NEFER BLANCHAR; JUAN CAMACHO; LEONARDO CABARCAS; JESUS HERNANDEZ; JAIME

SUAREZ.

QNET-010 DCMCT

Quanser Engineering Trainer

for NI-ELVIS

QNET DC Motor Control Trainer

Student Manual
Under the copyright laws, this publication may not be reproduced or transmitted in any form, electronic
or mechanical, including photocopying, recording, storing in an information retrieval system, or
translating, in whole or in part, without the prior written consent of Quanser Inc.

Copyright ©2009, by Quanser Inc. All rights reserved.

QNET-DCMCT Laboratory – Student Manual

Table of Contents

1. INTRODUCTION..........................................................................................................................................1

2. PREREQUISITES.........................................................................................................................................1

3. DCMCT VIRTUAL INSTRUMENTS.............................................................................................................2

3.1. Summary...........................................................................................................................................2
3.2. Description........................................................................................................................................3
3.2.1. Modeling................................................................................................................................................3
3.2.2. Speed Control.........................................................................................................................................5
3.2.3. Position Control.....................................................................................................................................7

4. IN-LAB EXPERIMENTS...............................................................................................................................9
4.1. Modeling...........................................................................................................................................9
4.1.1. Bumptest................................................................................................................................................9
4.1.2. Model Validation.................................................................................................................................11
4.1.3. Exercises..............................................................................................................................................13
4.2. Speed Control.................................................................................................................................17
4.2.1. Qualitative PI Control..........................................................................................................................17
4.2.2. PI Control according to Specifications.................................................................................................18
4.2.3. Effect of Set-Point Weight...................................................................................................................19
4.2.4. Tracking Triangular Signals.................................................................................................................19
4.2.5. Exercises..............................................................................................................................................20
4.3. Position Control..............................................................................................................................26
4.3.1. Qualitative PD Control.........................................................................................................................26
4.3.2. PD Control according to Specifications...............................................................................................27
4.3.3. Response to Load Disturbance.............................................................................................................28
4.3.4. Exercises..............................................................................................................................................29

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5. REFERENCES...........................................................................................................................................37

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1. Introduction
This manual contains experimental procedures and lab exercises for the QNET DC Motor Control
Trainer (DCMCT). The DCMCT is depicted in Figure 1 and the hardware of the device is explained in
Reference [1].

Figure 1: QNET DC motor control trainer on ELVIS II.

The prerequisites to run the LabVIEW Virtual Instruments (VIs) for the DCMCT are listed in Section 2
and described in Section 3. The in-lab procedures are given in Section 4 and split into three sections:
modeling, speed control, and position control. In Section 4.1, the bumptest method is used to find the
model parameters of the DC motor. This model is compared with the measured response by running the
simulation and actual system in parallel. The model parameters are then tuned for a better fit. In Section
4.2, a PI compensator is used to control speed of the motor. This section includes exercises that
demonstrates the effect of proportional and integral control, designing PI gains to meet specifications,
set-point weight, and tracking a triangular wave. In Section 4.3, a PID compensator is used to control
the position of motor. The effects of using only a PD controller is investigated and a PD controller is
designed for certain time-domain requirements. How the system handles disturbances when using PD
and PID compensators is then investigated. The exercises are given within the lab procedures and
labeled “Exercise”. In that case, enter your answer in the exercises number in the corresponding
section.

2. Prerequisites
The following system is required to run the QNET DCMCT virtual instruments:

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✔ PC equipped with either:

✔ NI-ELVIS I and an NI E-Series or M-Series DAQ card.
✔ NI ELVIS II
✔ Quanser Engineering Trainer (QNET) module.
✔ LabVIEW 8.6.1 with the following add-ons:
✔ DAQmx
✔ Control Design and Simulation Module
✔ When using ELVIS II: ELVISmx installed for required drivers.
✔ When using ELVIS I: ELVIS CD 3.0.1 or later installed.

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
Reference [1].

