Explain how the Nyquist stability criterion can be used to determine thestability of a closed-loop feedback system. Formulate the criterion for asystem with no right-half plane open-loop poles.(a)(b)Consider the Nyquist plot of the frequency response of the system G(jw) =500shown in Figure Q4 below.(jw+1)(jw+10)²i.Explain how the gain margin can be obtained from the Nyquist plotand determine its approximate value from Figure Q4. What is themaximum value of an additional gain K for which the closed loopwould still be stable?0.5-0.5-0.50.5Real AxisFigure Q4i.Explain how the phase margin can be obtained from the Nyquist plotand determine its approximate value from Figure Q4. Assuming thatthe corresponding point on the plot occurs at 4rad/s, what is themaximum delay which can be added to the system before the closedloop would become unstable?Sketch the approximate Bode diagram for the system in part (b) of thequestion, clearly showing the asymptotes and corner frequencies. Indicate thegain and phase margins in your diagram.(c)(d)Explain how the bode plot changes for the system in part (b) when anadditional gain of K = 10 is added. Sketch the Bode diagram of the modifiedsystem and comment on the stability of the closed loop in this case.Imaginary Axis

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(a) Explain how the Nyquist stability criterion can be used to determine the

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter12: Power System Controls

Section: Chapter Questions

Problem 12.3P

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Question

Explain how the Nyquist stability criterion can be used to determine the
stability of a closed-loop feedback system. Formulate the criterion for a
system with no right-half plane open-loop poles.
(a)
(b)
Consider the Nyquist plot of the frequency response of the system G(jw) =
500
shown in Figure Q4 below.
(jw+1)(jw+10)²
i.
Explain how the gain margin can be obtained from the Nyquist plot
and determine its approximate value from Figure Q4. What is the
maximum value of an additional gain K for which the closed loop
would still be stable?
0.5
-0.5
-0.5
0.5
Real Axis
Figure Q4
i.
Explain how the phase margin can be obtained from the Nyquist plot
and determine its approximate value from Figure Q4. Assuming that
the corresponding point on the plot occurs at 4rad/s, what is the
maximum delay which can be added to the system before the closed
loop would become unstable?
Sketch the approximate Bode diagram for the system in part (b) of the
question, clearly showing the asymptotes and corner frequencies. Indicate the
gain and phase margins in your diagram.
(c)
(d)
Explain how the bode plot changes for the system in part (b) when an
additional gain of K = 10 is added. Sketch the Bode diagram of the modified
system and comment on the stability of the closed loop in this case.
Imaginary Axis

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