Linearisation of systems from the real nonlinear world

Abstract

Previously in this book, we have met systems whose descriptions can be represented by a set of linear differential equations. These equations have then been transformed into a transfer function or a linear state variable representation. In practice, most system models comprise nonlinear equations or components with nonlinear descriptions. There is a wealth of knowledge on the control of nonlinear systems (beyond the scope of this book), but in many cases the first stage of analysis would be to consider whether the system could be approximated by a linear representation. If a linear form is valid then this linear representation is convenient and has the advantage that we are able to use linear analysis techniques. In this chapter we focus on simple nonlinear features in a system, how a linear approximation can be derived and the region over which this approximation remains valid.