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GATE EE Control Systems Previous Year Questions

60 solved GATE EE questions on Control Systems, drawn from 10 exam years and grouped by year. Every question shows the official answer and a step-by-step solution.

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Control Systems: check stability before analysing performance

Determine whether the closed-loop system is stable before computing steady-state error, bandwidth, or transient specifications. These selected foundations connect transfer functions, stability criteria, root locus, and frequency response through original analytical exercises. State the feedback configuration and sign convention explicitly.

Our study notes and original examples support the PYQs below; they are not official exam questions or a replacement for the current syllabus.

Before you start

  • Laplace transforms, partial fractions, and pole-zero concepts in the s-domain.
  • Complex-number magnitude and phase, and logarithmic (dB) scale conversions.

Concepts to revise before solving

Transfer function and block diagram algebra

The transfer function H(s) = Y(s)/X(s) describes an LTI system in the Laplace domain. Series blocks multiply; parallel blocks add. For negative unity feedback with forward gain G(s), the closed-loop transfer function is G(s)/(1 + G(s)). Mason's gain formula generalises to complex signal-flow graphs.

Check yourself: Is the feedback sign negative, and have you accounted for every loop?

Routh–Hurwitz stability criterion

Construct the Routh array from the characteristic polynomial's coefficients. The number of sign changes in the first column equals the number of right-half-plane roots. All first-column entries must be positive for all roots to lie in the left half-plane. A zero entry in the first column requires the epsilon method or the auxiliary polynomial.

Check yourself: Have you included every coefficient, including any that are zero?

Root locus

The root locus traces closed-loop pole locations as gain K varies from 0 to ∞. Branches start at open-loop poles and end at open-loop zeros or infinity. The number of branches equals the number of open-loop poles. Asymptote angles and centroid, breakaway points, and jω-axis crossings characterise the locus.

Check yourself: Does the number of branches match the polynomial degree?

Bode plot and frequency-domain analysis

A Bode plot consists of magnitude (in dB) and phase versus log frequency. A simple pole at s = −a contributes −20 dB/decade above ω = a and −45° at ω = a. Gain margin is measured at the phase-crossover frequency; phase margin at the gain-crossover frequency. Both must be positive for stability of a minimum-phase system.

Check yourself: Are you reading gain margin at the frequency where phase is −180°?

State-space representation

State equations ẋ = Ax + Bu and output y = Cx + Du describe an LTI system using matrix notation. The transfer function is C(sI − A)⁻¹B + D. Eigenvalues of A are the system poles. Controllability requires rank [B, AB, …, A^(n−1)B] = n; observability requires rank [C; CA; …; CA^(n−1)] = n.

Check yourself: Do the eigenvalues of A agree with the poles of the transfer function?

Mistakes to avoid

Confusing open-loop and closed-loop poles when assessing stability.
Stability depends on the closed-loop characteristic equation 1 + G(s)H(s) = 0, not on the open-loop poles alone.
Reading phase margin at the phase-crossover frequency instead of the gain-crossover frequency.
Phase margin is 180° + ∠G(jω_gc) at the frequency where |G(jω)| = 0 dB.
Applying the final-value theorem to an unstable system.
The final-value theorem requires all poles of sY(s) to have negative real parts (or at most a simple pole at s = 0). Unstable poles invalidate the result.

Original teaching example · not a PYQ

Work through the reasoning

Original mini-example: determine the range of gain K > 0 for which the system with characteristic equation s³ + 3s² + 2s + K = 0 is stable, using the Routh–Hurwitz criterion.

  1. Construct the Routh array. Row s³: [1, 2]. Row s²: [3, K]. Row s¹: [(3×2 − 1×K)/3] = [(6 − K)/3]. Row s⁰: [K].
  2. For stability, all first-column elements must be positive: 1 > 0, 3 > 0, (6 − K)/3 > 0, and K > 0.
  3. (6 − K)/3 > 0 requires K < 6. Combined with K > 0, the stable range is 0 < K < 6.
  4. Verify boundary: at K = 6, the s¹ row is zero. The auxiliary equation from s² is 3s² + 6 = 0, giving s = ±j√2, confirming imaginary-axis roots and marginal stability.

The system is stable for 0 < K < 6.

Try it before reading the answer

For the open-loop transfer function G(s) = 10/(s² + 3s + 2) in a unity negative-feedback configuration, find the steady-state output for a unit step input.

Show answer and reasoning

Steady-state output = 10/12 = 5/6.

Closed-loop transfer function T(s) = G(s)/(1 + G(s)) = 10/(s² + 3s + 12). Poles: s = (−3 ± √(9 − 48))/2 = (−3 ± j√39)/2, both in the LHP. By the final-value theorem: y_ss = lim(s→0) s × T(s)/s = T(0) = 10/12 = 5/6.

