WEEK 12 PI CONTROL THEORY & MODELLING
Week 12 Report
Oral presentations and submission of report.
Objectives
To observe the operation and behavior of your system's approximate linear FOPDT model with PI control. To observe the effect of the value of the proportional feedback gain, Kc and the integral time, tI. To observe the limits of stable operation of the closed loop system. To observe the response of a closed loop controlled system to a set point change. To tune the controller for quarter decay response.
Reference: Smith & Corripio, pp 163-168, 318-319
The quarter decay tuning parameters for a PI controller can be derived from Smith & Corripio, table on page 212 or 225. Use these values to see how your approximate model behaves with PI control.
Run your approximate linear FOPDT model with a much larger value
of Kc to see what impact that has on the response. Same for a
much smaller value of Kc. Same for tI.
Useful things to do with MATLAB: Plot the root locus for the problem. Label with the values of Kc on the Root Locus plot where the breakaway and crossover are. Draw the line from the origin to the point where Kc gives "quarter decay."
When you include MATLAB work: In the Theory section, include material
that shows what you're doing and any work you do in preparation
for MATLAB calculations. In the Appendix of your report, put tables
of your input, results and the raw plots.
Disk File Suggestion: For all your data files that you save this
week, start their names with "W12" (meaning week #12)
WEEK 13 PI CONTROL EXPERIMENT
Objectives
To observe the operation and behavior of your PI control system design. To observe the effect of the value of the proportional feedback gain, Kc and the integral time, tI. To observe the limits of stable operation of the closed loop system. To observe the response to a closed loop controlled system to a set point change and a disturbance input (as appropriate). To tune the controller with approximate modelling results for quarter decay response. To observe reset windup.
Reference: Smith & Corripio, pp 226-234
PROCEDURE FOR RUNNING THE PI CONTROLLER
Prepare system for operation
Open LabVIEW program labelled "(PI)". This program emulates a proportional-integral feedback controller. You should get a panel somewhat like the one shown in Figure 21.
Figure 21. PI automatic controller panel
Again on this panel, you put the "set point" with the control slide on the left. The "set point" is the value you want for the output variable. Set the values you want for Kc, the proportional controller gain, and tI, the integral or reset time, with the knobs or in the appropriate windows. Click on the RUN arrow.
Choose the values of Kc and tI that your theory and approximate modelling predict will be good for you system. You can observe the system's response to a step change in set point by changing the set point. You can observe the system's response to a disturbance by changing disturbance input.
Using the values of Kc and tI that your approximate modelling results gave for various system responses, observe the experimental system responses for the equivalent experiments.
Observe reset windup by choosing a set point that is about 5%
to 10% below the maximum operating point & then starting the
LabVIEW program.
Useful things to do with MATLAB: Plot the root locus for the problem. Label with the values of Kc on the Root Locus plot where the breakaway and crossover are. Draw the line from the origin to the point where Kc gives "quarter decay."
When you include MATLAB work: In the Theory section, include material
that shows what you're doing and any work you do in preparation
for MATLAB calculations. In the Appendix of your report, put tables
of your input, results and the raw plots.
Disk File Suggestion: For all your data files that you save this
week, start their names with "W13" (meaning week #13)
Week 14 Report
A draft of Week 14 Report is due the second school day before the next scheduled lab meeting.
WEEK 14 REPORT CONTENTS
PI CONTROLLER PERFORMANCE
Introduction
Theory Description & explanation of system components & connections
Schematic diagram
Input function(s) and output function
Theory & governing equations for components, system and PI feedback controller
Time domain and Laplace domain descriptions, OLTF, CLTF, characteristic equations, Kcu, wu
Quarter decay tuning parameters from theory
Block diagram. Root locus plots
Previous system results (gain, time constant, etc.)
Modelling Equations & methods used in modelling
Results Performance of experimental system with PI control
Modelling results for PI control
Discussion Comparison of theory, modelling and behavior of experimental system responses with PI control
Conclusions
Recommendation
Appendices Physical properties
Modelling diagram, equations
Attachments Include a sheet for each team member that describes the contribution to the work in the laboratory since last reported.
WEEK 14
Week 14 Report
Oral presentations and submission of report.