Q4 Consider the open-loop system 1000 Go(s) = (s + 5)(s+ 10)² Derive an expression for the frequency response G, (jw) for this system. What is the steady state gain of the open-loop system? (a) (b) Consider the Nyquist plot of the frequency response of this system shown in Fig Q4 below. (i) Explain how the gain margin can be obtained from the Nyquist plot and determine its approximate value from Fig Q4. What is the maximum value of an additional gain K, so that the system now has transfer function KG, (s), for which the closed loop would still be stable? (ii) Explain how the phase margin can be obtained from the Nyquist plot and determine its approximate value from Fig Q4. Assuming that the corresponding point on the plot occurs at a frequency of 5.7rad/s, what is the maximum delay which can be added to the system before the closed loop would become unstable? Nyquist Diagram -0.5 -1.5 -1 -0.5 0.5 1 1.5 2 Real Axis Figure Q4: The solid line is the Nyquist contour and the dotted line is the unit circle. Imaginary Axis
Q4 Consider the open-loop system 1000 Go(s) = (s + 5)(s+ 10)² Derive an expression for the frequency response G, (jw) for this system. What is the steady state gain of the open-loop system? (a) (b) Consider the Nyquist plot of the frequency response of this system shown in Fig Q4 below. (i) Explain how the gain margin can be obtained from the Nyquist plot and determine its approximate value from Fig Q4. What is the maximum value of an additional gain K, so that the system now has transfer function KG, (s), for which the closed loop would still be stable? (ii) Explain how the phase margin can be obtained from the Nyquist plot and determine its approximate value from Fig Q4. Assuming that the corresponding point on the plot occurs at a frequency of 5.7rad/s, what is the maximum delay which can be added to the system before the closed loop would become unstable? Nyquist Diagram -0.5 -1.5 -1 -0.5 0.5 1 1.5 2 Real Axis Figure Q4: The solid line is the Nyquist contour and the dotted line is the unit circle. Imaginary Axis
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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