Go deeper with free learning resources

Supplemental reading, not an official GATE reading list or an endorsement of these notes.

Apply this to the previous-year questions

Previous-year questions by year

This page shows 60 recent questions from the released archive, newest first. For older questions and complete papers, browse all GATE EE papers. Questions can carry more than one subject tag; counts are not marks weightage.

GATE EE 20264 questions

  1. Set 1 Q13The Laplace transform of the step response of a system is given by Y(s)=100s(s+100)Y(s) = \frac{100}{s(s + 100)} The rise time is defined as the time taken for the…MCQ · +1 marks · Medium
  2. Set 1 Q29The asymptotic Bode magnitude plot of a system is shown. [figure] Which one of the following options best represents the transfer function of the system?MCQ · +1 marks · Easy
  3. Set 1 Q52A system is characterized by the following state equation and output equation (uu: input, x\mathbf{x}: state vector, yy: output)…MCQ · +2 marks · Medium
  4. Set 1 Q53A system is represented in state-space form as follows: (uu: input, x\mathbf{x}: state vector, yy: output)…MCQ · +2 marks · Medium

GATE EE 20257 questions

  1. Set 1 Q22Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant,…MCQ · +1 marks · Medium
  2. Set 1 Q23The Nyquist plot of a strictly stable G(s)G(s) having the numerator polynomial as (s−3)(s - 3) encircles the critical point −1-1 once in the anti-clockwise…MCQ · +1 marks · Medium
  3. Set 1 Q29The open-loop transfer function of the system shown in the figure, is G(s)=Ks(s+2)(s+5)(s+7)G(s) = \frac{Ks(s + 2)}{(s + 5)(s + 7)} For K≥0K \geq 0, which of the following real…MSQ · +1 marks · Medium
  4. Set 1 Q41Let G(s)=1(s+1)(s+2)G(s) = \frac{1}{(s+1)(s+2)}. Then the closed-loop system shown in the figure below, is [figure]MCQ · +2 marks · Medium
  5. Set 1 Q54Consider ordinary differential equations given by x˙1(t)=2x2(t)\dot{x}_1(t) = 2x_2(t) x˙2(t)=r(t)\dot{x}_2(t) = r(t) with initial conditions x1(0)=1x_1(0) = 1 and x2(0)=0x_2(0) = 0. If…NAT · +2 marks · Easy
  6. Set 1 Q62Consider the state-space model x˙(t)=Ax(t)+Br(t),\dot{\mathbf{x}}(t) = A\mathbf{x}(t) + Br(t), y(t)=Cx(t)y(t) = C\mathbf{x}(t) where x(t),r(t),y(t)\mathbf{x}(t), r(t), y(t) are the state,…NAT · +2 marks · Easy
  7. Set 1 Q65A controller D(s)D(s) of the form (1+KDs)(1 + K_D s) is to be designed for the plant G(s)=10002s(s+10)2G(s) = \frac{1000\sqrt{2}}{s(s+10)^2} as shown in the figure. The value of…NAT · +2 marks · Medium

GATE EE 20246 questions

  1. Set 1 Q20For the block-diagram shown in the figure, the transfer function C(s)R(s)\frac{C(s)}{R(s)} is [figure]MCQ · +1 marks · Easy
  2. Set 1 Q21Consider the standard second-order system of the form ωn2s2+2ζωns+ωn2\frac{\omega_n^2}{s^2+2\zeta\omega_ns+\omega_n^2} with the poles pp and p∗p^* having negative real…MCQ · +1 marks · Medium
  3. Set 1 Q22Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a…MCQ · +1 marks · Medium
  4. Set 1 Q57Consider the closed-loop system shown in the figure with G(s)=K(s2−2s+2)(s2+2s+5).G(s) = \frac{K(s^2 - 2s + 2)}{(s^2 + 2s + 5)}. The root locus for the closed-loop system is to be…NAT · +2 marks · Hard
  5. Set 1 Q58Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of G(s)G(s) has a constant slope of −20-20 dB/decade at least till…NAT · +2 marks · Hard
  6. Set 1 Q59Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of G(s)G(s) are given in the table. The…NAT · +2 marks · Medium

GATE EE 20236 questions

  1. Set 1 Q12For the block diagram shown in the figure, the transfer function Y(s)R(s)\frac{Y(s)}{R(s)} is [figure]MCQ · +1 marks · Medium
  2. Set 1 Q13In the Nyquist plot of the open-loop transfer function G(s)H(s)=3s+5s−1G(s)H(s) = \frac{3s + 5}{s - 1} corresponding to the feedback loop shown in the figure, the infinite…MCQ · +1 marks · Easy
  3. Set 1 Q14Consider a unity-gain negative feedback system consisting of the plant G(s)G(s) (given below) and a proportional-integral controller. Let the proportional gain…MCQ · +1 marks · Medium
  4. Set 1 Q36The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is [figure]MCQ · +2 marks · Medium
  5. Set 1 Q38Consider a lead compensator of the form K(s)=1+sa1+sβa,β>1,a>0K(s) = \frac{1 + \frac{s}{a}}{1 + \frac{s}{\beta a}}, \beta > 1, a > 0 The frequency at which this compensator…MCQ · +2 marks · Medium
  6. Set 1 Q46Consider the state-space description of an LTI system with matrices…NAT · +2 marks · Medium

