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GATE control systems: 5 practice questions with solutions

By the PrepMatic team · Updated 9 Oct 2026 · 4 min read

Control Systems is a section in both the GATE EE and EC papers, and it is one of the most formula-friendly topics: a few standard second-order results, a stability test, error constants and frequency-response margins cover most questions. The five original questions below take one problem from each area and show the shortest route to the answer.

What GATE tests in control systems

Control Systems is a listed section in the 2027 EE and EC syllabi, and the lists were revised, so confirm yours on the official syllabus page. The standard content is modelling with block diagrams and signal-flow graphs, time response of first and second-order systems, steady-state error, stability (Routh-Hurwitz, root locus, Nyquist and Bode), compensators and state-space models.

Typical questions give a transfer function and ask for a damping ratio, peak overshoot, an error constant, the range of gain for stability, a breakaway point, or a margin. The real paper has MCQ, MSQ and NAT questions. All five below are MCQ.

Practice questions

Question 1

A unity-feedback system has the open-loop transfer function G(s) = 10 / [s(s + 2)]. The damping ratio of the closed-loop system is:

• A. 0.316
• B. 0.5
• C. 0.707
• D. 1.0

Question 2

The characteristic equation of a system is s³ + 6s² + 11s + K = 0. The largest value of K for which the system remains stable is:

• A. 72
• B. 66
• C. 60
• D. 36

Question 3

A unity-feedback system has G(s) = 20 / [s(s + 4)(s + 5)]. For the ramp input r(t) = 2t, the steady-state error is:

• A. 0.5
• B. 1
• C. 2
• D. infinite

Question 4

For a unity-feedback system with G(s) = K / [s(s + 2)(s + 4)] and K > 0, the breakaway point of the root locus on the real axis is approximately at s equal to:

• A. −3.15
• B. −2.00
• C. −1.00
• D. −0.85

Question 5

A unity-feedback system has the open-loop transfer function G(s) = 1 / (s + 1)³. The gain margin is closest to:

• A. 18 dB
• B. 12 dB
• C. 6 dB
• D. 3 dB

Answers and explanations

1. A. The closed-loop characteristic equation is s² + 2s + 10 = 0. Comparing with s² + 2ζωn s + ωn² = 0 gives ωn² = 10, so ωn = 3.162 rad/s, and 2ζωn = 2, so ζ = 2 / (2 × 3.162) = 0.316. The system is underdamped with a peak overshoot of about 35%.
2. B. Build the Routh array. The s³ row is 1 and 11, the s² row is 6 and K, and the s¹ entry is (6 × 11 − 1 × K) / 6 = (66 − K) / 6. For no sign change we need 66 − K > 0 and K > 0, so 0 < K < 66. At K = 66 the system is marginally stable, so 66 is the limit.
3. C. This is a type 1 system. The velocity error constant is Kv = lim s G(s) as s → 0 = 20 / (4 × 5) = 1. For a ramp of slope 2, the steady-state error is 2 / Kv = 2. First confirm that the closed loop is stable (s³ + 9s² + 20s + 20 has all positive Routh entries), because the error formula is only valid for a stable system.
4. D. The breakaway points satisfy d/ds [s(s + 2)(s + 4)] = 0, which is 3s² + 12s + 8 = 0. The roots are s = −2 ± 1.155, that is −0.845 and −3.155. The real-axis locus lies between 0 and −2 and to the left of −4, so only −0.845 is on the locus. Option A is the other root of the quadratic and is not on the locus.
5. A. The phase of G(jω) is −3 tan⁻¹ ω, which equals −180° when tan⁻¹ ω = 60°, so ω = √3 rad/s. There |G| = 1 / (1 + 3)^(3/2) = 1/8. The gain margin is 1 / (1/8) = 8, and 20 log 8 ≈ 18 dB. The loop gain can be raised by a factor of 8 before the system goes unstable.

How to prepare control systems

• Memorise the second-order formulas: ωn, ζ, damped frequency, peak overshoot exp(−πζ / √(1 − ζ²)), peak time, settling time of about 4 / (ζωn), and rise time estimates.
• Make the Routh array a habit, including special cases (a zero in the first column and a full row of zeros), and use it to find the range of K.
• Learn the error constants by system type: Kp, Kv and Ka, with the error for step, ramp and parabolic inputs. Always check stability first.
• Draw the root locus by rule, with the number of branches, asymptote angles and centroid, breakaway points, and the imaginary-axis crossing from Routh. Know the effect of adding poles and zeros.
• Practise Bode plots from the transfer function, with corner frequencies and slopes, and read gain and phase margins. Link Nyquist encirclements to stability.
• For state-space models, convert between a transfer function and the A, B, C, D matrices, and understand controllability and observability.

This section uses the Laplace transform from signals and systems and applies to the drives in electrical machines and the stability ideas in power systems. The GATE electrical preparation guide and GATE ECE preparation guide show where control fits in each plan.

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