Transcript
8.4.3. ~onsider-the system shown in Figure 4-54(a). The damping ratio of this system is 0.158 and the undamped nat-
ural frequency is 3.16 rad/sec. To improve the relative stability, we emploY tachometer feedback. Figure 4-54(b) shows ,such a tachometer-feedback system.
Determine the value of Kh so that the damping ratio of the system is 0.5. Draw unit-step response curves of both the original and tachometer-feedback systems.
Figure 4-54 (a) Control system; (b) control system with tachometer feedback.
B-4-5. Consider the unit-step response of a unity-feedback control system whose open-loop transfer function is
1 G(s) = ( ) s s + 1
Obtain the rise time, peak time, maximum overshoot, and settling time. .
8-6-2. Plot the root loci for a closed-loop control system
with
K(s + 9) G(s) = s(? + 4s + 11) ,
H(s) = 1
Locate the closed-loop poles on the root loci such that the dominant closed-loop poles have a damping ratio equal to 0.5. Determine the corresponding value of gain K.
B-6-11 •. Consider the system shown in Figure 6-68. The sy~tem mvolves velocity feedback. Determine the value of gam ~ such. that the, dominant closed-loop poles have a dampmg ratlO of 0.5. . '.
Figure 6-68 Control system.
II 0
C(s)
(a)
R(s)
(b)
B-4-6. Consider the closed-loop system given by
C(s) _ w~ R(s) - S2 + 21;wrrS + w~
Determine the values of 1; and Wn so that the system responds to a step input with approximately 5% overshoot
. and with a settling time of 2 sec. (Use the 2 % criterion.)
R(s) C(s)
C(s)
Modern Control Engineeringby Katsuhiko OgataChapter: 5 Problem:9P
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