot and center of the propeller as depicted in Figure 3 1 In terms of the current the thrust torque equals Tt Ky Tri 3 3 where K is the thrust current torque constant With respect to current the torque equation becomes 1 K Im Mo g l2 cos 0 t m g l cos 0 t 5 mn g Ln cos O t 0 3 4 The torque generated the propeller and the gravitational torque acting of
18. evice 15 Sampling Rate Sets the sampling rate of the VI Hz 16 Stop Stops the LabVIEW VI from running 17 Scope Pitch 0 Scope with reference position in blue deg and measured VTOL pitch position in red 18 Scope Current Tin Scope with reference current in blue A and measured current in red Table 5 4 QNET VTOL Flight Control VI Components O BUANSER 6 LAB REPORT This laboratory contains three groups of experiments namely 1 Current Control 2 Modeling and 3 Flight Control For each experiment follow the outline corresponding to that experiment to build the content of your report Also in Section 6 4 you can find some basic tips for the format of your report 6 1 Template for Content Current Control I PROCEDURE 1 Finding Resistance Briefly describe the main goal of the experiment Briefly describe the experimental procedure in Step 6 in Section 2 3 2 Qualitative Current Control Briefly describe the main goal of the experiment Briefly describe the experimental procedure in Step 7 in Section 2 4 Effect of eliminating integral gain in Step 7 in Section 2 4 Effect of eliminating proportional gain in Step 9 in Section 2 4 3 Current Control Design Briefly describe the main goal of this experiment Briefly describe the experimental procedure in Step 7 in Section 2 5 2 ll RESULTS Do not interpret or analyze the data in this section Just provide the re
19. f The base of the propeller assembly should rest lightly on the surface of the QNET board as shown in Figure 2 5 QNET VTOL Workbook Student Version 3 Set the Current Control ON switch to ON 4 Run the QNET VTOL Current Control vi 5 In the Current Setpoint section set Amplitude 0 20 A Frequency 0 40 Hz Offset 0 90 A 6 In the 6 Control Parameters section set the PI current gains to kpc 0 250 a kic 10 The VTOL Trainer propeller should begin turning at various speeds according to the current command Exam ine the reference and measured current response obtained in the Current A scope They should be tracking as shown in Figure 2 3 7 Show and explain the effect of not having any integral gain Attach a sample response 8 In the Control Parameters section set the PI current gains to e kp c 0 e kic 100 9 Show and explain the effect of not having any proportional gain Attach a sample response 10 Click on Stop button to stop the VI 2 5 Lab 3 Current Control Design 2 5 1 Pre Lab Exercises 1 Calculate the PI gains k and k necessary to satisfy the natural frequency and damping ratio specifications wn 42 5 rad s e 0 70 To compute the gains you will need the resistance found in Section 2 3 and assume the inductance of the motor is Lm 53 8 mH 2 5 2 In Lab Experiment 1 Open the QNET_VTOL_Current_Control vi as shown in Section 5 2 Make sure the correct Device i
20. he natural frequency of the system one can find the stiffness using Kau J 3 10 3 2 Modeling Virtual Instrument The virtual instrument used to validate a transfer function model on the QNET VTOL trainer is shown in Figure 3 2 This VI can also be used to find the VTOL device transfer function using the System Identification Toolkit 12 QNET_VTOL_Modeling vi File Edit View Project Operate Tools Window Help Q QNET VTOL Modeling G NATIONAL Device z Sampling Rate Hz INSTRUMENTS evi E 250 0 BANS Er Pitch deg 20 Digital Scopes Transfer Function Simulation 1 Parameters T z pan Position deg Numerator Current 2 2 a 5 Voltage 6 5 y Denominator 20 1 Cuprent Setpoint Sa 50 SM s 2 sj f Signal Type Ga Simulation Transfer Function z 30 2 Amplitude ffo10 a 45420 SCC NOUS Frequency 0 25 Hz r SAG A Order of Estimate Model ca ae T H Seen rrent A fi 3 0 2 Current Control Paramet z USL lel den order ar f kpe 0 250 vja 2 y aaa kic al 100 VKA s Estimated Transfer Function YTOL Offset deg 25 0 Figure 3 2 LabVIEW virtual instrument used to find and validate a model for the QNET VTOL trainer 3 3 Lab 1 Measure the Equilibrium Current 1 Ensure the QNET VTOL Current Control VI is open and configured as described in Section 5 2 Make sure the correct Device is chosen 2 Make sure that
