8 - Nonlinear Systems

Abstract

All the real-world systems exhibit nonlinear characteristics and do not satisfy the requirements of a linear system. The analysis of linear systems by z transform and Laplace transform is done to approximate nonlinear systems as linear ones. For successful application of linear systems to nonlinear systems, the chapter gives an insight into differences between the two and discusses the various aspects of nonlinear control system design and analysis. The chapter discusses different types of nonlinearities—sneaky nonlinearities, nonlinearities with memory, surface nonlinearities, actuator saturation, friction, and hysteresis—through illustrative examples. The chapter briefly describes the general steps to solve the nonlinear control problems: First, find a linear system model of the nonlinear system; second, design the controller assuming the system to be linear; third, embellish the linear model with easy and accurate features; and fourth, embellish the controller design with features to keep the system designs within parameters. The chapter lists common methods for analyzing nonlinear control systems: linearizing around the operating point, using describing functions, modeling with uncertain parameters, and modeling with apparent noise. The chapter discusses the various problems associated with designing and analyzing nonlinear systems. Inverse functions, gain scheduling, restricting the system state, pulsating drive, deadband, and changing the plant are the methods to deal with such problems.