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3. For the negative feedback system below: U(s) Y(s) + 1 G.(s) = K (s +2)(s +4) The time-domain specs are given as follows: The damping ratio lies in the range of 0.5 <5<0.8, the peak time is t,<- second and the settling for the 5% range is t, <3 second 3 a) Plot the region in the complex plane that satisfies these time-domain specs (. b) Determine whether the complex conjugate roots of S = -3± j3 are located in the region you have found in part a) and compute the corresponding gain of K such that the closed-loop system will have roots at s = -3+ j3 c) For K= 10, find the steady-state error when a unit step is applied and select a controller such that this steady-state error will be zero

3. For the negative feedback system below: U(s) Y(s) + 1 G.(s) = K (s +2)(s +4) The time-domain specs are given as follows: The damping ratio lies in the range of 0.5 <5<0.8, the peak time is t,<- second and the settling for the 5% range is t, <3 second 3 a) Plot the region in the complex plane that satisfies these time-domain specs (. b) Determine whether the complex conjugate roots of S = -3± j3 are located in the region you have found in part a) and compute the corresponding gain of K such that the closed-loop system will have roots at s = -3+ j3 c) For K= 10, find the steady-state error when a unit step is applied and select a controller such that this steady-state error will be zero

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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3. For the negative feedback system below: U(s) Y(s) + 1 G.(s) = K (s +2)(s +4) The time-domain specs are given as follows: The damping ratio lies in the range of 0.5 <5<0.8, the peak time is t,<- second and the settling for the 5% range is t, <3 second 3 a) Plot the region in the complex plane that satisfies these time-domain specs (. b) Determine whether the complex conjugate roots of S = -3± j3 are located in the region you have found in part a) and compute the corresponding gain of K such that the closed-loop system will have roots at s = -3+ j3 c) For K= 10, find the steady-state error when a unit step is applied and select a controller such that this steady-state error will be zero
Transcribed Image Text:3. For the negative feedback system below: U(s) Y(s) + 1 G.(s) = K (s +2)(s +4) The time-domain specs are given as follows: The damping ratio lies in the range of 0.5 <5<0.8, the peak time is t,<- second and the settling for the 5% range is t, <3 second 3 a) Plot the region in the complex plane that satisfies these time-domain specs (. b) Determine whether the complex conjugate roots of S = -3± j3 are located in the region you have found in part a) and compute the corresponding gain of K such that the closed-loop system will have roots at s = -3+ j3 c) For K= 10, find the steady-state error when a unit step is applied and select a controller such that this steady-state error will be zero
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