A temperature control system for a laboratory experiment can be modelled as a system with an open-loop trans fer function of Q3 (а) 1 G.(s) = K (s + 1)(s + 5)(s + 10) Identify the open-loop poles and zeros of the system, and the relative degree of the open-loop system. (i) (ii) Determine the number of asymptotes in the root-locus and where they meet. (iii) Calculate the location of any double point(s) of the root-locus. Sketch the root-locus for this system, using the information derived in (i)-(iii). Comment on the characteristics of this system for small K and for larger values of K. What is the maximal value of K for which the closed-loop system is overdamped? (iv) Hint: The equation s2 + 10.67s + 21.67 = 0 has the solutions s = -7.94 and S2 = -2.73. (b) In a modified system, an ideal proportional-derivative controller with the transfer function C(s) = K + Ks is used, so that the overall open-loop system is now 1 G,(s) = C(s); (s + 1)(s + 5)(s + 10) Determine the number of asymptotes in the root-locus of this system and where they meet, and sketch the approximate root-locus for this modified system. How has the change affected the stability of the closed-loop system? (Note that you are not required to calculate the exact location of any double point(s) for (b)).
A temperature control system for a laboratory experiment can be modelled as a system with an open-loop trans fer function of Q3 (а) 1 G.(s) = K (s + 1)(s + 5)(s + 10) Identify the open-loop poles and zeros of the system, and the relative degree of the open-loop system. (i) (ii) Determine the number of asymptotes in the root-locus and where they meet. (iii) Calculate the location of any double point(s) of the root-locus. Sketch the root-locus for this system, using the information derived in (i)-(iii). Comment on the characteristics of this system for small K and for larger values of K. What is the maximal value of K for which the closed-loop system is overdamped? (iv) Hint: The equation s2 + 10.67s + 21.67 = 0 has the solutions s = -7.94 and S2 = -2.73. (b) In a modified system, an ideal proportional-derivative controller with the transfer function C(s) = K + Ks is used, so that the overall open-loop system is now 1 G,(s) = C(s); (s + 1)(s + 5)(s + 10) Determine the number of asymptotes in the root-locus of this system and where they meet, and sketch the approximate root-locus for this modified system. How has the change affected the stability of the closed-loop system? (Note that you are not required to calculate the exact location of any double point(s) for (b)).
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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