A unity feedback system has been operated for 5 years and need to be evaluated. It has an open loop transfer function as follows: k G(s) s(s + 1)(s+3) When the system is operating at 4.32% overshoot to a unit step input, its dominant closed loop poles are located at -0.42 j0.42. a) Calculate the value of damping ratio and K at this instance. b) Design a suitable PD controller so that the system will produce a new settling time of T,= 2.86 s while maintaining the same percentage of overshoot as before.

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A unity feedback system has been operated for 5 years and need to be evaluated. It has
an open loop transfer function as follows:
k
G(s) :
%3D
s(s + 1)(s+3)
When the system is operating at 4.32% overshoot to a unit step input, its dominant closed
loop poles are located at -0.42 + j0.42.
a) Calculate the value of damping ratio and K at this instance.
b) Design a suitable PD controller so that the system will produce a new settling time of
T, = 2.86 s while maintaining the same percentage of overshoot as before.
c) From the new compensated system obtained, determined whether PI controller is
required to further improve your system. Explain your answer.
Transcribed Image Text:A unity feedback system has been operated for 5 years and need to be evaluated. It has an open loop transfer function as follows: k G(s) : %3D s(s + 1)(s+3) When the system is operating at 4.32% overshoot to a unit step input, its dominant closed loop poles are located at -0.42 + j0.42. a) Calculate the value of damping ratio and K at this instance. b) Design a suitable PD controller so that the system will produce a new settling time of T, = 2.86 s while maintaining the same percentage of overshoot as before. c) From the new compensated system obtained, determined whether PI controller is required to further improve your system. Explain your answer.
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