3. DCMCT Virtual Instruments

3.1. Summary

Table 1 below lists and describes the DCMCT LabVIEW VIs supplied with the QNET CD.
VI Description
QNET_DCMCT_Modeling.vi Run DC motor in open-loop.

QNET_DCMCT_Speed_Control.vi Control speed of DC motor load using a

proportional-integral (PI) compensator.
QNET_DCMCT_Position_Control.vi Control position of DC motor load using a
proportional-integral-derivative (PID)
compensator.

Table 1: DCMCT VIs supplied with the QNET CD.

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3.2. Description
3.2.1. Modeling
The DCMCT Modeling VI, shown in Figure 2 and Figure 3, runs the DC motor in open-loop and plots
the corresponding speed and input voltage responses. This VI can be used to take speed and voltage
measurements of the responses, as illustrated in Figure 3, and runs a simulation of the DC motor in
parallel. Table 2 lists and describes the main elements of the QNET-DCMCT Modeling virtual
instrument front panel. Every element is uniquely identified through an ID number and located in
Figure 2.

Figure 2: QNET-DCMCT Modeling virtual instrument.

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Figure 3: QNET DCMCT Modeling VI: "Measurement Graphs" tab selected.

ID # Label Parameter Description Unit

1 Speed m Motor output speed numeric display. rad/s
2 Current Im Motor armature current numeric display. A
3 Voltage Vm Motor input voltage numeric display. V
4 Signal Type Type of signal generated for the input
voltage signal.
5 Amplitude Generated signal amplitude input box. V
6 Frequency Generated signal frequency input box. Hz
7 Offset Generated signal offset input box. V
8 K K Motor model steady-state gain input box. rad/(V.s)
9 tau Motor model time constant input box. s
10 Graph Buffer Buffer length of graph data. s

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11 Device Selects the NI DAQ device.

12 Sampling Rate Sets the sampling rate of the VI. Hz
13 Stop Stops the LabVIEW VI from running.

14 Scopes: Speed m Scope with measured (in red) and rad/s

simulated (in blue) motor speeds.

15 Scopes: Voltage Vm Scope with applied motor voltage (in red). V

16 Measurement m Graph displays buffered measured motor rad/s
Graphs: Speed speed after VI is stopped.
17 Measurement Vm Graph displays buffered input voltage used V
Graphs: Voltage after VI is stopped.

Table 2: Nomenclature of QNET-DCMCT Modeling VI

3.2.2. Speed Control

In the QNET DCMCT Speed Control VI, a proportional-integral compensator is used to control the
speed of the motor. The PI control also includes set-point weight. Table 3 lists and describes the main
elements of the QNET-DCMCT Speed Control virtual instrument user interface. Every element is
uniquely identified through an ID number and located in Figure 4.

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Figure 4: QNET DCMCT Speed Control VI.

ID # Label Parameter Description Unit

1 Speed m Motor output speed numeric display. rad/s
2 Current Im Motor armature current numeric display. A
3 Voltage Vm Motor input voltage numeric display. V
4 Signal Type Type of signal generated for the motor
speed reference.
5 Amplitude Generated signal amplitude input box. V
6 Frequency Generated signal frequency input box. Hz
7 Offset Generated signal offset input box. V
8 Disturbance Vsd Apply simulated disturbance voltage. V
9 kp kp Controller proportional gain input box. V.s/rad

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10 ki ki Controller integral gain input box. V/rad

11 bsp bsp Controller set-point weight input box.
12 Device Selects the NI DAQ device.
13 Sampling Rate Sets the sampling rate of the VI. Hz
14 Stop Stops the LabVIEW VI from running.
15 Speed m Scope with reference (in blue) and rad/s
measured (in red) motor speeds.
16 Voltage Vm Scope with applied motor voltage (in red). V
Table 3: Nomenclature of QNET-DCMCT Speed Control VI.

