The GATE Grind

GATE Measurements and Control Systems: Control System Transfer Functions – Previous Year Questions

11 GATE previous year questions on Control System Transfer Functions (Measurements and Control Systems, Biomedical Engineering) with answers and explanations, from every paper.

  1. GATE 2020 BM Q11 (1 mark, Multiple choice) – For roots m₁,m₂ of a second-order characteristic equation, match P real distinct,Q equal,R complex conjugate with K critically damped,L overdamped,M…
  2. GATE 2020 BM Q20 (1 mark, Multiple choice) – A state model is X=pmatrix0&2\&0pmatrixX+pmatrixb\\0pmatrixU, Y=(1\ 0)X. Which condition makes it controllable?
  3. GATE 2020 BM Q44 (2 marks, Multiple choice) – A non-unity-feedback system has G(s)=12/(s+2) and H(s)=2/(s+3). Find the magnitude of steady-state tracking error for a unit step.
  4. GATE 2021 BM Q18 (1 mark, Multiple choice) – For a linear stable second-order system, the unit-step peak time is twice its rise time. The system is .
  5. GATE 2021 BM Q33 (1 mark, Numerical answer) – For a type-2 unity-feedback system, the extrapolated initial −40 dB/decade Bode segment crosses 0 dB at 2 rad/s. Find acceleration error constant Kₐ.
  6. GATE 2021 BM Q46 (2 marks, Multiple choice) – The closed-loop characteristic equation is s⁴+2s³+8s²+8s+16=0. Find its steady-state oscillation frequency in rad/s.
  7. GATE 2021 BM Q56 (2 marks, Numerical answer) – A unity-feedback system has closed-loop transfer function C(s)/R(s)=(s+90)/(s2+10s+90). Find steady-state error to a unit ramp, to one decimal place.
  8. GATE 2023 BM Q54 (2 marks, Numerical answer) – A system initially at rest satisfies 0.01y(t)+0.2y(t)+y(t)=6x(t), with t in seconds. A unit step is applied at t=0. Find y(1) to two decimal places.
  9. GATE 2025 BM Q19 (1 mark, Multiple choice) – Classify the closed-loop unity-negative-feedback system with G(s)=25/[s(s+5)].
  10. GATE 2025 BM Q20 (1 mark, Multiple choice) – Which statement about the integral component of a PID controller for a second-order linear system is correct?
  11. GATE 2026 BM Q24 (1 mark, Multiple choice) – The unity-negative-feedback system shown has forward gain G=100 and input Vin=5 V. Find Vout−Vin in volts.