Modern Control Engineering

62 Chapter 2 / Mathematical Modeling of Control Systems

B–2–8.Obtain a state-space representation of the system

shown in Figure 2–35.

B–2–9.Consider the system described by

Derive a state-space representation of the system.

B–2–10.Consider the system described by

Obtain the transfer function of the system.

y =[1 0]B

x 1

x 2

R

B

x# 1

x

2

R = B

- 4

3

- 1

- 1

RB

x 1

x 2

R +B

1

1

Ru

y%+3y$+2y#=u

uys+z

s+p

1

s^2

+

• 
  

Figure 2–35

Control system.

B–2–11.Consider a system defined by the following state-

space equations:

Obtain the transfer function G(s)of the system.

B–2–12.Obtain the transfer matrix of the system defined by

B–2–13.Linearize the nonlinear equation

z=x^2 +8xy+3y^2

in the region defined by 2x4, 10y12.

B–2–14.Find a linearized equation for

y=0.2x^3

about a point x=2.

B

y 1

y 2

R = B

1

0

0

1

0

0

RC

x 1

x 2

x 3

S

C

x# 1

x# 2

x# 3

S = C

0

0

- 2

1

0

- 4

0

1

- 6

SC

x 1

x 2

x 3

S + C

0

0

1

0

1

0

SB

u 1

u 2

R

y =[1 2]B

x 1

x 2

R

B

x# 1

x# 2

R = B

- 5

3

- 1

- 1

RB

x 1

x 2

R +B

2

5

Ru

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