3.2.3. Position Control

The QNET DCMCT Position Control VI controls the position of the motor using a proportional-
integral-derivative controller. The main elements of the VI front panel are summarized in Table 4 and
identified in Figure 5 through the corresponding ID number.

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Figure 5: QNET DCMCT Position Control VI.

ID # Label Parameter Description Unit

1 Position m Motor output speed numeric display. rad/s
2 Current Im Motor armature current numeric display. A
3 Voltage Vm Motor input voltage numeric display. V
4 Signal Type Type of signal generated for the position
reference.
5 Amplitude Generated signal amplitude input box. V
6 Frequency Generated signal frequency input box. Hz
7 Offset Generated signal offset input box. V
8 Disturbance Vsd Apply simulated disturbance voltage. V
9 kp kp Controller proportional gain input box. V.s/rad

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10 ki ki Controller integral gain input box. V/rad

11 kd kd Controller derivative gain input box. V.s/rad
12 fc fc Controller high-pass filter cutoff frequency. Hz
13 Device Selects the NI DAQ device.
14 Sampling Rate Sets the sampling rate of the VI. Hz
15 Stop Stops the LabVIEW VI from running.
16 Position m Scope with reference (in blue) and rad
measured (in red) motor positions.
17 Voltage Vm Scope with applied motor voltage (in red). V
Table 4: Nomenclature of QNET-DCMCT Position Control VI.

4. In-Lab Experiments

4.1. Modeling
4.1.1. Bumptest
1. Open the QNET_DCMCT_Modeling.vi.
2. Ensure the correct Device is chosen, as shown in Figure 6

Figure 6: Selecting correct device.

3. Run the QNET_DCMCT_Modeling.vi. The DC motor should begin spinning and the scopes
on the VI should appear similarity as shown in Figure 7.
4. In the Signal Generator section set:
Amplitude = 2.0 V
Frequency = 0.40 Hz
Offset = 3.0 V
5. Once you have collected a step response, click on the Stop button to stop running the VI.
6. Exercise 1: Attach the responses in the Speed (rad/s) and Voltage (V) graphs. See Reference
[1] for information on how to export a chart or graph to the clipboard.
7. Select the Measurement Graphs tab to view the measured response, similarly as depicted in
Figure 8.

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8. Exercise 2: Use the responses in the Speed (rad/s) and Voltage (V) graphs to compute the
steady-state gain of the DC motor. Make sure you fill out Table 5. See Reference [2] for
details on how to find the steady-state gain from a step response. Finally, you can use the
Graph Palette for zooming functions and the Cursor Palette to measure data. See the
LabVIEW help for more information on these tools.
9. Exercise 3: Based on the bumptest method, find the time constant. Make sure you complete
Table 6 and see Reference [2] for information on how to find the time constant of the step
response.
10. Enter the steady-state gain and time constant values found in this section in Table 7. These are
called the bumptest model parameters.

Figure 7: QNET DCMCT Modeling VI running.

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Figure 8: QNET DCMCT Modeling VI: sample response in Measurement Graphs.

4.1.2. Model Validation

1. Open the QNET_DCMCT_Modeling.vi.
2. Ensure the correct Device is chosen.
3. Run the QNET_DCMCT_Modeling.vi. You should hear the DC motor begin running and the
scopes on the VI should appear similarity as shown in Figure 7.
4. In the Signal Generator section set:
Amplitude = 2.0 V
Frequency = 0.40 Hz
Offset = 3.0 V
5. In the Model Parameters section of the VI, enter the bumptest model parameters, K and , that
were found in Section 4.1.1. The blue simulation should match the red measured motor speed
more closely.
6. Exercise 4: Attach the Speed (rad/s) and Voltage (V) chart responses from the Scopes tab.
How well does your model represent the actual system? If they do not match, name one
possible source for this discrepancy.

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7. Exercise 5: Tune the steady-state gain, K, and time constant, tau, in the Model Parameters
section so the simulation matches the actual system better. Enter both the bumptest and tuned
model parameters in Table 7.

