Modern Control Engineering

386 Chapter 6 / Control Systems Analysis and Design by the Root-Locus Method

Time (sec)

0 50 100 150 200 250 300

(b)

Amplitude

0.3

0.6

0

1

0.4

0.7

0.1

0.9

0.8

0.5

0.2

Unit-Step Response of Uncompensated System

R(s) C(s)

1

Rate gyro

Hydraulic servo Aircraft

1

s

2 s+ 0.1

s^2 + 0.1s+ 4

(a)

+–

Figure 6–93

(a) Attitude-rate

control system;

(b) unit-step

response.

It is desired to speed up the response and also eliminate the oscillatory mode at the beginning

of the response. Design a suitable compensator such that the dominant closed-loop poles are at

Solution.Figure 6–94 shows a block diagram for the compensated system. Note that the open-loop

zero at and the open-loop pole at s=0generate a closed-loop pole between s=0

ands=–0.05.Such a closed-loop pole becomes a dominant closed-loop pole and makes the re-

sponse quite slow. Hence, it is necessary to replace this zero by a zero that is located far away

from the jvaxis—for example, a zero at s=-4.

s=-0.05

s=- 2 ;j2 13.

Gc(s)

R(s) C(s)

1

Rate gyro

Hydraulic servo Aircraft

1

s

2 s+ 0.1

+– s (^2) + 0.1s+ 4
Figure 6–94
Compensated
attitude-rate control
system.
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