GATE Overflow for GATE BT - Recent questions and answers in Instrumentation and Process Control

GATE BT 2026 | Question: 5

Mon, 23 Feb 2026 14:22:23 +0000

The transfer function of a Proportional-Integral $\text{(PI)}$ controller $G_{C}(s)$ is given by

\[
G_{C}(s)=K_{C}\left(1+\frac{1}{\tau_{I} s}\right)
\]
where $K_{C}$ is the controller gain, $\tau_{I}$ is the controller integral time constant and $s$ is the Laplace variable. The role of the integral component of the controller is to $\_\_\_\_$.

integrate the difference between the process and manipulated variable
integrate the difference between the set point and disturbance variable
integrate the difference between the set point and the measured variable
integrate the difference between the input and output variable

GATE BT 2026 | Question: 26

Mon, 23 Feb 2026 14:21:31 +0000

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)

$y(t)=K_{p}\left(1-e^{-t / \tau_{p}}\right)$
$y(t)=M K_{p}\left(1-e^{-t / \tau_{p}}\right)$
$y(t)=K_{p}\left(M-e^{-t / \tau_{p}}\right)$
$y(t)=K_{p}\left(1-M e^{-t / \tau_{p}}\right)$

GATE BT 2025 | Question: 32

Thu, 06 Mar 2025 17:05:14 +0000

A thermometer measuring body temperature follows a first-order response with a time constant of $40$ seconds. The instrument will reach $95 \%$ of its steady-state output at $\_\_\_\_\_$ seconds.

(Round off to the nearest integer)

$60$
$80$
$120$
$160$

GATE BT 2025 | Question: 33

Thu, 06 Mar 2025 17:05:12 +0000

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

\[
\tau_{p} \frac{d y}{d t}+y=K_{p} f(t)
\]
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)

$\frac{K_{p}}{\tau_{p} s+1}$
$\frac{\tau_{p}}{K_{p} s+1}$
$\frac{\tau_{p}}{K_{p}(s+1)}$
$\frac{K_{p}}{\tau_{p}(s+1)}$

GATE BT 2024 | Question: 2

Mon, 25 Mar 2024 19:16:34 +0000

The transfer function of a process is $G(s)=\frac{K_{p}}{\tau_{p} s+1}$, where $K_{p}$ is the gain and $\tau_{p}$ is the time constant. This is a $\_\_\_\_\_\_$ process.

first order
multi-capacity
purely capacity
second order

GATE BT 2023 | Question: 54

Sun, 21 May 2023 02:58:13 +0000

A proportional controller is used to control the temperature of an autoclave from $60^{\circ} \mathrm{C}$ to $130^{\circ} \mathrm{C}$. If the proportional band setting of the controller is $25 \%$, the proportional gain value is ___________.

GATE BT 2022 | Question: 31

Sun, 20 Mar 2022 16:16:27 +0000

Which of the following statements are $\text{CORRECT}$ for a controller?

In a proportional controller, a control action is proportional to the error
In an integral controller, a control action is proportional to the derivative of the error
There is no “offset” in the response of the closed-loop first-order process with a proportional controller
There is no “offset” in the response of the closed-loop first-order process with a proportional-integral controller

$\text{P}$ and $\text{Q}$ Only
$\text{P}$ and $\text{R}$ Only
$\text{P}$ and $\text{S}$ Only
$\text{Q}$ and $\text{S}$ Only

GATE BT 2021 | Question: 13

Mon, 01 Mar 2021 03:19:50 +0000

The process and instrumentation diagram for a feedback control strategy to maintain the level $(h)$ of a liquid by regulating a valve $(V)$ in a tank is shown below. $F_1$ is inlet liquid flow rate, $F_2$ is outlet liquid flow rate, $LT$ is the liquid level transmitter, $LC$ is the liquid level controller, $h_{sp}$ is the setpoint value of the liquid level, $h_m$ is the measured value of the liquid level and $P_v$ is the valve pressure.

The manipulating variable(s) is/are

$F_1$ only
$F_2$ only
$h_m$ and $P_v$ only
$h_{sp}$ and $P_v$ only

GATE2019: 41

Tue, 03 Nov 2020 12:02:07 +0000

Which one of the following statements is $CORRECT$ about proportional controllers?

The initial change in control output signal is relatively slow
The initial corrective action is greater for larger error
They have no offset
There is no corrective action if the error is a constant

GATE2019: 42

Tue, 03 Nov 2020 12:02:07 +0000

Match the instruments in $Group\; I$ with their corresponding measurements in $Group\; II$.

$$\begin{array}&&\textbf{Group I} & \textbf{Group II} \\ &\text{P. Manometer} & \text{1. Agitator speed}\\
&\text{Q. Rotameter} & \text{2. Pressure difference} \\
&\text{R. Tachometer} & \text{3. Cell number} \\
&\text{S. Haemocytometer} & \text{4. Air flow rate} \\ \end{array}$$

$P-4, Q-1, R-2, S-3$
$P-3, Q-4, R-1, S-2$
$P-2, Q-4, R-1, S-3$
$P-2, Q-1, R-4, S-3$

GATE BT 2012 | Question: 37

Sun, 25 Mar 2018 08:38:46 +0000

Match the entries in $\text{Group I}$ with the process parameters in $\text{Group II}$.

$\begin{array}{|C|l|C|l|} \hline &\textbf{Group I} & {} & \text{Group II} \\\hline P. &\text{Clark electrode} & 1. &\text{Liquid level} \\\hline Q. &\text{Redox probe} & 2. &\text{Dissolved oxygen concentration} \\\hline R. &\text{Load cell} & 3. &\text{Vessel pressure} \\\hline S. &\text{Diaphragm gauge} & 4. &\text{pH (anaerobic process)} \\\hline\end{array}$

$\text{P-2, Q-1, R-3, S-4}$
$\text{P_4, Q-2, R-3, S-1}$
$\text{P-2, Q-4, R-1, S-3}$
$\text{P-2, Q-1, R-4, S-3}$