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4.1.3. Exercises
Exercise 1: Bumptest Response

0 1 2

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Exercise 2: Measure Steady-State Gain

Description Symbol Value Unit
Steady-state motor speed 121.8 rad/s 0 1 2
m,ss

Initial step motor speed 0

1,012 rad/s
Input step amplitude Av 4 V
Measured steady-state gain using bumptest Ke,b 30,7 rad/(V.s)
Table 5: Finding steady-state gain using bumptest.

Exercise 3: Measure Time Constant

Description Symbol Value Unit
78,603 rad/s 0 1 2
Decay speed m 1 (t )
Initial step time t0 1,326 s
Decay step time t1 1,566 s
Measured time constant using bumptest e,b 0,240
s
Table 6: Finding time constant using bumptest.

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Exercise 4: Bumptest Model Validation

0 1 2

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Exercise 5: Tuned Model Parameters

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Exercise 6: Results Summary

Description Symbol Value Unit
0 1 2
In-Lab: Bumptest Modeling
Open-Loop Steady-State Gain Ke,b 30,7 rad/(V.s)
Open-Loop Time Constant e,b 0,240 s
In-Lab: Model Validation
Open-Loop Steady-State Gain Ke,v 31,25 rad/(V.s)
Open-Loop Time Constant e,v 0,0936 s
Table 7: QNET DCMCT Modeling results summary

4.2. Speed Control

4.2.1. Qualitative PI Control
1. Open the QNET_DCMCT_Speed_Control.vi.
2. Ensure the correct Device is chosen.
3. Run the QNET_DCMCT_Speed_Control.vi. The motor should begin rotating and the scopes
should look similar as shown in Figure 9.
4. In the Signal Generator section set:
• Signal Type = 'square wave'
• Amplitude = 25.0 rad/s
• Frequency = 0.40 Hz
• Offset =100.0 rad/s
5. In the Control Parameters section set:
• kp = 0.0500 V.s/rad
• ki = 1.00 V/rad
• bsp = 0.00
6. Exercise 1: Examine the behaviour of the measured speed, shown in red, with respect to the
reference speed, shown in blue, in the Speed (rad/s) scope. Explain what is happening.
7. Increment and decrement kp by steps of 0.005 V.s/rad.
8. Exercise 2: Look at the changes in the measured signal with respect to the reference signal.
Explain the performance difference of changing kp.
9. Set kp to 0 V.s/rad and ki to 0 V/rad. The motor should stop spinning.
10. Increment the integral gain, ki, by steps of 0.05 V/rad. Vary the integral gain between 0.05
V/rad and 1.00 V/rad.
11. Exercise 3: Examine the response of the measured speed in the Speed (rad/s) scope and
compare the result when ki is set low to when it is set high.
12. Stop the VI by clicking on the Stop button

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Figure 9: Running the QNET Speed Control VI.

4.2.2. PI Control according to Specifications

1. Exercise 4: Using the equations in Reference [2], calculate the expected peak time, tp, and
percentage overshoot, PO, given the following Speed Lab Design (SLD) specifications:
• zeta = 0.75
• w0= 16.0 rad/s
Optional: You can also design a VI that simulates the DC motor first-order model with a PI
control and have it calculate the peak time and overshoot.
2. Exercise 5: Calculate the proportional, kp, and integral, ki, control gains according to the
model parameters found in Section 4.1.2 and the SLD specifications.
3. Run the QNET_DCMCT_Speed_Control.vi. The motor should begin spinning and the scopes
plotting traces similarly as illustrated in Figure 9, above.
4. In Signal Generator set:
• Signal Type ='square wave'
• Amplitude = 25.0 rad/s
• Frequency = 0.40 Hz

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• Offset = 100.0 rad/s

5. In the Control Parameters section, enter the SLD PI control gains found in Exercise 5 and
make sure bsp = 0.00.
6. Stop the VI when you collected two sample cycles by clicking on the Stop button.
7. Exercise 6: Capture the measured SLD speed response. Make sure you include both the Speed
(rad/s) and the control signal Voltage (V) scopes.
8. Exercise 7: Measure the peak time and percentage overshoot of the measured SLD response.
Are the specifications satisfied?
9. Exercise 8: What effect does increasing the specification zeta have on the measured speed
response? How about on the control gains? Use the damping ratio equation in Reference [2]
for more help if needed.
10. Exercise 9: What effect does increasing the specification w0 have on the measured speed
response and the generated control gains? Use the natural frequency equation in Reference [2]
for more help if needed.

