Modelling, dynamics and control by Anthony Rossiter

Tutorial sheets on Modelling and Behaviour

These tutorials link to the chapter on the theme of linear models, for example:
A d3x/dt3 + B d2x/dt2 + C dx/dt + D x = K u
where x(t) is the state, u(t) the input and A, B, C, D, K are model parameters.

These tutorials focus on principles.
1. How do I model core engineering components?
2. Are there analogies between different components?
3. Are there analogies between similar arrangements of different components?
4. How do I build simple dynamic models for different arrangements of components?
5. How do dynamic models/systems behave and how does this behaviour link to the choice of components?
Largely, these tutorials are limited to 1st and 2nd order modelling and dynamics, but the principles are easily extended.

1. Concepts and components: PDF files.
i. Using units in modelling.
ii. Modelling resistor circuits.
iii. Analogies between resistor and spring arrangements.
iv. Systems with mechanical and fluid components.

2. 1st and 2nd order modelling and analogies: Mixture of PDF files and videos.
i. Tutorial sheet on 1st order modelling.
ii. Tutorial sheet on 2nd order modelling.

iii. Video tutorial: Tank system modelling.
iv. Video tutorial: Heat exchanger modelling.
v. Video tutorial: Mixing tank.

3a. 1st order responses: There are overlaps in some of the later tutorial sheets so you could do a sample from each. PDF files.
i. Introductory questions.
ii. Using Laplace.
iii. Application and context questions.
iv. Parameter dependence question.
v. Challenging questions (e.g. exam level).

3b. Talk through video tutorials on youtube for 1st order systems: Videos only.
i. Video tutorial: Miscellaneous introductory questions.
ii. Video tutorial: Transfer functions.
iii. Video tutorial: Laplace.
iv. Video tutorial: Response dependence on parameters .
v. Video tutorial: System design.
vi. Video tutorial: Exam questions.

4. 2nd order responses: What behaviours do we get from 2nd order models and how do we exploit these for modelling and design?
i. Tutorial sheet on 2nd order responses (pdf file).

ii. Video tutorial: over-damped.
iii. Video tutorial: under-damped.
iv. Video tutorial: normalised forms.
v. Video tutorial: sketching.

5. Generic system behaviours: How do we characterise behaviours in general and for high order systems? Concepts of LHP and RHP.
i. Introductory tutorial sheet.
ii. Tutorial sheet 2.

iii. Video tutorial on behaviours.

6. Nonlinear models and linearisation: A number of questions on the linearisation of models which include non-linear functions.
Tutorial sheet on linearisation.

## MATLAB RESOURCES

Use the main MATLAB page to see all resources. Topic relevant resources are referenced directly as used in the sections.
To use these files in MATLAB, save the files into your own folder and then open, for example from the command window write: "open filename" .
More precise instructions for function files are provided where required.