3 - Time domain analysis

Abstract

The time response of any system has two components: transient response and steady-state response. The total response of the system is always the sum of the transient and steady-state components. Differences between the input function and system response are called transient errors during the transient period and are called steady-state errors during the steady-state period. One of the major objectives of control system design is to minimize these errors. This chapter presents various analytical and numerical techniques for time domain analysis. To compute the time response of a dynamic system, it is necessary to solve the differential equations for given inputs. There are a number of analytical and numerical techniques available to do this, but the most popular in use is the Laplace transform. A transfer function is the Laplace transform of a differential equation with zero initial conditions, used for time domain analysis. The chapter also illustrates the time domain response of first-order, second-order, and other higher order systems.