21. ition of the weight to be changed which in turn affects the dynamics of the system The arm assembly pivots about a rotary encoder shaft The VTOL pitch position can be acquired from this setup Some examples of real world VTOL devices are helicopters rockets balloons and harrier jets Aerospace devices are typically more difficult to model Usually this will involve using software system identification tools to determine parameters or actual dynamics Due to their inherent complexity flight systems are usually broken down into different subsystems to make it more manageable These subsystems can be dealt with individually and then integrated to provide an overall solution Figure 1 1 QNET Vertical Take off and Landing Trainer VTOL There are three experiments current control modeling and flight control The experiments can be performed independently Topics Covered Experimental Modelling e PID Control Current Control e Pitch Control Prerequisites In order to successfully carry out this laboratory the user should be familiar with the following Transfer function fundamentals e g obtaining a transfer function from a differential equation e Using LabVIEW to run VIs QNET VTOL Workbook Student Version 2 CURRENT CONTROL 2 1 Background 2 1 1 Cascade Control The VTOL device is broken down into two subsystems the voltage current dynamics of the motor and the current position dynamics of the VTOL body The
22. meters ef fJo 2s0 250 VIA 1 0 ke fo va 247 YTOL Offset deg j 12 Figure 5 1 QNET VTOL Current Control VI when in open loop current mode P 09 QNET_VTOL_Current_Control vi File Edit View Project Operate Tools Window Help QNET VTOL Current Control 11 5 Device Sampling Rate Hz NATIONAL BYINSTRUMENTS ag Jesoo 1 4 Pitch deg 1 Digital Scopes 1 Poston EEE ceo Current po a 2 vore Ny Current Control ON A 4 Open loop Yoltage u u i 40 5 0 6 o 10 0 11 0 120 130 14 0 Current A 3 Figure 5 2 QNET VTOL Current Control VI when in open loop voltage mode S QNET VTOL Workbook Student Version QUANSER BDR ID Label Symbol Description Unit 1 Position 0 Pitch position numeric display deg 2 Current Im Motor armature current numeric display A 3 Voltage Vin Motor input voltage numeric display V 4 Current Control Turns current control on and off ON 5 Open loop Voltage Input motor voltage to be fed V 6 Signal Type Type of signal generated for current ref erence 7 Amplitude Current setpoint amplitude input box A 8 Frequency Current setpoint frequency input box Hz 9 Offset T Current setpoint offset input box A 10 kp_c Current control proportional gain VIA 11 ki_c Current control derivative gain V s A 12 VTOL Offset Pitch calibration deg 13 Device Selects the NI DAQ device 14
23. ounter weight is placed as far from the propeller assembly as possible without lifting the propeller itself The base of the propeller assembly should rest lightly on the surface of the QNET board as shown in Figure 4 4 Boe Gy lt gt 1A CAEV Figure 4 4 VTOL initial position 3 Run the VI 4 Inthe Position Setpoint section set Amplitude 0 0 deg e Frequency 0 15 Hz Offset 0 0 deg 5 In the Position Control Parameters section set e kp 1 0 A rad ki 2 A rad s e kd 1 0 A s rad 6 Let the VTOL system stabilize about the 0 0 rad setpoint Examine if the VTOL Trainer body is horizontal If not then you can adjust the pitch offset by varying the VTOL Offset control By default this is set to 25 0 degrees 7 To use a PD control in the Position Control Parameters section set e kp 2 0 A rad ki 0 A rad s e kd 1 0 A s rad QNET VTOL Workbook Student Version Saree 8 In the Position Setpoint section set Amplitude 2 0 deg Frequency 0 40 Hz Offset 2 0 deg The VTOL Trainer should be going up and down and tracking the square wave setpoint 9 Capture the VTOL device step response when using this PD controller and measure the steady state error Enter the measured PD steady state error value in Table 4 1 How does it compare with the computed value in Section 4 3 1 10 In the Signal Generator section set Amplitude rad to 0 rad and slowly decrement Offset rad to 8 0 rad
