Chapter nine

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 linearisation of nonlinear models. 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 first and second order modelling and dynamics, but the principles are easily extended.

Concepts and components

• Using units in modelling (PDF, 581KB)

• Modelling resistor circuits (PDF, 656KB)

• Analogies between resistor and spring arrangements (PDF, 541KB)

• Systems with mechanical and fluid components (PDF, 804KB)

First and second order modelling and analogies

Mixture of PDF files and videos.

• Tutorial sheet on first order modelling (PDF, 925KB)

• Tutorial sheet on second order modelling (PDF, 319KB)

• Video tutorial: Tank system modelling

• Video tutorial: Heat exchanger modelling

• Video tutorial: Mixing tank

First order responses

There are overlaps in some of the later tutorial sheets so you could do a sample from each.

• Introductory questions (PDF, 234KB)

• Using Laplace (PDF, 156KB)

• Application and context questions (PDF, 252KB)

• Parameter dependence question (PDF, 237KB)

• Challenging questions eg exam level (PDF, 255KB)

Talk through video tutorials on YouTube for first order systems

• Video tutorial: Miscellaneous introductory questions

• Video tutorial: Transfer functions

• Video tutorial: Laplace

• Video tutorial: Response dependence on parameters

• Video tutorial: System design

• Video tutorial: Exam questions

Second order responses

What behaviours do we get from second order models and how do we exploit these for modelling and design?

• Tutorial sheet on second order responses (PDF, 319KB)

• Video tutorial: over-damped

• Video tutorial: under-damped

• Video tutorial: normalised forms

• Video tutorial: sketching

Generic system behaviours

How do we characterise behaviours in general and for high order systems? Concepts of LHP and RHP.

• Introductory tutorial sheet (PDF, 240KB)

• Tutorial sheet two (PDF, 306KB)

• Video tutorial on behaviours

Non-linear models and linearisation

A number of questions on the linearisation of models which include non-linear functions.

Tutorial sheet on linearisation (PDF, 339KB)