Modern Control Engineering

D(s)

R(s) Y(s)

N(s)

Gc 2

+– Gc 1 +–– Gc 3 G 1 G 2

+

• +––

+

+

+

Problems 645

B–8–9.Show that the control systems shown in Fig-
ures 8–77(a), (b), and (c) are two-degrees-of-freedom
systems. In the diagrams,Gc1andGc2are controllers andGp
is the plant.

B–8–10.Show that the control system shown in Figure 8–78

is a three-degrees-of freedom system. The transfer func-

tionsGc1,Gc2,andGc3are controllers. The plant consists of

transfer functionsG 1 andG 2.

(c)

D(s)

Y(s)

N(s)

Gc 1 Gp

Gc 2

R(s)

+

+

+

++

(b)

D(s)

Y(s)

N(s)

Gc 1 Gc 2 Gp

R(s)

+– +

+

++

D(s)

R(s) Y(s)

Gc 1 Gp

Gc 2

(a)

+

+

+

++ N(s)

Figure 8–77
(a), (b), (c) Two
degrees-of-freedom
systems.

Figure 8–78
Three-degrees-of-
freedom system.