ABSTRACT
This chapter introduces the Laplace transform as a technique for modelling signals and systems, and pole-zero diagrams as system models. It explains how the Laplace transform can be used to calculate the complete response of a system to an applied input. The chapter distinguishes between transient and steady-state components in complete system response, and shows how transient response is related to system pole positions. It presents an s-plane stability criterion and also explains the concept of dominant poles, and indicates when a higher-order system may be modelled by the dominant poles alone. Laplace transform methods are standard modelling tools in control engineering. The general idea is to convert a time domain, differential equation model of system behaviour into a form which is easier to manipulate and interpret. Extending step response approach to a general linear system allows an important link to be made between the system poles and the general nature of the response.
