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GATE 2023 EE – Question 14

Control Systems · Transient and Steady-state analysis of linear time invariant systems · 1 mark · Multiple choice

Consider a unity-gain negative feedback system consisting of the plant $G(s)$ (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

$$G(s)=\frac1{s-1}$$

  1. $\infty,\ \infty$
  2. $1,\ 0$
  3. $1,\ -1$
  4. $-1,\ 1$

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Correct answer: (D) $-1,\ 1$

Explanation

The closed-loop characteristic polynomial is $s(s-1)+3s+1=(s+1)^2$, so the loop is stable. The integral action drives the error to zero, so the plant output settles at 1. In steady state $\dot y=y+u=0$, so the controller output is $u=-y=-1$. The answers are $-1$ and $1$.