Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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A transfer function for a system for rudder control was obtained experimentally in frequency domain and Bode-plots of the open-loop system are given below. The slopes of asymptotes can be estimated from the diagrams. Assuming we use a unity-feedback to close the loop, analyze (with justification/explanation) the system: 60 Magnitude 40 20 믐 20 -40 -60 -80 -100 104 103 102 101 10° 10 102 103 104 105 Frequency [rad/s] Phase -30 -60 -90 -120 -150 -180 -210 -240 -270 -300 104 103 102 101 100 101 102 103 104 105 Frequency [rad/s] a) What is the type of the system (with respect to steady-state erroi b) What is the steady-state error ess when a unit-step input is applied to the closed-loop system – provide the exact value c) What is the crossover frequency we of the system? d) What is the Phase Margin of the system? Is this considered adequate for stability ( e) What is the Gain Margin of the system approximately f) Briefly mention at least 2 possible options/controllers ana pros/cons of using them that would reduce the closed-loop steady-state error by say, factor of 10, g) Assume we added +60dB of gain to the system to improve the ess, what would be the new w, and the Phase Margin (approximately)? Degrees
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Transcribed Image Text:A transfer function for a system for rudder control was obtained experimentally in frequency domain and Bode-plots of the open-loop system are given below. The slopes of asymptotes can be estimated from the diagrams. Assuming we use a unity-feedback to close the loop, analyze (with justification/explanation) the system: 60 Magnitude 40 20 믐 20 -40 -60 -80 -100 104 103 102 101 10° 10 102 103 104 105 Frequency [rad/s] Phase -30 -60 -90 -120 -150 -180 -210 -240 -270 -300 104 103 102 101 100 101 102 103 104 105 Frequency [rad/s] a) What is the type of the system (with respect to steady-state erroi b) What is the steady-state error ess when a unit-step input is applied to the closed-loop system – provide the exact value c) What is the crossover frequency we of the system? d) What is the Phase Margin of the system? Is this considered adequate for stability ( e) What is the Gain Margin of the system approximately f) Briefly mention at least 2 possible options/controllers ana pros/cons of using them that would reduce the closed-loop steady-state error by say, factor of 10, g) Assume we added +60dB of gain to the system to improve the ess, what would be the new w, and the Phase Margin (approximately)? Degrees
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