4.2.3. Effect of Set-Point Weight

1. Run the QNET_DCMCT_Speed_Control.vi. The motor should begin rotating back and forth.
2. In the Signal Generator section set:
• Signal Type = 'square wave'
• Amplitude = 25.0 rad/s
• Frequency = 0.40 Hz
• Offset = 100.0 rad/s
3. In the Control Parameters section set:
• kp = 0.050 V.s/rad
• ki = 1.50 V/rad
• bsp= 0.00
4. Increment the set-point weight parameter bsp in steps of 0.05. Vary the parameter between 0 and
1.
5. Exercise 10: Examine the effect that raising bsp has on the shape of the measured speed signal
in the Speed (rad/s) scope. Explain what the set-point weight parameter is doing.
6. Stop the VI by clicking on the Stop button.

4.2.4. Tracking Triangular Signals

1. Run the QNET_DCMCT_Speed_Control.vi. The motor should begin rotating back and forth
2. In Signal Generator set:
• Signal Type = 'triangular wave'
• Amplitude = 50.0 rad/s
• Frequency = 0.40 Hz
• Offset = 100.0 rad/s
3. In the Control Parameters section set:
• kp = 0.20 V.s/rad
• ki = 0.00 V/rad
• bsp = 1.00

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4. Exercise 11: Compare the measured speed and the reference speed. Explain why there is a
tracking error.
5. Increase ki to 0.1 V/rad and examine the response. Vary ki between 0.1 V/rad and 1.0 V/rad.
6. Exercise 12: What effect does increasing ki have on the tracking ability of the measured signal?
Explain using the observed behaviour in the scope.
7. Stop the VI by clicking on the Stop button

4.2.5. Exercises
Exercise 1: Describe the Speed Response

0 1 2

Exercise 2: Effect of Proportional Gain on Speed Control

0 1 2

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Exercise 3: Pure Integral Control Response

0 1 2

Exercise 4: Peak Time and Overshoot

Description Symbol Value Unit
Natural frequency specification 0 16.0 rad/s
Damping ratio specification 0.75
Peak time tp s
Percentage overshoot PO %
Table 8: Expected peak time and overshoot.

0 1 2

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Exercise 5: Design PI Gains to Specifications

Description Symbol Value Unit
Natural frequency specification 0 16.0 rad/s
Damping ratio specification 0.75
Steady-state model gain K rad/(V.s)
Model time constant s
Proportional gain kp V.s/rad
Integral gain ki V/rad
Table 9: PI speed control design.

0 1 2

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Exercise 6: Designed Speed Control Response

0 1 2

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Exercise 7: Peak Time and Overshoot of Response

0 1 2

Exercise 8: Effect of Increasing Damping Ratio

Description Symbol Behaviour Unit
0 1 2
Peak time tp s
Percentage overshoot PO %
Proportional gain kp V.s/rad
Integral gain ki V/rad

Exercise 9: Effect of Increasing Natural Frequency

Description Symbol Behaviour Unit
0 1 2
Peak time tp s
Percentage overshoot PO %
Proportional gain kp V.s/rad
Integral gain ki V/rad

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Exercise 10: Set-Point Weight

0 1 2

Exercise 11: Tracking Error

0 1 2

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Exercise 12: Effect of Integral Gain on Tracking Error

