GATE EE 2023 Set 1 — Question 14
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Control Systems → Compensators & Controllers → P, PI & PID Controllers
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Question
Consider a unity-gain negative feedback system consisting of the plant (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 and 1, respectively. For a unit step reference input, the final values of the controller output and the plant output, respectively, are
Correct answer
(D) -1, 1
Solution
1.Controller Transfer Function: A proportional-integral (PI) controller has the transfer function:
2.Open-Loop Transfer Function:
3.Closed-Loop Transfer Function (Plant Output): For a unity-gain negative feedback system, the transfer function from reference to output is:
For a unit step input , the final value of the plant output is:4.Controller Output: The transfer function from reference to controller output is:
For a unit step input , the final value of the controller output is:Thus, the final values of the controller output and plant output are and , respectively.
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