Page 157 - Modern Control Systems

Skills Check 131

graph. Thus, in Chapter 2, we have obtained a useful mathematical model for feedback
control systems by developing the concept of a transfer function of a linear system and
the relationship among system variables using block diagram and signal-flow graph
models. We considered the utility of the computer simulation of linear and nonlinear
systems to determine the response of a system for several conditions of the system pa-
rameters and the environment. Finally, we continued the development of the Disk Drive
Read System by obtaining a model in transfer function form of the motor and arm.

CHECK

In this section, we provide three sets of problems to test your knowledge: True or False, Multiple
Choice, and Word Match. To obtain direct feedback, check your answers with the answer key
provided at the conclusion of the end-of-chapter problems. Use the block diagram in Figure 2.79
as specified in the various problem statements.

w

Controller
o w G c(s) +
R{s) ) * V* • Y(s)

N{s)

FIGURE 2.79 Block diagram for the Skills Check.

In the following TVue or False and Multiple Choice problems, circle the correct answer.
1. Very few physical systems are linear within some range of the variables. True or False
2. The s-plane plot of the poles and zeros graphically portrays the character
of the natural response of a system. True or False
3. The roots of the characteristic equation are the zeros of the closed-loop
system. True or False
4. A linear system satisfies the properties of superposition and homogeneity. True or False
5. The transfer function is the ratio of the Laplace transform of the output
variable to the Laplace transform of the input variable, with all initial
conditions equal to zero. True or False
6. Consider the system in Figure 2.79 where
G c(*) = 10, H(s) = l, and G(s) = s + **
s* + 60.y + 500
If the input R(s) is a unit step input, T d(s) = 0, and N(s) = 0, the final value of the out-
put Y(s) is:
a. y ss = limy(t) = 100
f-»CO
b. y ss = lira y(t) = 1
t—*oo
c. y ss = lim y(t) = 50
f~»0O
d. None of the above