Page 308 - Modern Control Systems

282 Chapter 4 Feedback Control System Characteristics

Consider the block diagram in Figure 4.39 for Problems 13-14 with G c(s) = K and
W
5 + 1
13. The sensitivity S[ is:
1
s + Kb + 1
s + 1
b. Si =
s + Kb + 1
s + 1
c Sl =
s + Kb + 2
s
d. Sl =
s + Kb+ 2
14. Compute the minimal value of K so that the steady-state error due to a unit step distur-
bance is less than 10%.
a. K = 1 - 7
b
b. K = b
c. £ = 10 - |
o
d. The steady-state error is oo for any K
15. A process is designed to follow a desired path described by
2
r(t) = (5 - t + 0.5t )u{t)
where r(t) is the desired response and u{t) is a unit step function. Consider the unity
feedback system in Rgure 4.39. Compute the steady-state error (E(s) = R(s) — Y(s)
with T d(s) = 0) when the loop transfer function is
10(5 + 1)
5^(5 + 5)
a. e„ = lim e(f) -* oo
r—»oo
b. e s, = lime(0 = 1
J-.0 0
c. e iS - lim e(r) = 0.5
t—tac
d. e vs = lime(f) = 0
r-»oo
In the following Word Match problems, match the term with the definition by writing the
correct letter in the space provided.
a. Instability An unwanted input signal that affects the system output
signal.
b. Steady-state The difference between the desired output, R(s), and the
error actual output, Y(s).
c. System A system without feedback that directly generates the
sensitivity output in response to an input signal.
d. Components The error when the time period is large and the transient
response has decayed leaving the continuous response.