Controls Lab 2nd Week

1
Controls Lab (2nd Week)?
Objectives cont.

• Qualitatively observe the effects of the P, I,
  and D gains.
• Test the performance of the previously developed
  P, PD, and PID position controllers on a
  brushless DC motor.
• Adjust the PID gain to improve system
  performance.
• Post-laboratory work
• Compare the empirical performance of the various
  controllers to each other and to the simulated
  performance

2

Apparatus

• PC
• Quanser Data Acquisition
• Amplifier
• Motor and Flywheel
• Encoder

3
Background PID Performance
Motor Transfer function (Position output)?
PID controller transfer function
Feedback control block diagram
Figure 7. Control Feedback Block Diagram
4
Procedure Qualitative Observations
1. Use Control_Qualitative.mdl as shown on
Figure 5. 3. Specify gains (Kp,Ki,Kd) for P
controller. 4. Build model and hit START. 5. For
each controller turn the flywheel with your hand
(1) quickly, (2) slowly, and (3) turn and hold in
position. 6. What aspect is the restoring force
sensitive to? Record your observations in your
lab notebook. 7. Repeat for I and D controllers.
5
Quanser Consulting
Quanser Consulting
Transfer Fcn
Figure 5. SIMULINK Model for Qualitative
Observations
6
Procedure PID Controller Performance
1. Open Control_Template_2. Set constants
according to TA instructions 2. Set Kp, Ki, and
Kd to the values you calculated for each of the P
controller. 3. RTW Build 4. Plot both the shaft
position and the control signal (voltage) on the
same graph by selecting Plot -gt New -gt Scope...
from the WinCon Server toolbar and choosing
Scope1a and Scope1b. 5. Run the controller for at
least 1 complete period. 6. Save the graph with
both variables plotted as an M-file. 10. Repeat
for the PD, and PID controllers.
7
Block Diagram to Initiate Position Control of
Motor
 
Pulse Generator
VALUES ASSIGNED IN Procedure!
From Simulink Source (use time based)?
From Simulink Source
Parameters
Parameters
Amplitude
Constant Value
Period
Pulse width
Phase Delay
Figure 8. SIMULINK Model used for Position
Control of DC Motor
8
Simulink and Quanser Blocks
From Quanser Library Quanser Consulting MQ3
Series
From Quanser Library Quanser Consulting MQ3
Series
(leave parameters as default)
(leave parameters as default)
From Quanser Library Quanser Consulting MQ3
Series
(leave parameters as default)
From Simulink Continuous
From Simulink Math
Parameters
Parameters
Gain 1/2000
Numerator 25 0
Denominator 1 25
From Simulink Source
Parameters
Constant Value 0
From Simulink Math
Parameters
List of signs
List of signs
Figure 9. SIMULINK and Quansar Blocks Used in
Position Control
9
Procedure PID Controller Performance 2
SCORE-Change

• Open M Files.
• Measure the maximum overshoot, the 2 settling
  time, and the steady-state error for each graph
  (where applicable) and record the information in
  Table 1. See Figure 4 for an example.
• Calculate the score for the performance of the
  controller.
• SOmax x tsettle if steady state error is less
  than or equal to 0.5
• Adjust the gains of the best PID controller to
  improve the performance of the controller. Record
  the gains and the scores for each attempt in
  Table 1.

Figure 10. Example measured quantities settling
time and max overshoot.
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Non-Linear Simulink Model Verification

• Build the following Non-Linear Model to compare
  to experimental results.
• The Transfer Fcn2 on the right is really just
  (Km / (Tms2 s)).
• To Run your simulation, make sure to go to
  Simulation, then Configuration Parameters, and
  run Ode5, with a step size of 0.005. This will
  make your simulation run much quicker. Feel free
  to vary these values to make a higher resolution
  plot.
• Slight modification to this model will give a
  linear version to be tested as well. Which
  model works better?

See Procedure
Pulse Generator
See Procedure
Figure 11 Non-Linear Model
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Controller Performance Results
Table 4. Simulation and experimental performance
results for various controllers.