(a) Derive the system's loop transfer function L(s) and closed-loop transfer function T₁ (s) Y(s) R(S) (b) Determine the steady-state error E(s) (i.e., = R(s) - Y(s)), in terms of k, for a unit step input, R(s) == (c) Refer to the characteristic function of the closed-loop system of Fig. Q4 and with k set to 10, determine the percentage overshoot (P. O.) and 2% settling time of the closed-loop system's characteristic behaviour.
(a) Derive the system's loop transfer function L(s) and closed-loop transfer function T₁ (s) Y(s) R(S) (b) Determine the steady-state error E(s) (i.e., = R(s) - Y(s)), in terms of k, for a unit step input, R(s) == (c) Refer to the characteristic function of the closed-loop system of Fig. Q4 and with k set to 10, determine the percentage overshoot (P. O.) and 2% settling time of the closed-loop system's characteristic behaviour.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Q4 just answer a few of them no need to complete everything thank you.
Transcribed Image Text:Question 4
Consider the system in Fig. Q4 with the following transfer functions:
k(s+2)
s+6
Gc(s) =
G(s)
‚H(s) = 1.
S
s²+2s
Controller
Process
+ Eg(s)
R(S)
Ge(s)
G(s)
Y(s)
Sensor
H(s)
Fig. Q4
(a) Derive the system's loop transfer function L(s) and closed-loop transfer function T₁ (s) =
Y(s)
R(s)*
-
(b) Determine the steady-state error E (s) (i.e., = R(s) — Y(s)), in terms of k, for a unit step input,
R(s) = =
(c) Refer to the characteristic function of the closed-loop system of Fig. Q4 and with k set to 10,
determine the percentage overshoot (P. O.) and 2% settling time of the closed-loop system's
characteristic behaviour.
(d) With k set to 10, comment and explain whether the actual response of the system in Fig. Q4 (i.e.,
the closed-loop transfer function) will have the exact step response as described by the solutions
(P.O. and 2% settling time) in part (c).
=
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