Modelling, dynamics and control by Anthony Rossiter

Section on behaviour characterisation for any order system

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.

This section focuses on developing and applying core analysis tools to a variety of low and high order systems.
1. For simplicity, all models are expressed using Laplace tools.
2. How do I describe, analyse and contrast the behaviours of different systems, including those with varying orders?

1. What do we mean by behaviours? An introduction to basic concepts and distinctions between signals, systems and transfer functions.
i. Characterising signals.
ii. Transfer functions.

2. Behaviour analysis methodologies: Looks at the links between transfer function poles and system behaviour and thus inference of likely behaviour from poles.
i. Speed of response and convergence.
ii. Oscillation with decay.

3. Steady-state analysis: What values do signals and system outputs converge to?
i. Final value theorem and signals.
ii. Steady-state gain for systems.

4. Stability and overview of behaviour analysis: Do system outputs converge or diverge? How do I formally compare behaviours of different systems?
i. Stability.
ii. Evaluation of system behaviour.

5. Supporting videos:
i. Introduction to LHP and RHP and stability.
ii. Links between poles and behaviour.
iii. Speed of response and converence.
iv. Oscillation with decay.
v. Video tutorial 1.