Control System GATE Questions

A highly popular method used to prepare for the GATE Exam is to diligently practise all the previous years’ GATE Questions. Candidates can practise, analyse and understand concepts while solving them. It will also help you strengthen your time management skills. We have attempted to compile, here in this article, a collection of GATE Questions on Control System.

Candidates are urged to practise these Control System GATE previous year questions to get the best results. Control System is an important topic in the GATE ECE question paper, and solving these questions will help the candidates to prepare more proficiently for the GATE exams. Meanwhile, candidates can find the GATE Questions for Control System here, in this article below, to solve and practise before the exams. They can also refer to these GATE
previous year question papers and start preparing for the exams.

GATE Questions on Control System

1. Tachometer feedback in a D.C. position control system enhances stability.

(GATE ECE 1994)

1. True
2. False

Answer (b)

2. The transfer function of a tachometer is of the form

(GATE ECE 1998)

1. Ks
2. \(\begin{array}{l}\frac{K}{s}\end{array} \)
3. \(\begin{array}{l}\frac{K}{s+1}\end{array} \)
4. \(\begin{array}{l}\frac{K}{s(s+1)}\end{array} \)

Answer (a)

3. A linear time invariant system has an impulse response e^2t, t > 0. If the initial conditions are zero and the input is e^3t, the output for t > 0 is

(GATE ECE 2000)

1. \(\begin{array}{l}e^{3t}-e^{2t}\end{array} \)
2. \(\begin{array}{l}e^{5t}\end{array} \)
3. \(\begin{array}{l}e^{3t+e^{2t}}\end{array} \)
4. None of the above

Answer (a)

4. Let x(t) be the input to a linear, time-invariant system. The required output is 4x(t-2). The transfer function of the system should be

(GATE ECE 2003)

1. \(\begin{array}{l}4e^{i4\pi f}\end{array} \)
2. \(\begin{array}{l}2e^{-j8\pi f}\end{array} \)
3. \(\begin{array}{l}4e^{-j4\pi f}\end{array} \)
4. \(\begin{array}{l}2e^{i8\pi f}\end{array} \)

Answer (c)

5. Negative feedback in a closed-loop control system does NOT

(GATE ECE 2015 Set 1)

1. Reduce the overall gain
2. Reduce bandwidth
3. Improve disturbance rejection
4. Reduce sensitivity to parameter variation

Answer (b)

6. The impulse response of an LTI system can be obtained by

(GATE ECE 2015 Set 3)

1. Differentiating the unit ramp response
2. Differentiating the unit step response
3. Integrating the unit step response
4. Integrating the unit step response

Answer (b)

7. Despite the presence of negative feedback, control systems still have problems of instability because the

(GATE ECE 2005)

1. Components used have nonlinearities
2. Dynamic equations of the subsystems are not known exactly
3. Mathematical analysis involves approximations
4. System has large negative phase angle at high frequencies

Answer (a)

8. Consider a stable system with transfer function
\(\begin{array}{l}G(s)=\frac{s^{p}+b_{1}s^{p-1}+……+b_{p}}{s^{q}+a_{1}s^{q-1}+……+a_{q}}\end{array} \)

Where ,………., and ,…….., are real valued constants. The slope of the Bode log magnitude curve of G(s) converges to -60 dB/decade as ω→∞. A possible pair of values for p and q is

(GATE ECE 2017 Set 1)

1. p = 0 and q =3
2. p = 1 and q = 7
3. p = 2 and q = 7
4. p = 3 and q = 5

Answer (a)

9. A unity negative feedback system has an open–loop transfer function:
\(\begin{array}{l}G(s)=\frac{K}{s(s+1)}\end{array} \)

The gain K for the system to have a damping ratio of 0.25 is _____________

(GATE ECE 2015 Set 2)

1. 400
2. 500
3. 250
4. 475

Answer (a)

10. The open loop transfer function
\(\begin{array}{l}G(s)=\frac{s+1}{s^{p}(s+2)(s+3)}\end{array} \)

Where p is an integer, it is connected in unity feedback configuration as shown in figure,



Given that the steady state error is zero for unit step input and is 6 for unit ramp input, the value of the parameter p is _________

(GATE ECE 2017 Set 1)

1. 1
2. 0
3. Both (a) and (b)
4. None of the above

Answer (a)

11. For the unity feedback control system shown in the figure, the open-loop transfer function is given as,
\(\begin{array}{l}G(s)=\frac{2}{s(s+1)}\end{array} \)

The steady state error e_ss due to a unit step input is



(GATE ECE 2016 Set 3)

1. 0
2. 0.5
3. 1.0
4. ∞

Answer (a)

12. The response of the system
\(\begin{array}{l}G(s)=\frac{s-2}{(s+1)(s+3)}\end{array} \)

o the unit step input u(t) is y(t). The value of

\(\begin{array}{l}\frac{dy}{dt}\end{array} \)
at t = 0⁺ is _____________

(GATE ECE 2016 Set 2)

1. 0
2. 1
3. 0.5
4. None of the above

Answer (b)

13. Consider
    \(\begin{array}{l}p\left ( s \right )=s^{3}+a_{2}s^{2}+a_{1}s+a_0\end{array} \)
    with all real coefficients. It is known that its derivative has no real roots. The number of real roots of is

(GATE ECE 2018)

1. 0
2. 1
3. 2
4. 3

Answer (b)

14. A unity negative feedback system has the open-loop transfer function
\(\begin{array}{l}G\left ( s \right )=\frac{K}{s(s+1)(s+3)}\end{array} \)

The value of the gain K (>0) at which the root locus crosses the imaginary axis is _________

(GATE ECE 2015 Set 1)

1. 12
2. 15
3. 0
4. 1

Answer (a)

15. The popular plot of the transfer function
\(\begin{array}{l}G\left ( s \right )=\frac{10(s+1)}{(s+10)}\end{array} \)

for 0 ≤ ω < ∞ will be in the

(GATE ECE 2015 Set 1)

1. First quadrant
2. Second quadrant
3. Third quadrant
4. Fourth quadrant

Answer (a)