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Problem 5: Consider the following LTI system: D(s) G(s) where K2 D(s) = K1 + i+, G(s) = and K1, K2 # 0. (a) Show that the transfer function of the feedback system (that is, from r(t) to y(?)) is: K18+ K2 s2 + (K1 – 1)s + K2 T(s) (b) Assume that K, and K2 have been selected such that the system is asymptotically stable but the values a unknown. And assume that the input is r(t) = u(t). Show that the final value of the output y(t) is always to 1 regardless of the values of K1 and K2. (c) Now, assume that the parameters are selected as K1 = -3, K2 = . C'alculate the zero-state response of the system to input r(t) = u(t) and the final value of the response

Problem 5: Consider the following LTI system: D(s) G(s) where K2 D(s) = K1 + i+, G(s) = and K1, K2 # 0. (a) Show that the transfer function of the feedback system (that is, from r(t) to y(?)) is: K18+ K2 s2 + (K1 – 1)s + K2 T(s) (b) Assume that K, and K2 have been selected such that the system is asymptotically stable but the values a unknown. And assume that the input is r(t) = u(t). Show that the final value of the output y(t) is always to 1 regardless of the values of K1 and K2. (c) Now, assume that the parameters are selected as K1 = -3, K2 = . C'alculate the zero-state response of the system to input r(t) = u(t) and the final value of the response

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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Problem 5: Consider the following LTI system: r(t) y(1) D(s) G(s) where D(s) = K1 +2, G(s) = - and K1, K2 + 0. (a) Show that the transfer function of the feedback system (that is, from r(t) to y(?)) is: K1s + K2 s2 + (K1 – 1)s + K2' T(s) = (b) Assume that K1 and K2 have been selected such that the system is asymptotically stable but the values are unknown. And assume that the input is r(t) = u(t). Show that the final value of the output y(f) is always equal to 1 regardless of the values of K1 and K2. (c) Now, assume that the parameters are selected as K1 = -3, K2 = . Calculate the zero-state response of the system to input r(1) = u(1) and the final value of the response (d) Compare your results of (b) and (c) and comment on any common or differences between them.
Transcribed Image Text:Problem 5: Consider the following LTI system: r(t) y(1) D(s) G(s) where D(s) = K1 +2, G(s) = - and K1, K2 + 0. (a) Show that the transfer function of the feedback system (that is, from r(t) to y(?)) is: K1s + K2 s2 + (K1 – 1)s + K2' T(s) = (b) Assume that K1 and K2 have been selected such that the system is asymptotically stable but the values are unknown. And assume that the input is r(t) = u(t). Show that the final value of the output y(f) is always equal to 1 regardless of the values of K1 and K2. (c) Now, assume that the parameters are selected as K1 = -3, K2 = . Calculate the zero-state response of the system to input r(1) = u(1) and the final value of the response (d) Compare your results of (b) and (c) and comment on any common or differences between them.
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