The GATE Grind

GATE Control Systems: Bode and Root-Locus Plots – Previous Year Questions

10 GATE previous year questions on Bode and Root-Locus Plots (Control Systems, Electronics and Communication Engineering) with answers and explanations, from every paper.

  1. GATE 2017 EC Q57 (2 marks, Multiple choice) – A linear time invariant (LTI) system with the transfer function G(s) = K(s2 + 2s + 2)(s2 - 3s + 2) is connected in unity feedback configuration as…
  2. GATE 2015 EC Q30 (1 mark, Numerical answer) – A unity negative feedback system has the open-loop transfer function G(s) = Ks(s + 1)(s + 3). The value of the gain K (> 0) at which the root locus…
  3. GATE 2015 EC Q56 (2 marks, Numerical answer) – The open-loop transfer function of a plant in a unity feedback configuration is given as G(s) = K(s + 4)(s + 8)(s2 - 9). The value of the gain K (> 0)…
  4. GATE 2016 EC Q55 (2 marks, Numerical answer) – The open-loop transfer function of a unity-feedback control system is G(s) = Ks2 + 5s + 5 The value of K at the breakaway point of the feedback…
  5. GATE 2019 EC Q52 (2 marks, Numerical answer) – Consider a unity feedback system, as in the figure shown, with an integral compensator Ks and open-loop transfer function G(s)=1s2+3s+2 where K>0. The…
  6. GATE 2020 EC Q50 (2 marks, Multiple choice) – The characteristic equation of a system is s3+3s2+(K+2)s+3K=0. In the root locus plot for the given system, as K varies from 0 to , the break-away or…
  7. GATE 2022 EC Q22 (1 mark, Multiple choice) – The root-locus plot of a closed-loop system with unity negative feedback and transfer function KG(s) in the forward path is shown in the figure. Note…
  8. GATE 2023 EC Q57 (2 marks, Numerical answer) – The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is G(s)=k(s+z)asb(s+p)c,…
  9. GATE 2024 EC Q12 (1 mark, Multiple choice) – In the context of Bode magnitude plots, 40 dB/decade is the same as .
  10. GATE 2025 EC Q26 (1 mark, Multiple choice) – Consider the unity-negative-feedback system shown in Figure (i) below, where gain K0. The root locus of this system is shown in Figure (ii) below. For…