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Determine the open loop transfer function G(s) = C(s)P(s), and identify the open-loop poles and open-loop zeros of the system. (i) For the root locus of G(s), determine the number of asymptotes and where they meet, and calculate the location of any double point(s). (ii) (iii) Sketch the root-locus for this system, using the information derived in (i)-(ii) and comment on the characteristics of this system for different values of K, e.g. for small K and for larger values of K. Hint: You may find it useful to know that the equation s3 + 9.5s² + 28s + = -4.23 – 1.14i, = 0 has the solutions x1 and x3 = -1.04. 20 -4.23 + 1.14i, x2 %|

Determine the open loop transfer function G(s) = C(s)P(s), and identify the open-loop poles and open-loop zeros of the system. (i) For the root locus of G(s), determine the number of asymptotes and where they meet, and calculate the location of any double point(s). (ii) (iii) Sketch the root-locus for this system, using the information derived in (i)-(ii) and comment on the characteristics of this system for different values of K, e.g. for small K and for larger values of K. Hint: You may find it useful to know that the equation s3 + 9.5s² + 28s + = -4.23 – 1.14i, = 0 has the solutions x1 and x3 = -1.04. 20 -4.23 + 1.14i, x2 %|

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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Calculate Question 3a - ALL PARTS I.E-( i , ii, iii)

A laboratory experiment can be described as a system with an open-loop transfer function Q3 1 P(s) : (s + 2)(s + 5) Consider a Proportional-Integral (PI) controller C(s) with the transfer function K(s + z1) C(s) S (a) For the controller C(s) defined above with z, = 4: Determine the open loop transfer function G(s) = C(s)P(s), and identify the open-loop poles and open-loop zeros of the system. (i) For the root locus of G(s), determine the number of asymptotes and where they meet, and calculate the location of any double point(s). (ii) (iii) Sketch the root-locus for this system, using the information derived in (i)-(ii) and comment on the characteristics of this system for different values of K, e.g. for small K and for larger values of K. 9.5s? + 28s + know that the equation s3 = -4.23 + 1.14i, x2 = -4.23 – 1.14i, Hint: You may find it useful = 0 has the solutions x, and x3 = -1.04. 20
Transcribed Image Text:A laboratory experiment can be described as a system with an open-loop transfer function Q3 1 P(s) : (s + 2)(s + 5) Consider a Proportional-Integral (PI) controller C(s) with the transfer function K(s + z1) C(s) S (a) For the controller C(s) defined above with z, = 4: Determine the open loop transfer function G(s) = C(s)P(s), and identify the open-loop poles and open-loop zeros of the system. (i) For the root locus of G(s), determine the number of asymptotes and where they meet, and calculate the location of any double point(s). (ii) (iii) Sketch the root-locus for this system, using the information derived in (i)-(ii) and comment on the characteristics of this system for different values of K, e.g. for small K and for larger values of K. 9.5s? + 28s + know that the equation s3 = -4.23 + 1.14i, x2 = -4.23 – 1.14i, Hint: You may find it useful = 0 has the solutions x, and x3 = -1.04. 20
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