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(a) Figure Q.2(a) illustrates a unity feedback system with a forward transfer function of a plant having a unit step input. R(s) C(s) Ge(s) G(s) Figure Q.2(a) The open-loop transfer function G(s) is given as G(s) = 1 (s+2)(s+5)(s +20) A controller, Ge(s) is required to improve the performance of the uncompensated system G(s). The system is operated at 20% of overshoot with the dominant poles given as Sa=-2.67 ±j5.22. (i) (ii) Determine the gain, K, the settling time, T,, and the peak time, Tp, of the closed loop system at the given dominant poles. From Q.2(a)(i), determine the new dominant poles, San if the compensated system settles three time faster than the uncompensated system. (iii) Using the new dominant poles, Sans design the PD controller and determine the values of proportional gain, KP, and derivative gain, KD, of the controller.

(a) Figure Q.2(a) illustrates a unity feedback system with a forward transfer function of a plant having a unit step input. R(s) C(s) Ge(s) G(s) Figure Q.2(a) The open-loop transfer function G(s) is given as G(s) = 1 (s+2)(s+5)(s +20) A controller, Ge(s) is required to improve the performance of the uncompensated system G(s). The system is operated at 20% of overshoot with the dominant poles given as Sa=-2.67 ±j5.22. (i) (ii) Determine the gain, K, the settling time, T,, and the peak time, Tp, of the closed loop system at the given dominant poles. From Q.2(a)(i), determine the new dominant poles, San if the compensated system settles three time faster than the uncompensated system. (iii) Using the new dominant poles, Sans design the PD controller and determine the values of proportional gain, KP, and derivative gain, KD, of the controller.

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
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(a) Figure Q.2(a) illustrates a unity feedback system with a forward transfer function of a plant having a unit step input. R(s) C(s) Ge(s) G(s) Figure Q.2(a) The open-loop transfer function G(s) is given as G(s) = 1 (s+2)(s+5)(s +20) A controller, Ge(s) is required to improve the performance of the uncompensated system G(s). The system is operated at 20% of overshoot with the dominant poles given as Sa=-2.67 ±j5.22. (i) (ii) Determine the gain, K, the settling time, T,, and the peak time, Tp, of the closed loop system at the given dominant poles. From Q.2(a)(i), determine the new dominant poles, San if the compensated system settles three time faster than the uncompensated system. (iii) Using the new dominant poles, Sans design the PD controller and determine the values of proportional gain, KP, and derivative gain, KD, of the controller.
Transcribed Image Text:(a) Figure Q.2(a) illustrates a unity feedback system with a forward transfer function of a plant having a unit step input. R(s) C(s) Ge(s) G(s) Figure Q.2(a) The open-loop transfer function G(s) is given as G(s) = 1 (s+2)(s+5)(s +20) A controller, Ge(s) is required to improve the performance of the uncompensated system G(s). The system is operated at 20% of overshoot with the dominant poles given as Sa=-2.67 ±j5.22. (i) (ii) Determine the gain, K, the settling time, T,, and the peak time, Tp, of the closed loop system at the given dominant poles. From Q.2(a)(i), determine the new dominant poles, San if the compensated system settles three time faster than the uncompensated system. (iii) Using the new dominant poles, Sans design the PD controller and determine the values of proportional gain, KP, and derivative gain, KD, of the controller.
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