Consider the closed-loop system block diagram shown below: R(s) Ge(s) C(s) s(s+2)(s+3) S (a) Suppose the controller G.(s) is a constant gain given by G.(s) = K, find the range of K so that the steady-state error (ie., e(t) = r(t) - c(t) ast-> o) under a unit ramp input is less than 0.01. (b) The range of K that keeps the system stable. (c) The frequency of oscillation when K is set to the value that makes the system oscillate. ( (d) Suppose that we repiace the constant gain controller K with the more sophisticated PI controller, i.e., G(s) = K + (K/s), find the rango controller gains (K, Kil so the qu

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Consider the closed-loop system block diagram shown below:
R(s)
Go(s)
1
C(s)
s(s+2)(s+3)
(a) Suppose the controller G.(s) is a constant gain given by G(s) = K, find the
range of K so that the steady-state error (i e, e(t) = r(t) - c(t) as t -> ∞) under
a unit ramp input is less than 0.01.
(b) The range of K that keeps the system stable.
(c) The frequency of oscillation when K is set to the vaiue that makes the
system oscillate. (
(d) Suppose that we repiace the constant gain controller K with the more
sophisticated PI controller, i.e., G(s) = K + (K//s), find the range of the
controller gains (K, K¡) so the system is stable.
("
Transcribed Image Text:Consider the closed-loop system block diagram shown below: R(s) Go(s) 1 C(s) s(s+2)(s+3) (a) Suppose the controller G.(s) is a constant gain given by G(s) = K, find the range of K so that the steady-state error (i e, e(t) = r(t) - c(t) as t -> ∞) under a unit ramp input is less than 0.01. (b) The range of K that keeps the system stable. (c) The frequency of oscillation when K is set to the vaiue that makes the system oscillate. ( (d) Suppose that we repiace the constant gain controller K with the more sophisticated PI controller, i.e., G(s) = K + (K//s), find the range of the controller gains (K, K¡) so the system is stable. ("
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