(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)
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Solve the following question.
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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