Q5A laboratory experiment can be modelled as a system with an open-looptransfer function(a)1P(s) =(s2 + 4s + 3)with a controller C(s) which has the transfer functionK(s + 5)C(s) =s+8where K > 0.(i)Derive and sketch the root-locus of the corresponding closed loopsystem. In your answer, show all intermediate steps such as the locationsof the open-loop poles and zeros, the relative degree of the open-loopsystem, the number of asymptotes and their meeting point, and thelocation(s) of any double point(s) of the root locus.(ii)Comment on the characteristics of this system for small values of gainK and for larger values of K. Docs the system become unstable? Whatis the maximal value of K for which the closed-loop systemoverdamped?Hint: The equation x + 13.5x? + 60x + 75.5 = 0 has the solutionsx, = -2.09, x, = -5.71 + j1.90 and x, = -5.71 - j1.90.Part (b) can be found overleaf...Continued overleafPage 5 of 11Figure Q5 shows the Bode diagram for the frequency response of the systemfrom (a) with K = 10.(b)(i)Describe how the gain and the phase margins can be derived from theBode plot and determine their values.(ii)What is the maximal gain which can be applied to this system before itbecomes unstable.Bode Diagram-50-100-90-18010210°Frequency fradis)Figure Q510110102Magnitude (dB

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A laboratory experiment can be modelled as a system with an open-loop transfer function 05 (a) P(s) =- (s² + 4s + 3) with a controller C(s) which has the transfer function K(s + 5) C(s)= s+8 where K > 0. (i) Derive and sketch the root-locus of the corresponding closed loop system. In your answer, show all intermediate steps such as the locations of the open-loop poles and zeros, the relative degree of the open-loop system, the number of asymptotes and their meeting point, and the location(s) of any double point(s) of the root locus. (ii) Comment on the characteristics of this system for small values of gain K and for larger values of K. Does the system become unstable? What is the maximal value of K for which the closed-loop system overdamped? Hint: The equation x + 13.5x + 60x + 75.5 = 0 has the solutions x, = -2.09, x2 = -5.71 + j1.90 and x, = -5.71 - j1.90.

A laboratory experiment can be modelled as a system with an open-loop transfer function 05 (a) P(s) =- (s² + 4s + 3) with a controller C(s) which has the transfer function K(s + 5) C(s)= s+8 where K > 0. (i) Derive and sketch the root-locus of the corresponding closed loop system. In your answer, show all intermediate steps such as the locations of the open-loop poles and zeros, the relative degree of the open-loop system, the number of asymptotes and their meeting point, and the location(s) of any double point(s) of the root locus. (ii) Comment on the characteristics of this system for small values of gain K and for larger values of K. Does the system become unstable? What is the maximal value of K for which the closed-loop system overdamped? Hint: The equation x + 13.5x + 60x + 75.5 = 0 has the solutions x, = -2.09, x2 = -5.71 + j1.90 and x, = -5.71 - j1.90.

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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