Q1. Attempt all parts of this question. Consider the system shown in Figure Q1, where B is a constant term. Gp(s) D(s)|d(t) 1 s+ 1 Gc(s) C(s), c(t) R(s) E(s) e(t) K r(t) 2 2s + 3

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Q1. Attempt all parts of this question.
Consider the system shown in Figure Q1, where ß is a constant term.
Gp(s)
D(s)|d(t)
1
G(s)
s+ 1
E(s)
K
e(t)
R(s)
C(s)
c(t)
r(t)
2
2s + 3
Figure Q1
(a) Derive an expression for the transfer function T1(s) from input D(s) to output C(s).
(b) Find the steady-state value of the output a(t) resulting from a step disturbance
d(t), and hence sketch the time response of c(t) for ß = 8 and K = 8.
(c) Find the transfer function T2(s) from input R(s) to output C(s).
Transcribed Image Text:Q1. Attempt all parts of this question. Consider the system shown in Figure Q1, where ß is a constant term. Gp(s) D(s)|d(t) 1 G(s) s+ 1 E(s) K e(t) R(s) C(s) c(t) r(t) 2 2s + 3 Figure Q1 (a) Derive an expression for the transfer function T1(s) from input D(s) to output C(s). (b) Find the steady-state value of the output a(t) resulting from a step disturbance d(t), and hence sketch the time response of c(t) for ß = 8 and K = 8. (c) Find the transfer function T2(s) from input R(s) to output C(s).
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