GATE EE 20225 questions

  1. Set 1 Q17The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is…MCQ · +1 marks · Medium
  2. Set 1 Q19The open loop transfer function of a unity gain negative feedback system is given by G(s)=ks2+4s−5G(s) = \frac{k}{s^2+4s-5} The range of kk for which the system is…MCQ · +1 marks · Easy
  3. Set 1 Q37An LTI system is shown in the figure where G(s)=100s2+0.1s+10G(s) = \frac{100}{s^2 + 0.1s + 10} The steady state output of the system, to the input r(t)r(t), is given as…MCQ · +2 marks · Medium
  4. Set 1 Q38The open loop transfer function of a unity gain negative feedback system is given as G(s)=1s(s+1)G(s) = \frac{1}{s(s+1)} The Nyquist contour in the ss-plane encloses…MCQ · +2 marks · Medium
  5. Set 1 Q39The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as ζ\zeta and ωn\omega_n, respectively. The…MCQ · +2 marks · Medium

GATE EE 20215 questions

  1. Set 1 Q21For the closed-loop system shown, the transfer function E(s)R(s)\frac{E(s)}{R(s)} is [figure]MCQ · +1 marks · Easy
  2. Set 1 Q30The Bode magnitude plot for the transfer function Vo(s)Vi(s)\frac{V_o(s)}{V_i(s)} of the circuit is as shown. The value of RR is ______ Ω\Omega. (Round off to 2…NAT · +1 marks · Medium
  3. Set 1 Q56Consider a closed-loop system as shown. Gp(s)=14.4s(1+0.1s)G_p(s) = \frac{14.4}{s(1+0.1s)} is the plant transfer function and Gc(s)=1G_c(s) = 1 is the compensator. For a unit-step…NAT · +2 marks · Medium
  4. Set 1 Q57In the given figure, plant Gp(s)=2.2(1+0.1s)(1+0.4s)(1+1.2s)G_p(s) = \frac{2.2}{(1+0.1s)(1+0.4s)(1+1.2s)} and compensator Gc(s)=K(1+T1s1+T2s)G_c(s) = K \left( \frac{1+T_1s}{1+T_2s} \right). The external…NAT · +2 marks · Medium
  5. Set 1 Q59The state space representation of a first-order system is given as x˙=−x+u\dot{x} = -x + u y=xy = x where, xx is the state variable, uu is the control input…NAT · +2 marks · Easy

GATE EE 20205 questions

  1. Set 1 Q24Which of the options is an equivalent representation of the signal flow graph shown here? [figure]MCQ · +1 marks · Medium
  2. Set 1 Q34Consider a negative unity feedback system with forward path transfer function G(s)=K(s+a)(s−b)(s+c)G(s) = \frac{K}{(s+a)(s-b)(s+c)}, where K,a,b,cK, a, b, c are positive real numbers.…NAT · +1 marks · Hard
  3. Set 1 Q44Consider a permanent magnet dc (PMDC) motor which is initially at rest. At t=0t = 0, a dc voltage of 5 V5\text{ V} is applied to the motor. Its speed…MCQ · +2 marks · Medium
  4. Set 1 Q45Which of the following options is correct for the system shown below? [figure]MCQ · +2 marks · Medium
  5. Set 1 Q46Consider a negative unity feedback system with the forward path transfer function G(s)=s2+s+1s3+2s2+2s+KG(s) = \frac{s^2+s+1}{s^3+2s^2+2s+K}, where KK is a positive real number.…MCQ · +2 marks · Medium

GATE EE 20196 questions

  1. Set 1 Q23The output response of a system is denoted as y(t)y(t), and its Laplace transform is given by Y(s)=10s(s2+s+1002)Y(s) = \frac{10}{s(s^2+s+100\sqrt{2})} The steady state value…MCQ · +1 marks · Easy
  2. Set 1 Q24The open loop transfer function of a unity feedback system is given by G(s)=πe−0.25ssG(s) = \frac{\pi e^{-0.25s}}{s} In G(s)G(s) plane, the Nyquist plot of G(s)G(s) passes…MCQ · +1 marks · Medium
  3. Set 1 Q25The characteristic equation of a linear time-invariant (LTI) system is given by Δ(s)=s4+3s3+3s2+s+k=0.\Delta(s) = s^4 + 3s^3 + 3s^2 + s + k = 0. The system is BIBO stable ifMCQ · +1 marks · Easy
  4. Set 1 Q39The asymptotic Bode magnitude plot of a minimum phase transfer function G(s)G(s) is shown below. [figure] Consider the following two statements. Statement I:…MCQ · +2 marks · Medium
  5. Set 1 Q40The transfer function of a phase lead compensator is given by D(s)=3(s+13T)(s+1T)D(s) = \frac{3(s + \frac{1}{3T})}{(s + \frac{1}{T})} The frequency (in rad/sec), at which…MCQ · +2 marks · Easy
  6. Set 1 Q41Consider a state-variable model of a system…MCQ · +2 marks · Easy

