ABSTRACT
This chapter on ‘Nonlinear Systems’ discusses the topics, namely: Inherent characteristics of nonlinear systems, types of nonlinearity (saturation, deadzone, friction, backlash, relay), linearization using describing function, derivation of describing functions for different nonlinear elements (deadzone, saturation, deadzone and saturation, on–off controller with dead zone, backlash, relay with deadzone and hysteresis), phase plane definitions (phase plane, phase trajectory, phase portrait, singular point, behaviour of trajectories in the vicinity of singular point), limit cycle, phase plane analysis using analytical method, isocline method and delta method.
In practice, all the systems are nonlinear in nature. The nonlinearity can be incidental or intentional. The characteristics of nonlinear systems make it difficult to analyse. The nonlinear element can be approximated as a linear element using describing function approach. The describing function analysis is based on Fourier series approach. Phase plane analysis is used for investigating system behaviour and hence to design system parameters to achieve a desired response.
