Modelling and control by Anthony Rossiter

# SIMPLE FEEDBACK

This is a section in the chapter on introduction to the importance and impact of feedback. Use the left hand toolbar to access the other chapters and themes. It is implicit in several of these chapters that students have core competence in some mathematical topics such as polynomials, roots, complex numbers, exponentials and Laplace. More information on these can be found in the Mathematics theme on the left hand toobar.

This section contains the following topics. Under each topic there are hardcopy (pdf) notes, a video talk through of key derivations with example problems and also a tutorial sheet for users to test themselves.

## Simple feedback 1 - review of core concepts

This set of videos summarises a heuristic approach to control design by bringing together simple engineering intuition with basic analytic tools. Video one summarise the analysis tools commonly used on feedback loops.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

#### Quick test question

A good indicator of desireable behaviour is:
A. The open-loop pole positions.
B. The closed-loop zeros.
C. Damping of the dominant closed-loop poles.
D. None of the above.

## Simple feedback 2 - proportional design

This set of videos summarises a heuristic approach to control design by bringing together simple engineering intuition with basic analytic tools. Video two looks at the impact of changes in the proportional component of a compensator.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

#### Quick test question

With proportional only design.
A. Increasing proporitional nearly always improves behaviour.
B. Increasing proporitional nearly always makes behaviour worse.
C. Often the best value of proportional need not imply good closed-loop behaviour.
D. None of the above.

## Simple feedback 3 - integral design

This set of videos summarises a heuristic approach to control design by bringing together simple engineering intuition with basic analytic tools. Video three considers the efficacy of a purelyÂ  integral control law.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Simple feedback 4 - heuristic PI design

This set of videos summarises a heuristic approach to control design by bringing together simple engineering intuition with basic analytic tools. Video four summarises and illustrates a heuristic design rule for PI compensation.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Simple feedback 5 - tutorial on heuristic PI design

This tutorial gets students to compare and contrast given PI compensators with a heuristic design and draw conclusions from this. All the examples are first order and the insights are backed up with the use of MATLAB. Minor typo in example 1 around 5min where it should be uss = r/G(0).

• A talk through video is on youtube.

## Simple feedback 6 - tutorial on heuristic PI design for 2nd order systems

This tutorial gets students to compare and contrast given PI compensators with a heuristic design and draw conclusions from this. All the examples are second order and the insights are backed up with the use of MATLAB.

• A talk through video is on youtube.

#### Quick test question

When applying PI compensation to 2nd order systems.
A. There is a risk of under-damped behaviour in order to achieve satisfactory speed of response.
B. Responses will have no offset and good damping.
C. Poor tuning can never lead to instability.
D. None of the above.

## Simple feedback 7 - tutorial on PI design by trial and error with MATLAB

One advantage of an effective software package is the ability to perform rapid trial and error and thus gain insight. This video illustrates some simple MATLAB GUIs, created by the author, for investigating the impact of changes in PI parameters on classical problems of tank level, cruise control and heating. Initial design is done using the heuristic guidance. [N.B. There is a minor typo in cruise control closed loop model - should be 0.5/(s+0.5), GUIs available by request]

• A talk through video is on youtube.  