24. rocak Washington State University Vancouver USA for his help to include embedded outcomes assessment and Dr K J str m Lund University Lund Sweden for his immense contributions to the curriculum content Contents 1 2 O BUANSER Introduction Current Control 2 1 Background 2 2 Current Control Virtual Instrument 2 3 Lab 1 Finding Resistance 2 4 Lab 2 Qualitative Current Control 2 5 Lab 3 Current Control Design 2 6 Results Modeling 3 1 Background 3 2 Modeling Virtual Instrument 3 3 Lab 1 Measure the Equilibrium Current 3 4 Lab 2 Find Natural Frequency 3 5 Lab 3 Model Validation 3 6 Lab 4 Using the System Identification Tool 3 7 Results Flight Control 4 1 Background 4 2 Flight Control Virtual Instrument 4 3 Lab 1 PD Steady State Analysis 4 4 Lab 2 PID Steady State Error Analysis 4 5 Lab 3 PID Control Design 4 6 Results System Requirements 5 1 Overview of Files 5 2 Current Control Laboratory VI 5 3 Modeling Laboratory VI 5 4 Flight Control Laboratory VI Lab Report 6 1 Template for Content Current Control 6 2 Template for Content Modeling 6 3 Template for Content Flight Control 6 4 Tips for Report Format 31 32 33 34 1 INTRODUCTION The QNET vertical take off and landing VTOL trainer is shown in Figure 1 1 The system consists of a variable speed fan with a safety guard mounted on an arm At the other end of the arm an adjustable counterweight is attached This allows the pos
25. s cho sen 2 Make sure that the VTOL counter weight is placed as far from the propeller assembly as possible without lifting the propeller itself The base of the propeller assembly should rest lightly on the surface of the QNET board as shown in Figure 2 5 3 Set the Current Control ON switch to ON 4 Inthe Current Setpoint section set Amplitude 0 20 A e Frequency 0 40 Hz e Offset 0 90 A Q GUANSER 5 In the Current Control Parameters section set the PI current gains to those you found in Section 2 5 1 6 Run the VI The VTOL Trainer propeller should begin turning at various speeds according to the current com mand Examine the reference and measured current response obtained in the Current A scope They should be tracking 7 Include a plot showing the current response with your designed PI gains Compare the response to the quali tative responses in Section 2 4 8 Click on Stop button to stop the VI 2 6 Results Parameter Value Units Rm Ww Lm mH Wn rad s kpc V A kic VI A s Table 2 2 PI current control design summary 3 MODELING 3 1 Background Unlike a DC motor this system has to be characterized with at least a second order model The equation of motion is derived from first principles and then used to obtain the transfer function representing the current to position VTOL dynamics Various methods can be used to find the modeling parameters In th
26. set deg Jeo Figure 2 4 Virtual Instrument for VTOL voltage control Q GUANSER QNET VTOL Workbook Student Version 2 3 Lab 1 Finding Resistance 1 Ensure the QNET VTOL Current Control VI is open and configured as described in Section 5 2 Make sure the correct Device is chosen 2 Make sure that the VTOL counter weight is placed as far from the propeller assembly as possible without lifting the propeller itself The base of the propeller assembly should rest lightly on the surface of the QNET board as shown in Figure 2 5 an lt tA CABANE Figure 2 5 VTOL initial position 3 Run the QNET_VTOL_Current_Control vi 4 Set the Current Control ON switch to OFF 5 Set the Open loop Voltage knob to 4 0 V The VTOL Trainer propeller should begin turning as a voltage is applied to the motor 6 Vary the voltage between 4 0 and 8 0 V by steps of 1 0 V and measure the current at each voltage Input Voltage V Measured Current A Resistance w 4 NI O 01 Average Resistance Rm avg Table 2 1 QNET VTOL Finding Resistance 7 Click on Stop button to stop the VI 2 4 Lab 2 Qualitative Current Control 1 Ensure the QNET VTOL Current Control VI is open and configured as described in Section 5 2 Make sure the correct Device is chosen 2 Make sure that the VTOL counter weight is placed as far from the propeller assembly as possible without lifting the propeller itsel
27. sults 1 Current response plot from step 7 in Section 2 4 2 Current response plot from step 9 in Section 2 4 3 Current response plot from step 7 in Section 2 5 2 4 Provide applicable data collected in this laboratory from Table 2 2 IV CONCLUSIONS Interpret your results to arrive at logical conclusions for the following 1 How does the current response with tuned gains compare to the qualitative responses in Step 7 of Section 2 5 2 5 BUANSER 6 amp Template for Content Modeling I PROCEDURE 1 Measure the Equilibrium Current Briefly describe the main goal of the experiment Briefly describe the experiment procedure in Step 9 in Section 3 3 2 Find Natural Frequency Briefly describe the main goal of the experiment Briefly describe the experiment procedure in Step 7 in Section 3 4 3 Model Validation Briefly describe the main goal of the experiment e Briefly describe creating the model in Step 8 in Section 3 5 2 4 Using the System Identification Tool Briefly describe the main goal of the experiment Briefly describe creating the model in Step 6 in Section 3 6 ll RESULTS Do not interpret or analyze the data in this section Just provide the results 1 Pitch and current response from step 9 in Section 3 3 2 Equilibrium current step response from step 7 in Section 3 4 3 Transfer function response from step 9 in Section 3 4 4 Provide applicable data collected in this labora