0 1 2

4.3. Position Control

4.3.1. Qualitative PD Control
1. Open the QNET_DCMCT_Position_Control.vi.
2. Ensure the correct Device is chosen.
3. Run the QNET_DCMCT_Position_Control.vi. The DC motor should be rotating back and
forth and the scopes on the VI should appear similarity as shown in Figure 10.
4. In the Signal Generator section set:
• Amplitude = 2.00 rad
• Frequency = 0.40 Hz
• Offset = 0.00 rad
5. In the Control Parameters section set:
• kp = 2.00 V/rad
• ki = 0.00 V/rad
• kd = 0.00 V.s/rad
6. Change the proportional gain, kp, by steps of 0.25 V/rad. Try the following gains: kp = 0.5, 1,
2, and 4 V/rad.
7. Exercise 1: Examine the behaviour of the measured position (red line) with respect to the
reference position (blue line) in the Position (rad) scope. Explain what is happening.
8. Exercise 2: Describe the steady-state error to a step input.
9. Increment the derivative gain, kd, by steps of 0.01 V.s/rad.
10. Exercise 3: Looks at the changes in the measured position with respect to the desired position.
Explain what is happening.
11. Using the equations in Reference [2], calculate the expected peak time, tp, and percentage
overshoot, PO, given the following Speed Lab Design (SLD) specifications:
• zeta = 0.75
• w0= 16.0 rad/s

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Optional: You can also design a VI that simulates the DC motor first-order model with a PI
control and have it calculate the peak time and overshoot.
12. Exercise 5: Calculate the proportional, kp, and integral, ki, control gains according to the
model parameters found in Section 4.1.2 and the SLD specifications.
13. Stop the VI by clicking on the Stop button.

Figure 10: Running the QNET Position Control VI.

4.3.2. PD Control according to Specifications

1. Exercise 4: Using the equations in Reference [2], calculate the expected peak time, tp, and
percentage overshoot, PO, given
• zeta = 0.60
• w0 = 25.0 rad/s
• p0 = 0.0
Optional: You can also design a VI that simulates the DC motor first-order model with a PD
control and have it calculate the peak time and overshoot.

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2. Exercise 5: Calculate the proportional, kp, and derivative, kd, control gains according to the
model parameters found in Section 4.1.2 and the specifications above.
3. Run the QNET_DCMCT_Position_Control.vi. You should see the DC motor rotating back
and forth.
4. In the Signal Generator section set:
• Amplitude = 2.00 rad
• Frequency = 0.40 Hz
• Offset = 0.00 rad
5. In the Control Parameters section, set the PD gains found in Exercise 5.
6. Exercise 6: Capture the position response found in the Position (rad) scope and and control
signal used in the Voltage (V) scope.
7. Exercise 7: Measure the peak time and percentage overshoot of the measured position
response. Are the specifications satisfied? If they are not, then give one possible reason why
there would be discrepancy.
8. Exercise 8: What effect does changing the specification zeta have on the measured position
response and the generated control gains? See Reference [2] for more help.
9. Exercise 9: What effect does changing the specification w0 have on the measured position
response and the generated control gains? See Reference [2] for more help.
10. Stop the VI by clicking on the Stop button.

4.3.3. Response to Load Disturbance

1. Exercise 10: In Reference [2], the load disturbance to motor position closed-loop PID block
diagram is found. Consider the same regulation system, r = 0, when bsp=1 and bsd =1 and show
the block diagram representing the simulated disturbance to motor position closed-loop
interaction (in this case Td = 0).
2. Exercise 11: Find the closed-loop PID transfer function describing the position of the motor
with respect to the simulated disturbance voltage: G ,Vsd(s) = (s)/Vsd(s).
3. Exercise 12: Find the steady-state motor angle due to a simulated disturbance step of Vsd =
Vsd0 / s.
4. Exercise 13: A step of Vsd = Vsd0 / s with Vsd0 = 3 V is added to the motor voltage to simulate a
disturbance torque. Evaluate the steady-state angle of the motor when a PD controller is used
with the gains kp = 2 V/rad and kd = 0.02 V.s/rad. Then, calculate the steady-state angle when
using a PID controller with the gains kp = 2 V/rad, kd = 0.02 V.s/rad, and ki = 1 V/rad/s. Enter
your numeric answers in Table 14.
Optional: You can also design a VI that simulates the DC motor first-order model with a PID
control and a step disturbance and examine the steady-state angle obtained from the response.
5. Run the QNET_DCMCT_Position_Control.vi. The DC motor should be rotating back and
forth.
6. In the Signal Generator section set:
• Amplitude = 0 rad
• Frequency = 0.40 Hz
• Offset = 0 rad
7. In the Control Parameters section set:
• kp = 2.0 V/rad

