Modern Control Engineering

Problems 267

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B–5–15.Using MATLAB, obtain the unit-step response
curve for the unity-feedback control system whose open-
loop transfer function is

Using MATLAB, obtain also the rise time, peak time, max-
imum overshoot, and settling time in the unit-step response
curve.

B–5–16.Consider the closed-loop system defined by

wherez=0.2, 0.4, 0.6, 0.8, and 1.0. Using MATLAB, plot a
two-dimensional diagram of unit-impulse response curves.
Also plot a three-dimensional plot of the response curves.

B–5–17.Consider the second-order system defined by

wherez=0.2, 0.4, 0.6, 0.8, 1.0. Plot a three-dimensional
diagram of the unit-step response curves.

B–5–18.Obtain the unit-ramp response of the system
defined by

whereuis the unit-ramp input. Use the lsimcommand to
obtain the response.

y =[1 0]B

x 1

x 2

R

B

x# 1

x# 2

R =B

0

- 1

1

- 1

RB

x 1

x 2

R +B

0

1

Ru

C(s)

R(s)

=

s+ 1

s^2 + 2 zs+ 1

C(s)

R(s)

=

2 zs+ 1

s^2 + 2 zs+ 1

G(s)=

10

s(s+2)(s+4)

B–5–19.Consider the differential equation system given by

Using MATLAB, obtain the response y(t), subject to the

given initial condition.

B–5–20.Determine the range of Kfor stability of a unity-

feedback control system whose open-loop transfer function is

B–5–21.Consider the following characteristic equation:

Using the Routh stability criterion, determine the range of

Kfor stability.

B–5–22.Consider the closed-loop system shown in Figure 5–79.

Determine the range of Kfor stability. Assume that K>0.

s^4 +2s^3 +(4+K)s^2 +9s+ 25 = 0

G(s)=

K

s(s+1)(s+2)

y$+3y#+2y=0, y(0)=0.1, y#(0)=0.05

+–

R(s) C(s)

K (s+ 1)(ss 2 – +^2 6 s+ 25)

Figure 5–79Closed-loop system.

B–5–23.Consider the satellite attitude control system

shown in Figure 5–80(a). The output of this system exhibits

continued oscillations and is not desirable. This system can

be stabilized by use of tachometer feedback, as shown in

Figure 5–80(b). If K/J=4, what value of Khwill yield the

damping ratio to be 0.6?

+– +–

R(s) C(s)

(b)

Kh

K

Js

1

s

+

• 
  

R(s) C(s)

(a)

K^1

Js^2

Figure 5–80

(a) Unstable satellite

attitude control system;

(b) stabilized system.