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PID Control of Nonlinear Systems

This chapter introduces linearization of nonlinear models through several examples. It also shows how to apply the proportional integral derivative (PID) controllers to a nonlinear plant using the technique called gain scheduled control. 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. 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 to understand how the linearization is performed, the chapter examines the case of linearization of a nonlinear function. It then presents a case study based on a final year project performed by Mr John Lee. As part of the project, a prototype of a ball and plate balancing system was built and PID control systems were designed for this self‐made system.