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A dynamometer consists of an inner loop having a differentiator feedback, and a main loop which has unity feedback, as shown below. R(S) E(S) G((5) c) Here, the plant has the transfer function G,(s): Determine the value of K, for which the inner loop will have two equal negative real poles. Where are these negative real poles located? Also, determine the range of K,, for the determined value of K,, for system stability. a What is the value of K, (with K, set to the value determined in part (a)) that will cause the step response of the b system to break into oscillation? What is the frequency of this oscillation? What is the gain K, when there is a real closed-loop pole at s = -5? Can the step response of the closed-loop system be approximated by a second-order, underdamped response? Why or why not? If the second-order step response is justified, find %OS, T, and T, of the step response.

A dynamometer consists of an inner loop having a differentiator feedback, and a main loop which has unity feedback, as shown below. R(S) E(S) G((5) c) Here, the plant has the transfer function G,(s): Determine the value of K, for which the inner loop will have two equal negative real poles. Where are these negative real poles located? Also, determine the range of K,, for the determined value of K,, for system stability. a What is the value of K, (with K, set to the value determined in part (a)) that will cause the step response of the b system to break into oscillation? What is the frequency of this oscillation? What is the gain K, when there is a real closed-loop pole at s = -5? Can the step response of the closed-loop system be approximated by a second-order, underdamped response? Why or why not? If the second-order step response is justified, find %OS, T, and T, of the step 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
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A dynamometer consists of an inner loop having a differentiator feedback, and a main loop which has unity feedback, as shown below. R(s) E(s) C(s) K, G|(8) K, s Here, the plant has the transfer function G,(s) = - s(s+2)(s+4) Determine the value of K, for which the inner loop will have two equal negative real poles. Where are these negative real poles located? Also, determine the range of K, for the determined value of K2, for system stability. a What is the value of K, (with K, set to the value determined in part (a)) that will cause the step response of the system to break into oscillation? What is the frequency of this oscillation? b What is the gain K, when there is a real closed-loop pole at s = -5? Can the step response of the closed-loop system be approximated by a second-order, underdamped response? Why or why not? If the second-order step response is justified, find %OS, T, and T, of the step response.
Transcribed Image Text:A dynamometer consists of an inner loop having a differentiator feedback, and a main loop which has unity feedback, as shown below. R(s) E(s) C(s) K, G|(8) K, s Here, the plant has the transfer function G,(s) = - s(s+2)(s+4) Determine the value of K, for which the inner loop will have two equal negative real poles. Where are these negative real poles located? Also, determine the range of K, for the determined value of K2, for system stability. a What is the value of K, (with K, set to the value determined in part (a)) that will cause the step response of the system to break into oscillation? What is the frequency of this oscillation? b What is the gain K, when there is a real closed-loop pole at s = -5? Can the step response of the closed-loop system be approximated by a second-order, underdamped response? Why or why not? If the second-order step response is justified, find %OS, T, and T, of the step response.
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