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Transient and Steady-State

Response Analyses

5–1 Introduction

In early chapters it was stated that the first step in analyzing a control system was to de-

rive a mathematical model of the system. Once such a model is obtained, various meth-

ods are available for the analysis of system performance.

In practice, the input signal to a control system is not known ahead of time but is

random in nature, and the instantaneous input cannot be expressed analytically. Only in

some special cases is the input signal known in advance and expressible analytically or

by curves, such as in the case of the automatic control of cutting tools.

In analyzing and designing control systems, we must have a basis of comparison of

performance of various control systems. This basis may be set up by specifying particular

test input signals and by comparing the responses of various systems to these input signals.

Many design criteria are based on the response to such test signals or on the re-

sponse of systems to changes in initial conditions (without any test signals). The use of

test signals can be justified because of a correlation existing between the response char-

acteristics of a system to a typical test input signal and the capability of the system to cope

with actual input signals.

Typical Test Signals. The commonly used test input signals are step functions,

ramp functions, acceleration functions, impulse functions, sinusoidal functions, and white

noise. In this chapter we use test signals such as step, ramp, acceleration and impulse

signals. With these test signals, mathematical and experimental analyses of control sys-

tems can be carried out easily, since the signals are very simple functions of time.

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