60 solved GATE EC questions on Control Systems, drawn from 11 exam years and grouped by year. Every question shows the official answer and a step-by-step solution.
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Determine whether a system is stable before computing steady-state error or bandwidth. These selected foundations connect transfer functions, time-domain response, frequency-domain methods, and state-space representations. The original exercises use idealized linear models.
Our study notes and original examples support the PYQs below; they are not official exam questions or a replacement for the current syllabus.
A transfer function H(s) = Y(s)/X(s) assumes zero initial conditions. Block diagram reduction uses series (multiply), parallel (add), and feedback (H/(1+GH)) rules. Mason's gain formula provides a systematic alternative for complex diagrams.
Check yourself: Are initial conditions zero, and is the system linear time-invariant?
For a second-order underdamped system, the damping ratio ζ determines overshoot and the natural frequency ωn determines speed. Rise time decreases with increasing ωn. Percent overshoot = 100 exp(−πζ/√(1−ζ²)) for 0 < ζ < 1. Settling time depends on the dominant pole's real part.
Check yourself: Are the dominant poles truly second-order, or do other poles affect the response?
Form the Routh array from the characteristic polynomial. The number of right-half-plane roots equals the number of sign changes in the first column. All first-column entries must be positive for stability. A zero in the first column requires the epsilon method or auxiliary polynomial.
Check yourself: Have you checked every entry in the first column for sign changes?
Bode magnitude plot uses 20 log₁₀|H(jω)| in dB. Each real pole contributes −20 dB/decade above its corner frequency. Gain margin is measured at the phase crossover frequency; phase margin at the gain crossover frequency. The Nyquist criterion counts encirclements of −1 to determine closed-loop stability.
Check yourself: Is the gain margin measured where the phase is −180°, not where the magnitude is 0 dB?
ẋ = Ax + Bu, y = Cx + Du describes a system with state vector x. Eigenvalues of A determine stability. Controllability requires rank [B AB A²B ...] = n. Observability requires rank [C; CA; CA²; ...] = n. Transfer function H(s) = C(sI − A)⁻¹B + D relates the two representations.
Check yourself: Do the eigenvalues of A match the poles of the transfer function?
Original teaching example · not a PYQ
Original mini-example: use the Routh-Hurwitz criterion to determine the range of K > 0 for which the system with characteristic polynomial s³ + 3s² + 2s + K = 0 is stable.
The system is stable for 0 < K < 6.
A unity negative feedback system has open-loop transfer function G(s) = 10/(s(s + 5)). Find the steady-state error to a unit step input.
Steady-state error = 0.
The system is Type 1 (one integrator in the open-loop). For a unit step input, the steady-state error for a Type 1 or higher system is zero. Alternatively, the position error constant Kp = lim(s→0) G(s) = ∞, so ess = 1/(1 + Kp) = 0.
Supplemental reading, not an official GATE reading list or an endorsement of these notes.
Free supplemental lecture notes and problem sets covering transfer functions, stability, root locus, Bode plots, and state-space methods.
This page shows 60 recent questions from the released archive, newest first. For older questions and complete papers, browse all GATE EC papers. Questions can carry more than one subject tag; counts are not marks weightage.
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