(d) justify your answer. If NO, what is the actual steady-state error e(0)? Assume k = 10. Can this system track the reference input r(t) = 1 perfectly? If YES, (e) Suppose the above controller is replaced by a controller of the form: k Ci (s): Determine whether a controller of this form can produce a stable closed-loop system capable of tracking a step reference with zero steady-state-error e()step = 0.

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Solve d and e

• The unity feedback control structure has the following block diagram:
w
C(s)
P(s)
Transcribed Image Text:• The unity feedback control structure has the following block diagram: w C(s) P(s)
Suppose the open-loop unstable plant,
1
P(s) =
s2
s +4
and the controller,
ks
C(s) =
(s + 10)
are structured in a unity feedback control scheme.
(a)
Find the closed-loop transfer function from r to y as a ratio of polynomials in s:
Y(s)
G(s) =
R(s)
bmsm + bm-1sm-1
ans" + an-18n-1 +
+ bịs + bo
+ a1s + ao
+
...
...
(b)
Find the range of k such that the closed-loop system G(s) is stable.
(c)
Regarding the steady-state error for tracking, what is the System TYPE?
(d)
Assume k = 10. Can this system track the reference input r(t) = 1 perfectly? If YES,
justify your answer. If NO, what is the actual steady-state error e(0)?
(e)
Suppose the above controller is replaced by a controller of the form:
k
C1(s)
Determine whether a controller of this form can produce a stable closed-loop system capable
of tracking a step reference with zero steady-state-error e()step = 0.
Transcribed Image Text:Suppose the open-loop unstable plant, 1 P(s) = s2 s +4 and the controller, ks C(s) = (s + 10) are structured in a unity feedback control scheme. (a) Find the closed-loop transfer function from r to y as a ratio of polynomials in s: Y(s) G(s) = R(s) bmsm + bm-1sm-1 ans" + an-18n-1 + + bịs + bo + a1s + ao + ... ... (b) Find the range of k such that the closed-loop system G(s) is stable. (c) Regarding the steady-state error for tracking, what is the System TYPE? (d) Assume k = 10. Can this system track the reference input r(t) = 1 perfectly? If YES, justify your answer. If NO, what is the actual steady-state error e(0)? (e) Suppose the above controller is replaced by a controller of the form: k C1(s) Determine whether a controller of this form can produce a stable closed-loop system capable of tracking a step reference with zero steady-state-error e()step = 0.
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