Modern Control Engineering

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Problems 265

+

• 
  

+

• 
  

R(s) 1 C(s)

s

16

s+ 0.8

k

R(s) 1 C(s)

s

K

s+ 2

k

+

• 
  

+

• 
  

Figure 5–75

Closed-loop system.

Figure 5–76

Block diagram of a system.

B–5–8.Referring to the system shown in Figure 5–75, de-
termine the values of Kandksuch that the system has a
damping ratio zof 0.7 and an undamped natural frequency
vnof 4 radsec.

B–5–9.Consider the system shown in Figure 5–76. Deter-
mine the value of ksuch that the damping ratio zis 0.5. Then
obtain the rise time tr, peak time tp, maximum overshoot
Mp, and settling time tsin the unit-step response.

B–5–10.Using MATLAB, obtain the unit-step response,
unit-ramp response, and unit-impulse response of the fol-
lowing system:

whereR(s)andC(s)are Laplace transforms of the input
r(t)and output c(t), respectively.

C(s)

R(s)

=

10

s^2 +2s+ 10

B–5–11.Using MATLAB, obtain the unit-step response,

unit-ramp response, and unit-impulse response of the fol-

lowing system:

whereuis the input and yis the output.

B–5–12.Obtain both analytically and computationally

the rise time, peak time, maximum overshoot, and settling

time in the unit-step response of a closed-loop system

given by

C(s)

R(s)

=

36

s^2 +2s+ 36

y =[1 0]B

x 1

x 2

R

B

x# 1

x# 2

R =B

- 1 - 0.5

10

RB

x 1

x 2

R+ B

0.5

0

Ru