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Control Systems and Actuators

26 Questions
GATE→2026→Control Systems→Control Systems and Actuators
Q1
MCQ[1 Mark]
Among the following, the differential equation(s) not representative of a linear dynamical system is/are
GATE→2026→Control Systems→Control Systems and Actuators
Q2
MCQ[2 Marks]
A linear time invariant (LTI) system is described by state space matrices. The poles of the system are
GATE→2026→Control Systems→Control Systems and Actuators
Q3
NAT[2 Marks]
A linear time invariant (LTI) system has a transfer function G(s)=10(s+1)s(s2+2s+5)G(s) = \frac{10(s+1)}{s(s^{2}+2s+5)}. The system is placed in unity negative feedback configuration. For a unit ramp reference, the steady state error is (rounded off to two decimal places)
GATE→2026→Control Systems→Control Systems and Actuators
Q4
NAT[2 Marks]
G(s)=K(s+1)4G(s) = \frac{K}{(s+1)^{4}}. The system has a gain margin of 20 dB. The value of K is (rounded off to two decimal places)
GATE→2025→Control Systems→Control Systems and Actuators
Q5
MCQ[1 Mark]
For the transfer function G(s)=1+2s−1s3+5s2+3s+22G(s) = 1 + \frac{2s - 1}{s^{3} + 5s^{2} + 3s + 22}, the number of zeros lying in the left half of the s-plane is
Figure for Question 5
GATE→2025→Control Systems→Control Systems and Actuators
Q6
MCQ[1 Mark]
Consider the control system block diagram given in Figure (a)... Choose the correct statement from the following options for closed loop stability of the system.
Figure for Question 6
GATE→2025→Control Systems→Control Systems and Actuators
Q7
MCQ[2 Marks]
The figure shows a closed-loop system with a plant G(s)=1s2G(s) = \frac{1}{s^{2}} and a lead compensator C(s)C(s). The compensator is designed to place the dominant closed-loop poles at −1.5±j272-1.5 \pm j\frac{\sqrt{27}}{2}. From the following options, choose the phase lead that the compensator needs to contribute.
Figure for Question 7
GATE→2025→Control Systems→Control Systems and Actuators
Q8
MSQ[2 Marks]
The plant in the feedback control system shown in the figure is P(s)=as2−b2P(s) = \frac{a}{s^{2} - b^{2}} where a>0a > 0 and b>0b > 0. The type(s) of controller C(s)C(s) that CANNOT stabilize the plant is/are
Figure for Question 8
GATE→2025→Control Systems→Control Systems and Actuators
Q9
NAT[2 Marks]
A feedback control system is shown in the figure. The maximum allowable value of n such that the output y(t)y(t), due to any step disturbance signal d(t)d(t), becomes zero at steady-state, is (in integer).
Figure for Question 9
GATE→2024→Control Systems→Control Systems and Actuators
Q10
MCQ[1 Mark]
The pressure drop across a control valve is constant. The control valve with inherent characteristic has decreasing sensitivity. If x represents the fraction of maximum stem position of the control valve, then the function f(x)f(x) representing the fraction of maximum flow is
GATE→2024→Control Systems→Control Systems and Actuators
Q11
MCQ[1 Mark]
Consider the state-space representation of a system x˙=Ax+Bu\dot{x} = Ax + Bu... Choose the matrix A from the following options such that the system has a pole at the origin.
GATE→2024→Control Systems→Control Systems and Actuators
Q12
MCQ[1 Mark]
The sinusoidal transfer function corresponding to the polar plot shown in the figure, for T>0T > 0, is
Figure for Question 12
GATE→2024→Control Systems→Control Systems and Actuators
Q13
MCQ[2 Marks]
Consider the feedback control system shown in the figure. The steady-state error ess=lim⁡t→∞(r(t)−y(t))e_{ss} = \lim_{t \to \infty}(r(t) - y(t)) due to unit step reference r(t)r(t) is
Figure for Question 13
GATE→2024→Control Systems→Control Systems and Actuators
Q14
MCQ[2 Marks]
The transfer function of a system is G(s)=ωn2s2+2ξωns+ωn2G(s) = \frac{\omega_{n}^{2}}{s^{2} + 2\xi\omega_{n}s + \omega_{n}^{2}}. Choose the range of ξ\xi and ωn\omega_{n} (in rad/s) from the following options such that the poles lie on the shaded region of the s-plane as shown in the figure.
Figure for Question 14
GATE→2024→Control Systems→Control Systems and Actuators
Q15
NAT[2 Marks]
Consider a unity negative feedback system with its open-loop pole-zero map as shown in the figure. If the points s=jαs = j\alpha, α>0\alpha > 0, lies on the root locus, the value of α\alpha is (rounded off to nearest integer).
Figure for Question 15
GATE→2023→Control Systems→Control Systems and Actuators
Q16
NAT[1 Mark]
The number of zeros of the polynomial P(s)=s3+2s2+5s+80P(s) = s^{3} + 2s^{2} + 5s + 80 in the right-half plane is
GATE→2023→Control Systems→Control Systems and Actuators
Q17
NAT[1 Mark]
The number of times the Nyquist plot of G(s)H(s)=12(s−1)(s−2)(s+1)(s+2)G(s)H(s) = \frac{1}{2} \frac{(s-1)(s-2)}{(s+1)(s+2)} encircles the origin is
GATE→2023→Control Systems→Control Systems and Actuators
Q18
MCQ[2 Marks]
The magnitude and phase plots shown in the figure match with the transfer-function
Figure for Question 18
GATE→2023→Control Systems→Control Systems and Actuators
Q19
NAT[2 Marks]
Consider a standard negative feedback configuration with G(s)G(s) and controller C(s)C(s)... The value of KDK_{D} is (rounded off to one decimal place).
Figure for Question 19
GATE→2023→Control Systems→Control Systems and Actuators
Q20
NAT[2 Marks]
The phase margin of the transfer function G(s)=2(1−s)(1+s)2G(s) = \frac{2(1-s)}{(1+s)^{2}} is degrees (rounded off to the nearest integer).
GATE→2022→Control Systems→Control Systems and Actuators
Q21
MCQ[1 Mark]
A unity-gain negative-feedback control system has a loop-gain L(s)L(s) given by L(s)=6s(s−5)L(s) = \frac{6}{s(s-5)}. The closed-loop system is
GATE→2022→Control Systems→Control Systems and Actuators
Q22
NAT[1 Mark]
The transfer function of a system is... In the state-space representation of the system, the minimum number of state variables (in integer) necessary is
GATE→2022→Control Systems→Control Systems and Actuators
Q23
MCQ[2 Marks]
The signal flow graph of a system is shown. The expression for Y(s)/X(s)Y(s)/X(s) is
Figure for Question 23
GATE→2022→Control Systems→Control Systems and Actuators
Q24
MCQ[2 Marks]
A proportional-integral-derivative (PID) controller is employed to stably control a plant... the steady-state error in tracking a ramp reference signal
GATE→2022→Control Systems→Control Systems and Actuators
Q25
MCQ[2 Marks]
The Nyquist plot of a stable open-loop system G(jω)G(j\omega) is plotted... The phase margin (PM) and the gain margin (GM) of the system are
Figure for Question 25
GATE→2022→Control Systems→Control Systems and Actuators
Q26
NAT[2 Marks]
In a unity-gain feedback control system, the plant... The slope (in dB/decade) of the asymptotic Bode magnitude plot of the loop gain at ω=3\omega = 3 rad/s is (in integer).