Modelling, dynamics and control by Anthony Rossiter

Section on linearisation of nonlinear models

This section is part of 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.

This section focuses on linearisation of nonlinear models.
1. Linear models are easier ot analyse and generic insights and solvers exist.
2. Despite being non-linear in reality, a linearised approximation which is valid locally is often good enough for design decisions, control and insight.

1. What do we mean by a linear model and superposition? Students often confuse straight lines and linear models. It is important to form a clear distinction and to emphasis the concept of superposition which is a powerful model and simulation device.
Linear models and superposition.

2. Linearisation using Taylor series: Gives a brief introduction to a Taylor series and illustrates its use to linearise non-linear functions.
1st order Taylor series and linearisation.

3. Linearisation of models: This note gives a simple algorithm and then some worked examples of developing linear model approximations to nonlinear models.
Linearised modelling case studies.

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.