Page 331 - Modern Control Systems

Section 5.2 Test Input Signals 305
5.1 INTRODUCTION

The ability to adjust the transient and steady-state performance is a distinct advan-
tage of feedback control systems. To analyze and design a control system, we must
define and measure its performance. Based on the desired performance of the con-
trol system, the system parameters may be adjusted to provide the desired response.
Because control systems are inherently dynamic, their performance is usually speci-
fied in terms of both the transient response and the steady-state response. The
transient response is the response that disappears with time. The steady-state response
is the response that exists for a long time following an input signal initiation.
The design specifications for control systems normally include several time-
response indices for a specified input command, as well as a desired steady-state
accuracy. In the course of any design, the specifications are often revised to effect a
compromise. Therefore, specifications are seldom a rigid set of requirements, but
rather a first attempt at listing a desired performance.The effective compromise and
adjustment of specifications are graphically illustrated in Figure 5.1. The parameter
p may minimize the performance measure M 2 if we select p as a very small value.
However, this results in large measure M\, an undesirable situation. If the perfor-
provides the best
mance measures are equally important, the crossover point at p mm
compromise. This type of compromise is normally encountered in control system
design. It is clear that if the original specifications called for both M^ and M 2 to be
zero, the specifications could not be simultaneously met; they would then have to be
altered to allow for the compromise resulting with p min [1,10,15,20],
The specifications, which are stated in terms of the measures of performance,
indicate the quality of the system to the designer. In other words, the performance
measures help to answer the question, How well does the system perform the task
for which it was designed?

5.2 TEST INPUT SIGNALS

The time-domain performance specifications are important indices because control
systems are inherently time-domain systems. That is, the system transient or time
performance is the response of prime interest for control systems. It is necessary to

Performance Performance
measure. A/, measure. M-,

FIGURE 5.1
Two performance
measures versus /'min 3
parameter p. Parameter, p