Modern Control Engineering

In the following we shall examine the transient-response characteristics of the compensated

system. (The gain-adjusted but uncompensated system is unstable.) The closed-loop transfer func-

tion of the compensated system is

The unit-step and unit-ramp response curves obtained with MATLAB are shown in Figures 7–113

and 7–114, respectively.

C(s)

R(s)

=

95.381s^2 +81s+ 10

4.7691s^5 +47.7287s^4 +110.3026s^3 +163.724s^2 +82s+ 10

516 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method

Output

1.6

0.6

0

1

1.4

0.4

0.2

1.2

0.8

t Sec

042 6 8 10 12 14 16 18 20

Unit-Step Response of Compensated System

Figure 7–113

Unit-step response of

the compensated

system (Example

7–28).

Output

20

8

0

12

18

4

2

16

10

14

6

t Sec

042 6 8 10 12 14 16 18 20

Unit-Ramp Response of Compensated System

Figure 7–114

Unit-ramp response

of the compensated

system (Example

7–28).

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