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(a) Find the transfer functions H(s) = X( and He(s) = x(s). Y(s) (s) (b) Now set G(s) = 10. This is termed "proportional feedback," where the feedback is propor- tional to the error. (i) Find y(t) and e(t) for x(t) = sin 10t. (ii) How do your answers change (provide a qualitative discussion) for x(t) = sint and x(t): sin 100t? (iii) For x(t) u(t) (unit step), find and sketch y(t) and e(t), and specify their asymptotic values as t→∞. (iv) For x(t) = tu(t) (ramp starting at time zero), find the asymptotic value of the error e(t) as t →∞. Hint: You can simply use the final value theorem in (iii). (c) Redo (b)(iv) for G(s) = 10 + 2 ("proportional plus integral" feedback).

(a) Find the transfer functions H(s) = X( and He(s) = x(s). Y(s) (s) (b) Now set G(s) = 10. This is termed "proportional feedback," where the feedback is propor- tional to the error. (i) Find y(t) and e(t) for x(t) = sin 10t. (ii) How do your answers change (provide a qualitative discussion) for x(t) = sint and x(t): sin 100t? (iii) For x(t) u(t) (unit step), find and sketch y(t) and e(t), and specify their asymptotic values as t→∞. (iv) For x(t) = tu(t) (ramp starting at time zero), find the asymptotic value of the error e(t) as t →∞. Hint: You can simply use the final value theorem in (iii). (c) Redo (b)(iv) for G(s) = 10 + 2 ("proportional plus integral" feedback).

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Y(s) (a) Find the transfer functions H(s) = X(3) and He(s) = x(s). (b) Now set G(s) = 10. This is termed "proportional feedback," where the feedback is propor- tional to the error. (i) Find y(t) and e(t) for r(t) = sin 10t. (ii) How do your answers change (provide a qualitative discussion) for x(t) = sint and r(t) = sin 100t? (iii) For x(t) = u(t) (unit step), find and sketch y(t) and e(t), and specify their asymptotic values as t→∞. (iv) For r(t) = tu(t) (ramp starting at time zero), find the asymptotic value of the error e(t) as t→∞. Hint: You can simply use the final value theorem in (iii). (c) Redo (b)(iv) for G(s) = 10 + 2 ("proportional plus integral" feedback). S
Transcribed Image Text:Y(s) (a) Find the transfer functions H(s) = X(3) and He(s) = x(s). (b) Now set G(s) = 10. This is termed "proportional feedback," where the feedback is propor- tional to the error. (i) Find y(t) and e(t) for r(t) = sin 10t. (ii) How do your answers change (provide a qualitative discussion) for x(t) = sint and r(t) = sin 100t? (iii) For x(t) = u(t) (unit step), find and sketch y(t) and e(t), and specify their asymptotic values as t→∞. (iv) For r(t) = tu(t) (ramp starting at time zero), find the asymptotic value of the error e(t) as t→∞. Hint: You can simply use the final value theorem in (iii). (c) Redo (b)(iv) for G(s) = 10 + 2 ("proportional plus integral" feedback). S
x(t)- Figure y(t) e(t) G(s) 1/s Consider a feedback-based causal LTI system with input r(t) shown in Figure 6.40, where G(s) is the transfer function of a "loop filter" and 1/s is an integrator. The idea is to use the error e(t) to drive these, so as to make y(t) track x(t).
Transcribed Image Text:x(t)- Figure y(t) e(t) G(s) 1/s Consider a feedback-based causal LTI system with input r(t) shown in Figure 6.40, where G(s) is the transfer function of a "loop filter" and 1/s is an integrator. The idea is to use the error e(t) to drive these, so as to make y(t) track x(t).
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