Modelling and control by Anthony Rossiter

# Uncertainty and the importance of 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.

## Uncertainty 1 - introduction

A short set of videos on when feedback is important and the impact of uncertainty on system behaviour with and without feedback. This is an introduction.

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

#### Quick test question

The prime purpose of feedback is to do what?
A. Improve the system dynamics.
B. Get good gain and phase margins.
C. Give behaviour that is robust to unknowns.
D. None of the above.

## Uncertainty 2 - role of feedback

A short set of videos on when feedback is important and the impact of uncertainty on system behaviour with and without feedback. This is video gives more examples of the impact of uncertainty.

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

#### Quick test question

Feedback is able too:
A. Reduce sensitivity to disturbances.
B. Reduce sensitivity to modelling errors.
C. Improve system dynamics
D. All of the above.

## Uncertainty 3 - quantifying effects of uncertainty

A short set of videos on when feedback is important and the impact of uncertainty on system behaviour with and without feedback. The third video shows how one might quantify the effects of uncertainty on behaviour.

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

## Uncertainty 4 - Matlab GUIs: tank level with disturbances

This GUI builds on the previous one and introduces uncertainty that is present in real world scenarios. The main purpose is to help students understand the need for closed-loop control. The system is affected by small but time varying disturbances to the inflow rate and outlet resistance. Users are challenged to maintain the desired depth in the tank using open-loop or manual control (dynamically changing the in flow directly through a slider) and then to compare this with automatic control.

## Uncertainty 5 - Matlab GUIs: heat exchanger with disturbances

This GUI builds on the previous one and introduces uncertainty that is present in real world scenarios. The main purpose is to help students understand the need for closed-loop control. The system is affected by small but time varying disturbances to the inflow temperature and flow rate. Users are challenged to maintain the desired outlet temperature using open-loop or manual control (dynamically changing the steam flow directly through a slider) and then to compare this with automatic control.