GATE EE 20185 questions

  1. Set 1 Q19Match the transfer functions of the second-order systems with the nature of the systems given below. | Transfer functions | Nature of system | | :--- | :--- |…MCQ · +1 marks · Easy
  2. Set 1 Q35Consider a unity feedback system with forward transfer function given by G(s)=1(s+1)(s+2)G(s) = \frac{1}{(s+1)(s+2)} The steady-state error in the output of the system for…NAT · +1 marks · Easy
  3. Set 1 Q43Consider a system governed by the following equations dx1(t)dt=x2(t)−x1(t)\frac{dx_1(t)}{dt} = x_2(t) - x_1(t) dx2(t)dt=x1(t)−x2(t)\frac{dx_2(t)}{dt} = x_1(t) - x_2(t) The initial conditions…MCQ · +2 marks · Medium
  4. Set 1 Q44The number of roots of the polynomial, s7+s6+7s5+14s4+31s3+73s2+25s+200s^7 + s^6 + 7s^5 + 14s^4 + 31s^3 + 73s^2 + 25s + 200, in the open left half of the complex plane isMCQ · +2 marks · Medium
  5. Set 1 Q56The unit step response y(t) of a unity feedback system with open loop transfer function G(s)H(s)=K(s+1)2(s+2)G(s)H(s) = \frac{K}{(s+1)^2(s+2)} is shown in the figure. The value…NAT · +2 marks · Medium

GATE EE 201711 questions

  1. Set 1 Q11A closed loop system has the characteristic equation given by s3+Ks2+(K+2)s+3=0s^3 + Ks^2 + (K + 2)s + 3 = 0. For this system to be stable, which one of the following…MCQ · +1 marks · Easy
  2. Set 1 Q22Consider the unity feedback control system shown. The value of KK that results in a phase margin of the system to be 30∘30^\circ is ______. (Give the answer up…NAT · +1 marks · Medium
  3. Set 1 Q32In the system whose signal flow graph is shown in the figure, U1(s)U_1(s) and U2(s)U_2(s) are inputs. The transfer function Y(s)U1(s)\frac{Y(s)}{U_1(s)} is [figure]MCQ · +1 marks · Medium
  4. Set 1 Q33The transfer function of the system Y(s)/U(s)Y(s)/U(s) whose state-space equations are given below is:…MCQ · +1 marks · Easy
  5. Set 1 Q50For a system having transfer function G(s)=−s+1s+1G(s) = \frac{-s + 1}{s + 1}, a unit step input is applied at time t=0t = 0. The value of the response of the system at…NAT · +2 marks · Easy
  6. Set 2 Q6When a unit ramp input is applied to the unity feedback system having closed loop transfer function…MCQ · +2 marks · Medium
  7. Set 2 Q7The transfer function C(s)C(s) of a compensator is given below. C(s)=(1+s0.1)(1+s100)(1+s)(1+s10)C(s) = \frac{(1 + \frac{s}{0.1})(1 + \frac{s}{100})}{(1 + s)(1 + \frac{s}{10})} The frequency…MCQ · +2 marks · Medium
  8. Set 2 Q34The root locus of the feedback control system having the characteristic equation s2+6Ks+2s+5=0s^2 + 6Ks + 2s + 5 = 0 where K>0K > 0, enters into the real axis atMCQ · +1 marks · Medium
  9. Set 2 Q35The range of KK for which all the roots of the equation s3+3s2+2s+K=0s^3 + 3s^2 + 2s + K = 0 are in the left half of the complex ss-plane isMCQ · +1 marks · Easy
  10. Set 2 Q36Which of the following systems has maximum peak overshoot due to a unit step input?MCQ · +2 marks · Easy
  11. Set 2 Q46Consider the system described by the following state space representation…NAT · +2 marks · Medium

Other GATE EE topics

General Aptitude(181)Engineering Mathematics(173)Electric Circuits(139)Electrical Machines(129)Analog & Digital Electronics(111)Power Systems(108)Signals & Systems(107)Power Electronics(101)Electromagnetic Fields(56)Electrical & Electronic Measurements(36)

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