A laboratory experiment can be modelled as a system with an open-looptransfer functionQ31P(s) =(s + 2)(s + 5)Consider a PI controller C(s) with the transfer functionK(s + z1)C(s) =(a)For the controller C(s) defined above with z, = 4:Continued overleafPage 3 of 10Determine the open loop transfer function G(s) = C(s)P(s), andidentify the open-loop poles and open-loop zeros of the system.(i)For the root locus of G(s), determine the number of asymptotes andwhere they meet, and calculate the location of any double point(s).(ii)Sketch the root-locus for this system, using the information derived in(i)-(ii) and comment on the characteristics of this system for differentvalues of K, e.g. for small K and for larger values of K.(iii)Hint: You may find it useful to know that the equation s3 + 9.5s² + 28s +20 = 0 has the solutions x, = -4.23 + 1.14i, x2 = -4.23 – 1.14i,and x3 = -1.04.(b)The Bode diagram of G(s) is shown in Figure Q3 below. Determineapproximate values for the gain and phase margins from this plot.Bode Diagram4020-40-135-1801010010'102Frequency (radis)Figure Q3Using root locus analysis, for the plant P(s) and controller C(s) presented atthe start of the question, determine the smallest value of z, for which theclosed loop system may become unstable for large values of K. Sketch acorresponding root locus diagram and discuss the differences to the diagramwhich you obtained in (a).(c)[51(Gap) aseyd

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A laboratory experiment can be modelled as a system with an open-loop transfer function Q3 1 P(s) (s + s)(Z + s) Consider a PI controller C(s) with the transfer function K(s + z1) C(s) (a) For the controller C(s) defined above with z, = 4: Continued overleaf Page 3 of 10 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) (ii) 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). 1 (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 + 20 = 0 has the solutions x, = -4.23 + 1.14i, x2 = -4.23 - 1.14i, and x3 = -1.04.

A laboratory experiment can be modelled as a system with an open-loop transfer function Q3 1 P(s) (s + s)(Z + s) Consider a PI controller C(s) with the transfer function K(s + z1) C(s) (a) For the controller C(s) defined above with z, = 4: Continued overleaf Page 3 of 10 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) (ii) 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). 1 (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 + 20 = 0 has the solutions x, = -4.23 + 1.14i, x2 = -4.23 - 1.14i, and x3 = -1.04.

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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