Chapter 6 - Application of Laplace Analysis to Control

Abstract

In this chapter we illustrate how the Laplace transform is related to the classical and modern theories of control. In classical control, frequency-domain methods are used to change the dynamics of a plant—to achieve a desired response—typically connecting in feedback a controller to the plant. The concepts of transfer function, stability of systems and different types of responses obtained through the Laplace transform are useful in the analysis and design of control systems. Modern control, on the other hand, uses a time-domain approach to characterize and control systems. The state-variable representation used is more general than the transfer function, and it allows multiple inputs and outputs. In this chapter, we introduce the concept of state variables, its connection with the transfer function and the use of the Laplace transform to find the complete response and the transfer function from the state and output equations. This chapter illustrates problems in classical and modern control and link them with the Laplace analysis. MATLAB is used to illustrate some of the concepts covered in this chapter.