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Problem 10.06PP
Consider the block diagram for the servomechanism drawn in Fig. Which of the following claims 
are true?
(a) The actuator dynamics (the pole at 1000 rad/sec) must be included in an analysis to evaluate 
a usable maximum gain for which the control system is stable.
(b) The gain K must be negative for the system to be stable.
(c) There exists a value of K for which the control system will oscillate at a frequency between 4 
and 6 rad/sec.
tfW_The_system is Iins tah ip if IAC1 in
(d) The system is unstable if |/C| 10.
(e) If K must be negative for stability, the control system cannot counteract a positive disturbance.
(f) A positive constant disturbance will speed up the load, thereby making the final value of e 
negative.
(g) With only a positive constant command input r, the error signal e must have a final value 
greater than zero.
(h) For K = -1 the closed-loop system is stable, and the disturbance results in a speed emor 
whose steady-state magnitude is less than 5 rad/sec.
Figure Servomechanism
Distmbance (0.1 N*m)
S tep -by-s tep s o lu tio n
Step 1 of 7
a) Tme. even though it is tempting to ^proxim ate the actuator as infinitely &st 
and hence, not important The Actuator pole dramatically alters the root locus 
plot of the system to be controlled.
Step 2 of 7
b) True
Step 3 of 7
c) True
Step 4 of 7
d)True
Step 5 of 7
e) False
Step 6 of 7
£) True
Step 7 of 7
U False