Modern Control Engineering

60 Chapter 2 / Mathematical Modeling of Control Systems

Thus

Hence a linear approximation of the given nonlinear equation near the operating point is

z-30x-72y+ 243 = 0

z- 243 =30(x-9)+72(y-3)

R(s) C(s)

G 1 G 2 G 3

H 1

H 2

H 3

+

• 
  

+– +– ++

Figure 2–31

Block diagram of a system.

B–2–1.Simplify the block diagram shown in Figure 2–29

and obtain the closed-loop transfer function C(s)/R(s).

B–2–2.Simplify the block diagram shown in Figure 2–30

and obtain the closed-loop transfer function C(s)/R(s).

B–2–3.Simplify the block diagram shown in Figure 2–31

and obtain the closed-loop transfer function C(s)/R(s).

Problems

R(s) C(s)

G 1

G 2

G 3

G 4

+

• 
  
  
  
  • 
    
    
    
    • 
      
    
    
    
    
  
  
  
  

+

+

Figure 2–29

Block diagram of a system.

R(s) C(s)

G 1

G 2

H 1

H 2

+

• 
  

++

+

• 
  

Figure 2–30

Block diagram of a system.

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