Modelling, dynamics and control by Anthony Rossiter

Chapter on Modelling and Behaviour

This chapter is 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.

Core skills are things such as:
1. How do I find a mathematical model representation of a real physical system?
2. How do such systems behave and how does the behaviour link to the model parameters?
3. Are there generic analysis tools that help with understanding?
It is implicit that students have core competence in some mathematical topics such as polynomials, roots, complex numbers, exponentials and Laplace.

1. Modelling principles: How do we do physical modelling? Are there common concepts we can exploit? What are the analogies between different disciplines? Derive models for example scenarios. Link here.

2. First order modelling: Define a number of engineering scenarios which lead to first order models. Demonstrate the modelling from first principles and illustrate analogies. Link here.

3. First order model behaviours: How do first order systems behave? Are there efficient and insightful ways of defining and illustrating behaviour. How do we choose system parameters to achieve the desired behaviour? Link here .

4. Second order modelling: Define a number of engineering scenarios which lead to second order models. Demonstrate the modelling from first principles and illustrate analogies. Link here.

5. Second order model behaviours: How do second order systems behave? Are there efficient and insightful ways of defining and illustrating behaviour. How do we choose system parameters to achieve the desired behaviour? Link here.

6. Generic behaviours: Discussion of how to characterise behaviour in general, including for higher order systems. Link here.

7. Case studies: Examples of a variety of engineering scenarios and modelling from first principles leading to models with different orders and attributes. Link here.

8. Linearisation of non linear models: Most real models included nonlienar ocmponents and relationships, but can be approximated well enough locally by a linear model. Link here.

## 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.