Modern Control Engineering

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

B–7–30.Draw Bode diagrams of the PI controller given by

and the PD controller given by

B–7–31.Figure 7–165 shows a block diagram of a space-

vehicle attitude-control system. Determine the proportional

gain constant Kpand derivative time such that the band-

width of the closed-loop system is 0.4 to 0.5 radsec. (Note

that the closed-loop bandwidth is close to the gain crossover

frequency.) The system must have an adequate phase mar-

gin. Plot both the open-loop and closed-loop frequency re-

sponse curves on Bode diagrams.

Td

Gc(s)=5(1+0.5s)

Gc(s)= 5 a 1 +

1

2s

b

Kp(1+Tds)^1

s^2

+

+– Gc(s) s(0.1s+ 1)(K s+ 1)

Figure 7–166

Closed-loop system.

B–7–32.Referring to the closed-loop system shown in Fig-

ure 7–166, design a lead compensator Gc(s)such that the

phase margin is 45°, gain margin is not less than 8 dB, and the

static velocity error constant Kvis 4.0 sec–1. Plot unit-step

and unit-ramp response curves of the compensated system

with MATLAB.

B–7–33.Consider the system shown in Figure 7–167. It is

desired todesign a compensator such that the static

velocity error constant is 4 sec–1, phase margin is 50°, and

gain margin is 8 dB or more. Plot the unit-step and unit-

ramp response curves of the compensated system with

MATLAB.

Gc(s)

1

Hydraulic servo

1

s

Aircraft

2 s+ 0.1

s^2 + 0.1s+ 4

Rate gyro

R C

+

Figure 7–167

Control system.

Gc(s)^1

s(s+ 1)(s+ 5)

+

Figure 7–168

Control system.

B–7–34.Consider the system shown in Figure 7–168. De-

sign a lag–lead compensator such that the static velocity

error constant Kvis 20 sec–1, phase margin is 60°, and gain

margin is not less than 8 dB. Plot the unit-step and unit-

ramp response curves of the compensated system with

MATLAB.

Figure 7–165

Block diagram of space-vehicle attitude-control system.

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