Page 305 - Modern Control Systems

Skills Check 279

Table 4.5 System Response of the System Shown in Figure 4.38(a)
Open Loop* Closed Loop
K= 1 K= 1 K=8 K= 10
Rise time (s) (10% to 90% of final value) 3.35 1.52 0.45 0.38
Percent overshoot (%) 0 4.31 33 40
Final value of y(t) due to a disturbance, T (i(s) = l/s 1.0 0.50 0.11 0.09
Percent steady-state error for unit step input 0 50% 11% 9%
Percent change in steady-state error due to 10% 10% 5.3% 1.2% 0.9%
decrease in K
*Response only when K = 1 exactly.

the gain is increased. Also, the feedback system demonstrates excellent reduction of
the steady-state error as the gain is increased. Finally, Figure 4.38(b) shows the re-
sponse for a unit step disturbance (when R(s) = 0) and shows how a larger gain will
reduce the effect of the disturbance.
Feedback control systems possess many beneficial characteristics. Thus, it is not
surprising that there is a multitude of feedback control systems in industry, govern-
ment, and nature.

m SKILLS 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
4.39 as specified in the various problem statements.

W

Controller Process
. E a(s) +
R(s) G c(s) o G(.v) + Y(s)
K> ) * ^

FIGURE 4.39 Block diagram for the Skills Check.
In the following True or False and Multiple Choice problems, circle the correct answer.
1. One of the most important characteristics of control systems is their
transient response. True or False
2. The system sensitivity is the ratio of the change in the system transfer
function to the change of a process transfer function for a small
incremental change. True or False
3. A primary advantage of an open-loop control system is the ability to
reduce the system's sensitivity. True or False
4. A disturbance is a desired input signal that affects the system output
signal. True or False