Modelling and behaviour
Section eight: linearisation of non-linear models
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.
Linear models are easier to analyse and generic insights and solvers exist.
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 (PDF, 180 KB)
2. Linearisation using Taylor series
Gives a brief introduction to a Taylor series and illustrates its use to linearise non-linear functions.
First order Taylor series and linearisation (PDF, 290 KB)
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 (PDF, 274 KB)