WEEK 10 PROPORTIONAL CONTROL THEORY & MODELLING

Week 10 Report

Submission of final report and oral presentations (10 minute limits).

Background

Brief description of system, "input" and "output"

Brief description of performance curves (SSOC)

Objective of controller design

Theory

Brief review of system transfer function (FOPDT or other) (include parameter values)

Description of feedback control in your system

CLTF for your system

Root locus

Modelling

Model & parameters

Results

Sample time-response graphs

Offset as function of Kc

Kcu, Kc for quarter decay, Kc for critical damping, range of Kc for underdamped, range of Kc for overdamped

Conclusions

"For a response with an offset of ,

our system needs a proportional controller with a Kc of ."

Some suggested slides for Week 10 Report

Background Theory Modelling Results Conclusions	Theory Transfer function Parameters Feedback control CLTF	Results Time response Offset Kc results (table)
Background System Input Output SSOC Operating Range Root locus Controller objectives	Modelling Model equations Parameters Feedback control	Conclusions

Objectives

To observe the operation and behavior of your system's approximate linear FOPDT model with proportional control. To observe the effect of the value of the proportional feedback gain, Kc. 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 find Kc for critically damped response, quarter decay response and Kcu.

Reference: Smith & Corripio, pp 159-163, 225-226

Smith & Corripio (p. 209) has a formula for finding Kcu if you know the FOPDT parameters.

Disk File Suggestion: For all your data files that you save this week, start their names with "W10" (meaning week #10)

Note about "Marginally Stable Behavior"

For linear systems (the subject of ENGR 328), if Kc > Kcu , the output will be increasingly oscillatory without any bounds. For real systems (like in ENGR 329), the output can never grow without bounds because eventually the system will go outside of its operating range and reach a physical limit. Examples of limits are (1) an Accuspede power supply can only put out voltages within some finite range and (2) water level in a tank can not be negative.

So, the Kc for "marginally stable behavior" in the real world means that at smaller values of Kc, the oscillations are damped and for larger values of Kc, the oscillations are not damped. That is, the oscillations are sustained indefinitely.

WEEK 11 PROPORTIONAL CONTROL EXPERIMENT

PROPORTIONAL CONTROL EXPERIMENTS

Objectives

To observe the operation and behavior of your proportional control system design. To observe the effect of the value of the proportional feedback gain, Kc. To determine the ultimate gain and ultimate period for 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 critically damped response, quarter decay and at the limit of stability.

Reference: Smith & Corripio, pp 211-213

PROCEDURE FOR RUNNING THE PROPORTIONAL-ONLY CONTROLLER

Prepare system for operation

Open LabVIEW program labeled "(P-only)". This program emulates an automatic feedback controller. You should get a panel somewhat like the one shown in Figure 19. 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 value you want for Kc, the proportional controller gain, with the knob or in the appropriate window. Click on the RUN arrow.

Figure 19. Proportional-only automatic controller panel

Choose the value of Kc 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 the disturbance input.

The meter in the lower left is the controller output. It is the signal (the "manipulated" variable) sent by the controller to the system.

Experimentally determine what value of Kc gives marginally stable operation (Kcu) and determine that frequency (wu or fu, and Tu --see Smith & Corripio, p. 211).

Using the values of Kc that your approximate modelling results gave for various system responses, observe the experimental system responses for the equivalent experiments.

Be sure to remember the note about marginally stable behavior on page 48, above.

Disk File Suggestion: For all your data files that you save this week, start their names with "W11" (meaning week #11)

Week 12 Report

A draft of Week 12 Report is due the second school day before the next scheduled lab meeting.

WEEK 12 REPORT CONTENTS

PROPORTIONAL CONTROLLER PERFORMANCE

Introduction

Theory & Background

Description & explanation of system components & connections

Schematic diagram

Input function 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 system with proportional-only control. (Week 11 experiments)

Estimates of errors in results.

Discussion

Comparison of theory, modelling and behavior of experimental system responses with proportional only control

Conclusions

Values of Kc, tI, for specified system response

Recommendation

Appendices

Physical properties

Modelling diagram, equations

Data curves & calculations

Attachments

Include a sheet for each team member that describes the contribution to the work in the laboratory since last reported.