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1. Consider the following feedback system. Bode plot of G(s) is shown below. Phase (deg) Magnitude (dB) -50 -100 -150 -200 0 -90 -180 -270 101 System: sys Frequency (rad/s): 0.117 Magnitude (dB): -74 10° K G(s) Bode Diagram System: sys Frequency (rad/s): 36.8 Magnitude (dB): -99.7 System: sys Frequency (rad/s): 20 Magnitude (dB): -89.9 System: sys Frequency (rad/s): 20 Phase (deg): -143 System: sys Frequency (rad/s): 36.8 Phase (deg): -180 101 Frequency (rad/s) a) Determine the range of K for which the closed-loop system is stable. 102 10³ b) If we want the gain margin to be exactly 50 dB, what is value for K we should choose? c) If we want the phase margin to be exactly 37°, what is value of K we should choose? What will be the corresponding rise time (T) for step-input? d) If we want steady-state error of step input to be 0.6, what is value of K we should choose?

1. Consider the following feedback system. Bode plot of G(s) is shown below. Phase (deg) Magnitude (dB) -50 -100 -150 -200 0 -90 -180 -270 101 System: sys Frequency (rad/s): 0.117 Magnitude (dB): -74 10° K G(s) Bode Diagram System: sys Frequency (rad/s): 36.8 Magnitude (dB): -99.7 System: sys Frequency (rad/s): 20 Magnitude (dB): -89.9 System: sys Frequency (rad/s): 20 Phase (deg): -143 System: sys Frequency (rad/s): 36.8 Phase (deg): -180 101 Frequency (rad/s) a) Determine the range of K for which the closed-loop system is stable. 102 10³ b) If we want the gain margin to be exactly 50 dB, what is value for K we should choose? c) If we want the phase margin to be exactly 37°, what is value of K we should choose? What will be the corresponding rise time (T) for step-input? d) If we want steady-state error of step input to be 0.6, what is value of K we should choose?

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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1. Consider the following feedback system. Bode plot of G(s) is shown below. Phase (deg) Magnitude (dB) -50 -100 -150 -200 0 -90 -180 -270 101 System: sys Frequency (rad/s): 0.117 Magnitude (dB): -74 10° K G(s) Bode Diagram System: sys Frequency (rad/s): 36.8 Magnitude (dB): -99.7 System: sys Frequency (rad/s): 20 Magnitude (dB): -89.9 System: sys Frequency (rad/s): 20 Phase (deg): -143 System: sys Frequency (rad/s): 36.8 Phase (deg): -180 101 Frequency (rad/s) a) Determine the range of K for which the closed-loop system is stable. 102 10³ b) If we want the gain margin to be exactly 50 dB, what is value for K we should choose? c) If we want the phase margin to be exactly 37°, what is value of K we should choose? What will be the corresponding rise time (T) for step-input? d) If we want steady-state error of step input to be 0.6, what is value of K we should choose?
Transcribed Image Text:1. Consider the following feedback system. Bode plot of G(s) is shown below. Phase (deg) Magnitude (dB) -50 -100 -150 -200 0 -90 -180 -270 101 System: sys Frequency (rad/s): 0.117 Magnitude (dB): -74 10° K G(s) Bode Diagram System: sys Frequency (rad/s): 36.8 Magnitude (dB): -99.7 System: sys Frequency (rad/s): 20 Magnitude (dB): -89.9 System: sys Frequency (rad/s): 20 Phase (deg): -143 System: sys Frequency (rad/s): 36.8 Phase (deg): -180 101 Frequency (rad/s) a) Determine the range of K for which the closed-loop system is stable. 102 10³ b) If we want the gain margin to be exactly 50 dB, what is value for K we should choose? c) If we want the phase margin to be exactly 37°, what is value of K we should choose? What will be the corresponding rise time (T) for step-input? d) If we want steady-state error of step input to be 0.6, what is value of K we should choose?
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