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A laboratory experiment can be modelled as a system with an open-loop transfer function Q3 1 P(s) = (s + 2)(s + 3) A controller C(s) with the transfer function K C(s) = is used to control P(s) ir a unity-feedback configuration. (a) (i) 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. W. hat is the relative degree of G(s)? Determine the number of asymptotes of the root locus 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). Discuss the characteristics of the closed loop system for different values of K, e.g. for small K and for larger values of K.

A laboratory experiment can be modelled as a system with an open-loop transfer function Q3 1 P(s) = (s + 2)(s + 3) A controller C(s) with the transfer function K C(s) = is used to control P(s) ir a unity-feedback configuration. (a) (i) 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. W. hat is the relative degree of G(s)? Determine the number of asymptotes of the root locus 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). Discuss the characteristics of the closed loop system for different values of K, e.g. for small K and for larger values of K.

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
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A laboratory experiment can be modelled as a system with an open-loop transfer function Q3 P(s) = (s + 2)(s + 3) A controller C(s) with the transfer function K C(s) = is used to control P(s) ir a unity-feedback configuration. (a) (i) Determine the open loop transfer function G(s) = C(s)P(s), and identifv the open-loop poles and open-loop zeros of the system. (ii) What is the relative degree of G(s)? Determine the number of asymptotes of the root locus and where they meet, and calculate the location of any double point(s). (iii) Sketch the root-locus for this system, using the information derived in (i) (ii). Discuss the characteristics of the closed loop system for different values of K, e.g. for small K and for larger values of K. (b) Explain how the controller C(s) could be modified to guarantee that the closed loop system is stable for any value of K > 0. What additional term can be added? Sketch a root locus diagram for your chosen additional term and discuss the differences to the diagram which you obtained in (a).
Transcribed Image Text:A laboratory experiment can be modelled as a system with an open-loop transfer function Q3 P(s) = (s + 2)(s + 3) A controller C(s) with the transfer function K C(s) = is used to control P(s) ir a unity-feedback configuration. (a) (i) Determine the open loop transfer function G(s) = C(s)P(s), and identifv the open-loop poles and open-loop zeros of the system. (ii) What is the relative degree of G(s)? Determine the number of asymptotes of the root locus and where they meet, and calculate the location of any double point(s). (iii) Sketch the root-locus for this system, using the information derived in (i) (ii). Discuss the characteristics of the closed loop system for different values of K, e.g. for small K and for larger values of K. (b) Explain how the controller C(s) could be modified to guarantee that the closed loop system is stable for any value of K > 0. What additional term can be added? Sketch a root locus diagram for your chosen additional term and discuss the differences to the diagram which you obtained in (a).
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