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Instructions: Transient analysis is with reference to step response. Peak overshoot is mentioned in per cent. Settling time is to be found out for 2% tolerance. Steady state error is to be computed in absolute magnitude (not in per cent). For frequency response analysis, if the cross-over frequency, the gain margin or the phase margin is unbounded or does not exist, then write the answer for that part as -1. Problem statement: A unity gain negative feedback control system is given with the plant transfer function G(s) = 8(s + 4)2 and a series compensator G_{c}{s)= k, where k>=0. Part A Consider the closed-loop system. 1. Steady state error e_fss) = Using Routh array answer the following: 2. Maximum value of k for stability (kmarginal) = Part B For the control system described in Part A, Choose the value of the gain G_c(s) = k = 64. For the dominant subsystem (of the closed-loop system) obtain the step response and answer the following: 3. Peak time T_p =

Instructions: Transient analysis is with reference to step response. Peak overshoot is mentioned in per cent. Settling time is to be found out for 2% tolerance. Steady state error is to be computed in absolute magnitude (not in per cent). For frequency response analysis, if the cross-over frequency, the gain margin or the phase margin is unbounded or does not exist, then write the answer for that part as -1. Problem statement: A unity gain negative feedback control system is given with the plant transfer function G(s) = 8(s + 4)2 and a series compensator G_{c}{s)= k, where k>=0. Part A Consider the closed-loop system. 1. Steady state error e_fss) = Using Routh array answer the following: 2. Maximum value of k for stability (kmarginal) = Part B For the control system described in Part A, Choose the value of the gain G_c(s) = k = 64. For the dominant subsystem (of the closed-loop system) obtain the step response and answer the following: 3. Peak time T_p =

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Instructions: Transient analysis is with reference to step response. Peak overshoot is mentioned in per cent. Settling time is to be found out for 2% tolerance. Steady state error is to be computed in absolute magnitude (not in per cent). For frequency response analysis, if the cross-over frequency, the gain margin or the phase margin is unbounded or does not exist, then write the answer for that part as -1. Problem statement: A unity gain negative feedback control system is given with the plant transfer function G(s) = s(8 + 1)2 and a series compensator G_{c}(s)= k, where k>=0. Part A Consider the closed-loop system. 1. Steady state error e_{ss) = Using Routh array answer the following: 2. Maximum value of k for stability (kmarginal) = Part B For the control system described in Part A, Choose the value of the gain G c(s) = k = 64. For the dominant subsystem (of the closed-loop system) obtain the step response and answer the following: 3. Peak time T_p = 4. Settling time T_s = Part C From the root locus analysis, answer the following 5. Breakaway point: s_BA = - 6. Gain at breakaway point: k_BA = 7. Imaginary axis crossing: smarginal = j (Write a positive value in this box, that is, smarginal corresponding to the positive imaginary axis.)
Transcribed Image Text:Instructions: Transient analysis is with reference to step response. Peak overshoot is mentioned in per cent. Settling time is to be found out for 2% tolerance. Steady state error is to be computed in absolute magnitude (not in per cent). For frequency response analysis, if the cross-over frequency, the gain margin or the phase margin is unbounded or does not exist, then write the answer for that part as -1. Problem statement: A unity gain negative feedback control system is given with the plant transfer function G(s) = s(8 + 1)2 and a series compensator G_{c}(s)= k, where k>=0. Part A Consider the closed-loop system. 1. Steady state error e_{ss) = Using Routh array answer the following: 2. Maximum value of k for stability (kmarginal) = Part B For the control system described in Part A, Choose the value of the gain G c(s) = k = 64. For the dominant subsystem (of the closed-loop system) obtain the step response and answer the following: 3. Peak time T_p = 4. Settling time T_s = Part C From the root locus analysis, answer the following 5. Breakaway point: s_BA = - 6. Gain at breakaway point: k_BA = 7. Imaginary axis crossing: smarginal = j (Write a positive value in this box, that is, smarginal corresponding to the positive imaginary axis.)
Part D Using Bode plots (asymptotic magnitude plot and exact phase plot) determine, 8. Gain crossover frequency (rad/s) = 9. Phase margin (degrees) = 10. Phase crossover frequency (rad/s) = 11. Gain margin (dB) = Compare the stability margins as obtained above with the stability margin calculated from the polar plot. Using polar plot (exact magnitude plot and exact phase plot) determine, 12. Gain crossover frequency (rad/s) = 13. Phase margin (degrees) = 14. Phase crossover frequency (rad/s) = 15. Gain margin (dB) = Observe the relation of the gain margin obtained from the frequency response analysis with the stability margin (kmarginal) calculated using Routh array. Part E: The following is not part of the Assignment. You may complete the following part as homework. Now for the open loop transfer function G(s) given in part A, assume that the gain is reduced to k=0.02 . From the frequency response calculate the stability margins. Using Bode plots (asymptotic magnitude plot and exact phase plot) determine, 1. Gain crossover frequency (rad/s) = 2. Gain margin (dB) = 3. Phase crossover frequency = 4. Phase margin (degrees) = Compare the stability margins as obtained above with the stability margin calculated from the polar plot as follows: Using Polar plot (exact magnitude plot and exact phase plot) determine, 5. Gain crossover frequency (rad/s) = 6. Gain margin (dB) = 7. Phase crossover frequency (rad/s) = 8. Phase margin (degrees) = Observe the effect of the reduction in gain on the stability margins and cross-over freqiencies.
Transcribed Image Text:Part D Using Bode plots (asymptotic magnitude plot and exact phase plot) determine, 8. Gain crossover frequency (rad/s) = 9. Phase margin (degrees) = 10. Phase crossover frequency (rad/s) = 11. Gain margin (dB) = Compare the stability margins as obtained above with the stability margin calculated from the polar plot. Using polar plot (exact magnitude plot and exact phase plot) determine, 12. Gain crossover frequency (rad/s) = 13. Phase margin (degrees) = 14. Phase crossover frequency (rad/s) = 15. Gain margin (dB) = Observe the relation of the gain margin obtained from the frequency response analysis with the stability margin (kmarginal) calculated using Routh array. Part E: The following is not part of the Assignment. You may complete the following part as homework. Now for the open loop transfer function G(s) given in part A, assume that the gain is reduced to k=0.02 . From the frequency response calculate the stability margins. Using Bode plots (asymptotic magnitude plot and exact phase plot) determine, 1. Gain crossover frequency (rad/s) = 2. Gain margin (dB) = 3. Phase crossover frequency = 4. Phase margin (degrees) = Compare the stability margins as obtained above with the stability margin calculated from the polar plot as follows: Using Polar plot (exact magnitude plot and exact phase plot) determine, 5. Gain crossover frequency (rad/s) = 6. Gain margin (dB) = 7. Phase crossover frequency (rad/s) = 8. Phase margin (degrees) = Observe the effect of the reduction in gain on the stability margins and cross-over freqiencies.
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