Modern Control Engineering

644 Chapter 8 / PID Controllers and Modified PID Controllers

B–8–7.Consider the system shown in Figure 8–75. Obtain

the closed-loop transfer functionC(s)/R(s)for the refer-

ence input and the closed-loop transfer function C(s)/D(s)

for the disturbance input. When consideringR(s)as the

input, assume thatD(s)is zero, and vice versa.

B–8–8.Consider the system shown in Figure 8–76(a),

whereKis an adjustable gain and G(s)andH(s)are fixed

components. The closed-loop transfer function for the

disturbance is

To minimize the effect of disturbances, the adjustable gain

Kshould be chosen as large as possible.

Is this true for the system in Figure 8–76(b), too?

C(s)

D(s)

=

1

1 +KG(s)H(s)

G 1 (s) G 2 (s)

R(s) C(s)

D(s)

G 3 (s)

H 1 (s)

H 2 (s)

+– +– +

+

Figure 8–75

Control system.

G(s)

R(s) C(s)

D(s)

D(s)

K

H(s)

G(s)

R(s) C(s)

K

H(s)

(a)

(b)

+ ++

++

+

Figure 8–76

(a) Control system with disturbance entering in the

feedforward path; (b) control system with disturbance

entering in the feedback path.

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