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• ki = 0.0 V/(rad.s)
• kd = 0.02 V.s/rad
8. Apply the disturbance by clicking on the Disturbance toggle switch situated below the Signal
Generator.
9. Exercise 14: Examine the effect of the disturbance on the measured position. Attach a
response of the motor position when the disturbance is applied, record the obtained steady-
state angle, and compare it to the value estimated in Exercise 13.
10. Turn OFF the Disturbance switch
11. In the Control Parameters section set:
• kp = 2.0 V/rad
• ki = 2.0 V/(rad.s)
• ki = 0.02 V.s/rad
12. Apply the disturbance by clicking on the Disturbance toggle switch.
13. Exercise 15: Examine the effect of the disturbance on the measured position. Explain the
difference of the disturbance response with the integral action added and compare to the result
you obtained in Exercise 13.
14. Stop the VI by clicking on the Stop button.

4.3.4. Exercises
Exercise 1: Pure Proportional Control

0 1 2

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Exercise 2: PD Steady-State Error

0 1 2

Exercise 3: Adding Derivative Control

0 1 2

Exercise 4: Peak Time and Overshoot

Description Symbol Value Unit
0 1 2
Natural frequency specification 0 25.0 rad/s
Damping ratio specification 0.6
Peak time tp s
Percentage overshoot PO %
Table 10: Expected peak time and overshoot.

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Exercise 5: Design PD Gains to Specifications

Description Symbol Value Unit
Natural frequency specification 0 25.0 rad/s
Damping ratio specification 0.6
Steady-state model gain K rad/(V.s)
Model time constant s
Proportional gain kp V.s/rad 0 1 2
Integral gain ki V/rad
Table 11: PD speed control design.

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Exercise 6: Designed PD Position Control Response

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Exercise 7: Peak Time and Overshoot of PD Response

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Exercise 8: Effect of Increasing Damping Ratio

Description Symbol Behaviour Unit
0 1 2
Peak time tp s
Percentage overshoot PO %
Proportional gain kp V.s/rad
Derivative gain kd V/rad
Table 12: Effect of increasing damping ratio specification in position control.

Exercise 9: Effect of Increasing Natural Frequency

Description Symbol Behaviour Unit
0 1 2
Peak time tp s
Percentage overshoot PO %
Proportional gain kp V.s/rad
Derivative gain kd V/rad
Table 13: Effect of increasing natural frequency specification in position control.

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Exercise 10: Block Diagram of PID Simulated Disturbance

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Exercise 11: PID Simulated Disturbance Transfer Function

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Exercise 12: PD Steady-State Angle

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Exercise 13: Evaluate PD and PID Steady-State Angles

Description Symbol Value Unit
0 1 2
Proportional gain kp 2.0 V/rad
Integral gain ki 1.0 V/(rad.s)
Derivative gain kd 0.02 V.s/rad
Simulated disturbance Vsd 3.0 V
PD steady-state angle ss,d rad
PID steady-state angle ss,pid rad
Table 14: Motor position steady-state angle due to simulated disturbance.

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Exercise 14: Measured PD Disturbance

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Exercise 15: Measured PID Disturbance

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5. References
[1] QNET User Manual
[2] QNET Practical Control Guide

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