28. t is uniquely identified by an ID number in Figure 5 4 11 QNET_VTOL_Flight_Control vi File Edit View Project Operate Tools Window Help DSO QNET VTOL Flight Control 16 Q J RSTRUMENTS pe g eaa 14 15 Pitch deg 10 Position 1 9 deg 1 Current 8 6 4 Voltage isa y A Position Setpoint 0 me Keio 9 a ic Amplitude Af200 deg 5 Frequency p e m 6 8 j 10 Offset 0 00 deg 7 Position Control Parameters Current A 9 0 500 8 z Jt d s 4 0 700 10 a Current Control Parameters S pe ozs vja Pi l 1 c J100 vita A 2 l YTOL Offset deg Jf os 0 1 3 e lt Figure 5 4 QNET VTOL Flight Control VI ID Label Symbol Description 1 Position 0 Pitch position numeric display 2 Current Im Motor armature current numeric display A 3 Voltage Vri Motor input voltage numeric display V 4 Signal Type Type of signal generated for the current reference 5 Amplitude Pitch setpoint input box A 6 Frequency Pitch setpoint frequency input box Hz 7 Offset Pitch setpoint offset input box A 8 kp kp Position control proportional gain Alrad 9 ki ki Position control integral gain Al rad s 10 kd ka Position control derivative gain A s rad 11 kp_c kpc Current control proportional gain V A 12 ki_c kie Current control integral gain Vcdots A 13 VTOL Offset Pitch calibration deg 14 Device Selects the NI DAQ d
29. the counter weight act in the same direction and oppose the gravitational torques on the helicopter body and propeller assembly We define the VTOL trainer as being in equilibrium when the thrust is adjusted until the VTOL is horizontal and parallel to the ground At equilibrium the torques acting on the system are described by the equation 1 Ki leg magle migh 3 Mag Lr 0 3 5 where Teq is the current required to reach equilibrium 3 1 2 Equation of Motion The angular motions of the VTOL trainer with respect to a thrust torque 7 can be expressed by the equation J6 B04 K0 3 6 where is the pitch angle J is the equivalent moment of inertia acting about the pitch axis B is the viscous damping and K is the stiffness With respect to current this becomes J6 B64 K0 KiIm 3 7 As opposed to finding the moment of inertia by integrating over a continuous body when finding the moment of inertia of a composite body with n point masses its easiest to use the formula ES ig 3 8 i 1 3 1 3 Process Transfer Function Model The transfer function representing the current to position dynamics of the VTOL trainer is P s K 3 9 a RE ts J s 7 This is obtained by taking the Laplace transform of Equation 3 6 and solving for Q s Im s Notice that the denom inator NET VTOL Workbook Student Version EEN FARER J J matches the characteristic second order transfer function Equation 2 1 By determining t
30. tory from Table 3 1 lll ANALYSIS Provide details of your calculations methods used for analysis for each of the following 1 Natural frequency determination from Step 7 of Section 3 4 2 How well does the simulation match the measured signal in Step 8 of Section 3 5 2 3 Calculation of the model parameters from the identified transfer function in Step 11 of Section 3 6 IV CONCLUSIONS Interpret your results to arrive at logical conclusions for the following 1 How is the simulation matching the measured signal compared to the transfer function with manually estimated parameters in Step 9 of Section 3 4 2 How do the generated parameters compare to the manually estimated parameters in Step 11 of Section 3 6 6 3 Template for Content Flight Control I PROCEDURE 1 PD Steady State Analysis Briefly describe the main goal of the experiment Briefly describe the experimental procedure in Step 9 in Section 4 3 2 2 PID Steady State Error Analysis e Briefly describe the main goal of the experiment Briefly describe the experimental procedure in Step 3 in Section 4 4 2 3 PID Control Design e Briefly describe the main goal of this experiment Briefly describe the experimental procedure in Step 8 in Section 4 5 2 ll RESULTS Do not interpret or analyze the data in this section Just provide the results 1 Pitch response plot from Step 9 in Section 4 3 2 2 PID response plot from Step 3 in Section 4 4 2 3
