PID Control System Design and Automatic Tuning using MATLAB/Simulink

6PID Control of Nonlinear Systems

6.1 Introduction

One of the approaches to obtain the models for the control system design is based on analysis of the system dynamics using first principles, such as mass balance, Newton's laws, current law and voltage law. The majority of these types of models are nonlinear in nature. Thus, in order to use them for the PID controller design or other linear time invariant controller design, these nonlinear models need to be linearized around the operating conditions of the system.

This chapter will introduce linearization of nonlinear models through several examples and case studies. It will also show how to apply the PID controllers to a nonlinear plant using the technique called gain scheduled control.

6.2 Linearization of the Nonlinear Model

The starting point of designing a PID controller for a nonlinear plant is to obtain a linear time invariant model through linearization around the chosen operating conditions of the system.

6.2.1 Approximation of a Nonlinear Function

Assume that the nonlinear models have the general form:

(6.1)

where is a nonlinear function. The purpose of linearization is to find a linear function (a set of linear functions) to describe the dynamics of the nonlinear model at a given operating condition.

In order ...