Solution: Yref (t) e(t) u(t) y(t) Controller Actuator Plant + K(s) F(s) G(s) Sensor H(s) Show that the closed - loop transfer function from the current reference signal, yref (t) to the controlled current signal, y(t) is given by, y(s) G(s)F(s)K(s) Yref (S) 1+G(s)F(s)K(s)H(s) y(s) = G(s)F(s)K(s) (Yref (S) − H(s)y(s)) ⇒ => ⇒ (1 + G(s)F(s)K(s)H(s))y(s) = G(s)F(s)K(S)yref(s) ⇒ y(s) Yref (S) = G(s)F(s)K(s) 1 + G(s)F(s)K(s)H(s)

Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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the question with its answer but i still dont see how the expansion and the calculation done. please show detailed steps. 

Solution:
Yref (t)
e(t)
u(t)
y(t)
Controller
Actuator
Plant
+
K(s)
F(s)
G(s)
Sensor
H(s)
Show that the closed - loop transfer function from the current reference signal, yref (t)
to the controlled current signal, y(t) is given by,
y(s)
G(s)F(s)K(s)
Yref (S) 1+G(s)F(s)K(s)H(s)
y(s) = G(s)F(s)K(s) (Yref (S) − H(s)y(s)) ⇒
=>
⇒ (1 + G(s)F(s)K(s)H(s))y(s) = G(s)F(s)K(S)yref(s) ⇒
y(s)
Yref (S)
=
G(s)F(s)K(s)
1 + G(s)F(s)K(s)H(s)
Transcribed Image Text:Solution: Yref (t) e(t) u(t) y(t) Controller Actuator Plant + K(s) F(s) G(s) Sensor H(s) Show that the closed - loop transfer function from the current reference signal, yref (t) to the controlled current signal, y(t) is given by, y(s) G(s)F(s)K(s) Yref (S) 1+G(s)F(s)K(s)H(s) y(s) = G(s)F(s)K(s) (Yref (S) − H(s)y(s)) ⇒ => ⇒ (1 + G(s)F(s)K(s)H(s))y(s) = G(s)F(s)K(S)yref(s) ⇒ y(s) Yref (S) = G(s)F(s)K(s) 1 + G(s)F(s)K(s)H(s)
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