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Diagram (applies to all subsequent problems): W(s) Y(s) R(s) U(s) Da (s) Gpi (s) H(s)

Diagram (applies to all subsequent problems): W(s) Y(s) R(s) U(s) Da (s) Gpi (s) H(s)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Diagram (applies to all subsequent problems): W(s) R(s) U(s) Y(s) Da (s) Gpl (s) H(s)
Transcribed Image Text:Diagram (applies to all subsequent problems): W(s) R(s) U(s) Y(s) Da (s) Gpl (s) H(s)
Given a system as in the diagram above, where K is an adjustable parameter. 1 K1 Det (s) = Kp + Gpi(s) H(s) = 1 s + 4 S a) Assuming W=0, find the transfer function Y(s)/R(s) b) Assuming R=0, find the transfer function Y(s)/W(s) c) Assume r(t)=0, what is the response of the system to w(t) = u(t) (unit-step)? What is the steady- state response to the disturbance (derive in terms of parameters ? d) Ignoring the effects of the zero (numerator of the closed-loop function), determine the range of constants Kp and Ki such that the rise-time of the closed-loop system is equal (or less than) 0.36 s and so that the damping factor { is equal to (or greater than) 0.8. Use the textbook approximation for the rise-time. e) For the values of constants Kp and Ki that correspond to the borderline cases of rise-time and damping-factor in problem 2d), determine the settling time of the closed-loop system to within 1% of the final value.
Transcribed Image Text:Given a system as in the diagram above, where K is an adjustable parameter. 1 K1 Det (s) = Kp + Gpi(s) H(s) = 1 s + 4 S a) Assuming W=0, find the transfer function Y(s)/R(s) b) Assuming R=0, find the transfer function Y(s)/W(s) c) Assume r(t)=0, what is the response of the system to w(t) = u(t) (unit-step)? What is the steady- state response to the disturbance (derive in terms of parameters ? d) Ignoring the effects of the zero (numerator of the closed-loop function), determine the range of constants Kp and Ki such that the rise-time of the closed-loop system is equal (or less than) 0.36 s and so that the damping factor { is equal to (or greater than) 0.8. Use the textbook approximation for the rise-time. e) For the values of constants Kp and Ki that correspond to the borderline cases of rise-time and damping-factor in problem 2d), determine the settling time of the closed-loop system to within 1% of the final value.
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