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.


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