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.

RAPID SUMMARY: Relatively quick overview videos introducing the core topics.

1) Modelling concepts and analogies: basics of 1st principles modelling and links between systems.
2) 1st order modelling: Examples of several 1st order models and analogies between them.
3) 1st order responses and related problem solving: how do 1st order models behave and why? Concepts of time constant and gain.
4) 2nd order modelling: Examples of several 1st order models and analogies between them.
5) 2nd order responses: how do 2nd order models behave and why? Concepts of damping/oscillation.
6) Generic behaviours: overview of characterisation of system behaviours. Stability, LHP and RHP.

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.

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.

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?

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.

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?

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

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

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.

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