Modern Control Engineering

Example Problems and Solutions 385

A–6–18. Figure 6–93(a) is a block diagram of a model for an attitude-rate control system. The closed-loop

transfer function for this system is

The unit-step response of this system is shown in Figure 6–93(b). The response shows high-

frequency oscillations at the beginning of the response due to the poles at

The response is dominated by the pole at s=-0.0167.The settling time is approximately 240 sec.

s=-0.0417;j2.4489.

=

2(s+0.05)

(s+0.0417+j2.4489)(s+0.0417-j2.4489)(s+0.0167)

C(s)

R(s)

=

2s+0.1

s^3 +0.1s^2 +6s+0.1

t Sec

0 2 4 6 8 10 12 14

(a)

Output

0.4

0.8

1.4

0

1.2

0.6

1

0.2

Unit-Step Response of Compensated System

t Sec

071 2 3 4 5 6 8 9 10

(b)

Output

3

7

0

9

4

8

2

6

5

1

10

Unit-Ramp Response of Compensated System

Figure 6–92
(a) Unit-step
response of the
compensated system;
(b) unit-ramp
response of the
compensated system.