The GATE Grind

GATE 2025 BT – Question 43

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

The output $y(t)$ of a first-order process is governed by the following differential equation

$\tau_p\frac{dy}{dt} + y = K_pf(t)$

where $\tau_p$ is a non-zero time constant, $K_p$ is the gain and $f(t)$ is the input with $f(0) = 0$. Assume $y(0) = 0$. The transfer function for this process is (consider $s$ as the independent variable in the Laplace domain)

  1. $\frac{K_p}{\tau_ps + 1}$
  2. $\frac{\tau_p}{K_ps + 1}$
  3. $\frac{\tau_p}{K_p(s + 1)}$
  4. $\frac{K_p}{\tau_p(s + 1)}$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $\frac{K_p}{\tau_ps + 1}$

Explanation

The Laplace transform with zero initial conditions gives $\tau_psY + Y = K_pF$, so $\frac{Y}{F} = \frac{K_p}{\tau_ps + 1}$.