SYSTEM CONTROLLER R(s) +, Y (s) 2s + 2 C(s) s(s + 5)(s – 2) Consider the system below. For this question, let C (s) = K. here K is a positive real number. a) Prove that if the root locus of the system is drawn, the points s1,2 be on the curve. (Show it by doing mathematical calculation without drawing the curve.) -0.3214 ± 2.8951j will b) Draw the root locus of the system. c) It is desired that the dominant (= near the imaginary axis) poles of the closed loop system be at the points s12 =-0.3214 ± 2.8951j. What should K be for this? What can be said about the stability of the closed loop system for this K value? d) What are the unit step, ramp and parabolic reference tracking errors of the system for K in the option c?
SYSTEM CONTROLLER R(s) +, Y (s) 2s + 2 C(s) s(s + 5)(s – 2) Consider the system below. For this question, let C (s) = K. here K is a positive real number. a) Prove that if the root locus of the system is drawn, the points s1,2 be on the curve. (Show it by doing mathematical calculation without drawing the curve.) -0.3214 ± 2.8951j will b) Draw the root locus of the system. c) It is desired that the dominant (= near the imaginary axis) poles of the closed loop system be at the points s12 =-0.3214 ± 2.8951j. What should K be for this? What can be said about the stability of the closed loop system for this K value? d) What are the unit step, ramp and parabolic reference tracking errors of the system for K in the option c?
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Question
Please answer the attached question.
Transcribed Image Text:SYSTEM
CONTROLLER
R(s)
2s + 2
Y (s)
C(s)
s(s + 5)(s – 2)
Consider the system below. For this question, let C (s) = K. here K is a positive real number.
a) Prove that if the root locus of the system is drawn, the points s1,2
-0.3214 + 2.8951j will
be on the curve. (Show it by doing mathematical calculation without drawing the curve.)
Draw the root locus of the system.
c) It is desired that the dominant (= near the imaginary axis) poles of the closed loop system
be at the points s12 =-0.3214 ± 2.8951j. What should K be for this? What can be said about
the stability of the closed loop system for this K value?
d) What are the unit step, ramp and parabolic reference tracking errors of the system for K in
the option c?
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