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R(s) U(s) Y(s) Da (s) Gpi (s) E(s) H(s) Given a system as in the diagram above to solve the problems: Assume we want the closed-loop system rise time to be t, <0.18 sec 1 s+z De(s) = K - s+p' Gp1(s) = H(s) = 1 s(s + 3) a) Assume W(s)=0. Draw the root locus of the system assuming compensator consists only of the adjustable gain parameter K, i.e. Da(s) = K b) Determine the approximate range of values of K for which this is true (using the textbook approximation for rise-time. What is the minimum overshoot (maximum damping factor) you can achieve with the P-type control? c) Choose K to satisfy the rise-time requirement and plot the time-domain response of the closed- loop system to the unit step-input reference signal. What is the settling-time equal to?

R(s) U(s) Y(s) Da (s) Gpi (s) E(s) H(s) Given a system as in the diagram above to solve the problems: Assume we want the closed-loop system rise time to be t, <0.18 sec 1 s+z De(s) = K - s+p' Gp1(s) = H(s) = 1 s(s + 3) a) Assume W(s)=0. Draw the root locus of the system assuming compensator consists only of the adjustable gain parameter K, i.e. Da(s) = K b) Determine the approximate range of values of K for which this is true (using the textbook approximation for rise-time. What is the minimum overshoot (maximum damping factor) you can achieve with the P-type control? c) Choose K to satisfy the rise-time requirement and plot the time-domain response of the closed- loop system to the unit step-input reference signal. What is the settling-time equal to?

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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W(s) R(s) U(s) Y(s) Da (s) Gpl (s) E(s) H(s) Given a system as in the diagram above to solve the problems: Assume we want the closed-loop system rise time to be t,<0.18 sec 1 s + z Gpi(s) De(s) = K s +p' H(s) = 1 a) Assume W(s)=0. Draw the root locus of the system assuming compensator consists only of the adjustable gain parameter K, i.e. Da(s) = K b) Determine the approximate range of values of K for which this is true (using the textbook approximation for rise-time. What is the minimum overshoot (maximum damping factor) you can achieve with the P-type control? c) Choose K to satisfy the rise-time requirement and plot the time-domain response of the closed- loop system to the unit step-input reference signal. What is the settling-time equal to? d) A lead-compensator Da(s) is added to the system, so that the magnitude of zero |z| = 10 Draw Root-locus for various values of |p| (say, p=20, p=30, p=40 etc) and observe the behavior of the closed-loop poles. Pick a suitable value of p, so that the rise-time requirement for the closed-loop system is satisfied, and so that the damping factor is at least {2 0.5. What is the settling time for this case? Plot the time domain response of the system to a unit-step input. Compare to the unit-step response in part c)
Transcribed Image Text:W(s) R(s) U(s) Y(s) Da (s) Gpl (s) E(s) H(s) Given a system as in the diagram above to solve the problems: Assume we want the closed-loop system rise time to be t,<0.18 sec 1 s + z Gpi(s) De(s) = K s +p' H(s) = 1 a) Assume W(s)=0. Draw the root locus of the system assuming compensator consists only of the adjustable gain parameter K, i.e. Da(s) = K b) Determine the approximate range of values of K for which this is true (using the textbook approximation for rise-time. What is the minimum overshoot (maximum damping factor) you can achieve with the P-type control? c) Choose K to satisfy the rise-time requirement and plot the time-domain response of the closed- loop system to the unit step-input reference signal. What is the settling-time equal to? d) A lead-compensator Da(s) is added to the system, so that the magnitude of zero |z| = 10 Draw Root-locus for various values of |p| (say, p=20, p=30, p=40 etc) and observe the behavior of the closed-loop poles. Pick a suitable value of p, so that the rise-time requirement for the closed-loop system is satisfied, and so that the damping factor is at least {2 0.5. What is the settling time for this case? Plot the time domain response of the system to a unit-step input. Compare to the unit-step response in part c)
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