Modern Control Engineering

46 Chapter 2 / Mathematical Modeling of Control Systems

Example Problems and Solutions

A–2–1. Simplify the block diagram shown in Figure 2–17.

Solution.First, move the branch point of the path involving H 1 outside the loop involving H 2 ,as

shown in Figure 2–18(a). Then eliminating two loops results in Figure 2–18(b). Combining two

blocks into one gives Figure 2–18(c).

A–2–2. Simplify the block diagram shown in Figure 2–19. Obtain the transfer function relating C(s)and

R(s).

R(s) C(s)

G

H 1

H 2

+

++

Figure 2–17

Block diagram of a

system.

R(s) C(s)

R(s) C(s)

C(s)

G

H 2

(a)

(b)

(c)

H 1

G

G

1 + GH 2

R(s)

1 +H^1

G

G+ H 1

1 + GH 2

+– +

+

Figure 2–18

Simplified block

diagrams for the

system shown in

Figure 2–17.

G 1 G 2

R(s) X(s) C(s)

++ ++

Figure 2–19

Block diagram of a

system.

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