AP2.3 Consider the feedback control system in Figure AP2.3. Define the tracking error asE(s)=R(s)-Y(s).(a) Determine a suitable H(s) such that the tracking error is zero for any input R(s) in theabsence of a disturbance input (that is, when Td(s)=0.(b) Using H(s) determined in part (a), determine the response Y(s) for adisturbance Td(s)when the input R(s)=0.(c) Is it possible to obtain Y(s)=0 for an arbitrary disturbance Td(s) when Gd(s)#0? Expyour answer.T«(s)G«(s)R(s)G(s)G(s)Y(s)H(s)Figure AP2.3 Feedback system with a disturbance input.+++

The tracking error is given as E(s)= R(s)-Y(s) Since here the feedback is non unity feedback, the…

Answered: AP2.3 Consider the feedback control…

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AP2.3 Consider the feedback control system in Figure AP2.3. Define the tracking error as
E(s)=R(s)-Y(s).
(a) Determine a suitable H(s) such that the tracking error is zero for any input R(s) in the
absence of a disturbance input (that is, when Td(s)=0.
(b) Using H(s) determined in part (a), determine the response Y(s) for a
disturbance Td(s)when the input R(s)=0.
(c) Is it possible to obtain Y(s)=0 for an arbitrary disturbance Td(s) when Gd(s)#0? Exp
your answer.
T«(s)
G«(s)
R(s)
G(s)
G(s)
Y(s)
H(s)
Figure AP2.3 Feedback system with a disturbance input.
+
+
+

Expert Solution

Concept

The tracking error is given as $\begin{array}{rcl} E (s) & = & R (s) - Y (s) \end{array}$

Since here the feedback is non unity feedback, the error is defined as

$E (s) = R (s) \times [\frac{1}{K_{h}} - \frac{G_{1} (s)}{1 + G_{1} (s) H_{1} (s)}]$ , where G₁(s) is the combined total forward path gain and H₁(s) is the feedback path gain of the given system and K_h is the DC gain of feedback.

$K_{h} = \lim_{s \to 0} H (s)$

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