31. ure 3 3 Set the Current Control ON switch to ON Inthe Current Control Parameters section set the PI current gains found in Section 2 5 In the Current Setpoint section set Amplitude 0 00 A e Frequency 0 40 Hz e Offset Teq equilibrium current found in Section 3 3 Run the VI QNET VTOL Workbook Student Version 7 When the VI starts and the equilibrium current step is applied the VTOL Trainer will shoot upwards quickly and then oscillate about its horizontal Capture this response and measure the natural frequency 8 Click on Stop button to stop the VI 3 5 Lab 3 Model Validation 3 5 1 Pre Lab Exercises 1 Using the VTOL Trainer model given in Section 3 1 2 and the specifications listed in the VTOL User Manual 1 compute the moment of inertia acting about the pitch axis Enter the value in Table 3 1 2 Based on the natural frequency found in Section 3 4 and the moment of inertia calculated above find the stiffness of the VTOL Trainer Enter the value in Table 3 1 3 Using the equations presented in Section 3 1 and the equilibrium current found in Section 3 3 calculate the thrust current torque constant K Enter the value in Table 3 1 4 Compute the VTOL Trainer transfer function coefficients based on the previously found parameters K J B and K 3 5 2 In Lab Experiment 1 Ensure the QNET VTOL Modelling VI is open and configured as described in Section 5 3 Make sure the correct Device
32. using correct format REFERENCES 1 Quanser Inc QNET VTOL Control Trainer User Manual 2011 Six QNET Trainers to teach introductory controls using NI ELVIS gt QNET DC Motor Control Trainer gt QNET HVAC Trainer gt QNET Mechatronic Sensors Trainer teaches fundamentals of DC motor control teaches temperature process control teaches functions of 10 different sensors Fa oy Wen aD gt QNET Rotary Inverted gt QNET Myoelectric Trainer gt QNET VTOL Trainer Pendulum Trainer teaches control using principles of teaches basic flight dynamics and control teaches classic pendulum control experiment electromyography EMG Quanser QNET Trainers are plug in boards for NI ELVIS to teach introductory controls in undergraduate labs Together they deliver added choice and cost effective teaching solutions to engineering educators All six QNET Trainers are offered with comprehensive ABET aligned course materials that have been developed to enhance the student learning experience To request a demonstration or quote please email info ni com ABET Inc is the recognized accreditor for college and university programs in applied science computing engineering and technology Among the most respected accreditation organizations in the U S ABET has provided leadership and quality assurance in higher education for over 75 years 2013 Quanser Inc All rights reserved LabVIEW is a trademark of National Instruments INFO
33. using the final value theorem FVT ss lim sE s s 0 Using FVT the steady state error of the VTOL trainer closed loop PID step response is oie im HERR 4 2 s gt 0 8 J Bs Kikas sK Kikps Krki 4 1 2 PID Control Design The PID control loop used for the VTOL device is depicted in Figure 4 2 Actuator Model sat Figure 4 2 VTOL PID Control Loop The transfer function representing the VTOL trainer position current relation in Equation 3 9 is used to design the PID controller The input output relation in the time domain for a PID controller is u kolla 8 k f Ba 8 dt hy 8 4 3 where kp is the proportional gain k is the integral gain and k is the velocity gain Remark that only the measured velocity is used i e instead of using the derivative of the error The closed loop transfer function from the position reference r to the angular VTOL position output 0 is Ki kps ki Gorle o s Js3 B Kik s K Kikp s Kiki 4 4 The prototype third order characteristic polynomial is o QNETVTOL Workbook Student Version i aa s 2Cwns w2 5 po s 2Cwn po s w2 2Cwnpo s w2po where wn is the natural frequency is the damping ratio and po is a zero 4 5 The characteristic equation in Equation 4 4 the denominator of the transfer function can match the desired char acteristic equation Equation 4 5 with the following gains _ K
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