The GATE Grind

GATE 2026 BT – Question 36

Fundamentals of Biological Engineering · Process Control: Measurement devices, valves, first and second order systems, feedback and feed forward control, P, I and D controllers and tuning · 2 marks · Multiple choice

In the open-loop process shown in the figure, the input $U(s)$, the transfer function $G_p(s)$ and the output $Y(s)$ are given in the Laplace domain in terms of the Laplace variable s. For this process, which of the following is true?

(where $M$, $\tau_p$, $K_P$, are the magnitude of the input, the characteristic time and the gain for the process, respectively)

A block diagram. The input is $U(s) = \frac{M}{s}$ and the block is $G_p(s) = \frac{K_p}{\tau_ps + 1}$, with the output $Y(s)$.
  1. $y(t) = K_p(1 - e^{-t/\tau_p})$
  2. $y(t) = MK_p(1 - e^{-t/\tau_p})$
  3. $y(t) = K_p(M - e^{-t/\tau_p})$
  4. $y(t) = K_p(1 - Me^{-t/\tau_p})$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) $y(t) = MK_p(1 - e^{-t/\tau_p})$

Explanation

$Y(s) = \frac{M}{s}\cdot\frac{K_p}{\tau_ps + 1} = MK_p\left[\frac{1}{s} - \frac{\tau_p}{\tau_ps + 1}\right]$, whose inverse transform is $y(t) = MK_p(1 - e^{-t/\tau_p})$, the first-order step response.