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Consider the feedback system in Figure Q4 with controller G.(s)= and plant s+a 100 G,(s)=- s+25 Specify K and a of G,(s) such that the overall closed-loop response to a unity step reference input has a maximum percentage overshoot (%OS) of 25% and a 1% settling time of 0.1sec. [Hint: use the approximate relationship %OS = 1 x100% ] 0.6

Consider the feedback system in Figure Q4 with controller G.(s)= and plant s+a 100 G,(s)=- s+25 Specify K and a of G,(s) such that the overall closed-loop response to a unity step reference input has a maximum percentage overshoot (%OS) of 25% and a 1% settling time of 0.1sec. [Hint: use the approximate relationship %OS = 1 x100% ] 0.6

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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a) Consider the feedback system in Figure Q4 with controller G (s)=- and plant s+a 100 G,(s)=- s+25 Specify K and a of G,(s) such that the overall closed-loop response to a unity step reference input has a maximum percentage overshoot (%OS) of 25% and a 1% settling time of 0.1sec. [Hint: use the approximate relationship %OS = 1 x100% ] 0.6 b) To make the steady-state error to a unit step reference input zero, add an integrator to K. the controller of Q4a, i.e. G,(s)=- Assuming that a has the value derived in s(s+a) Q4a do the following: (0 Draw the root-locus of the closed-loop system, as K takes all positive real values, by computing the locus on the real axis, the angles of asymptotes, the point of intersection of the asymptotes with the real axis and the break points. Show clearly with arrows the direction of the loci. (ii) Find the value of K so the closed-loop system becomes marginally stable. In that case compute the points of intersection of the loci with the imaginary axis. R(s)+ Els) Y(s) G,(s) G,(s) Figure Q4: Unity feedback system
Transcribed Image Text:a) Consider the feedback system in Figure Q4 with controller G (s)=- and plant s+a 100 G,(s)=- s+25 Specify K and a of G,(s) such that the overall closed-loop response to a unity step reference input has a maximum percentage overshoot (%OS) of 25% and a 1% settling time of 0.1sec. [Hint: use the approximate relationship %OS = 1 x100% ] 0.6 b) To make the steady-state error to a unit step reference input zero, add an integrator to K. the controller of Q4a, i.e. G,(s)=- Assuming that a has the value derived in s(s+a) Q4a do the following: (0 Draw the root-locus of the closed-loop system, as K takes all positive real values, by computing the locus on the real axis, the angles of asymptotes, the point of intersection of the asymptotes with the real axis and the break points. Show clearly with arrows the direction of the loci. (ii) Find the value of K so the closed-loop system becomes marginally stable. In that case compute the points of intersection of the loci with the imaginary axis. R(s)+ Els) Y(s) G,(s) G,(s) Figure Q4: Unity feedback system
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