STUDY MATERIAL · GATE EC · EE · IN
GATE Control Systems: questions and notes
Control Systems questions from 21 GATE papers (2018–2026) with the official answers, 119 of 120 solved step by step, plus notes for each topic, a formula sheet and practice questions.
- previous-year questions
- 120previous-year questions
- solved step by step
- 119solved step by step
- GATE papers, 2018–2026
- 21GATE papers, 2018–2026
- topics with notes
- 9topics with notes
TOPICS
Nine topics, in the order they are taught
Taken from the official GATE 2027 syllabus. Each topic has notes, the formulas you need, its previous-year questions with the official answers, most of them solved step by step, and practice questions.
Modelling, block diagrams and signal flow graphs
This topic covers how a physical system (a circuit, a mass-spring-damper, a motor, a sensor loop) becomes a transfer function, and how a network of such transfer functions is reduced to one closed-loop transfer function using block-diagram algebra or Mason's gain formula.
10 previous-year questions · 13 marks · 7 practice questions
Time response and steady-state error
Time response is how a control system's output moves after a standard test input is applied.
22 previous-year questions · 36 marks · 6 practice questions
Stability and the Routh–Hurwitz criterion
Stability tells you whether a closed-loop system's natural response dies out, keeps going or grows, and that depends only on where the roots of the characteristic equation lie.
15 previous-year questions · 24 marks · 6 practice questions
Root locus
The root locus shows where the closed-loop poles of a negative-feedback system move in the s-plane as the loop gain K goes from 0 to ∞.
7 previous-year questions · 11 marks · 6 practice questions
Frequency response: Bode and polar plots, gain and phase margins
Frequency response describes what a stable linear system does to a sinusoid at each frequency: it scales the sinusoid by |G(j ω)| and shifts it by ∠ G(j ω).
27 previous-year questions · 42 marks · 6 practice questions
The Nyquist stability criterion
The Nyquist stability criterion tells you whether a closed loop is stable using only the open-loop frequency response G(j ω)H(j ω).
11 previous-year questions · 14 marks · 5 practice questions
Compensators and PID controllers
Compensators (lead, lag and lead-lag) and PID controllers are blocks added in cascade with a plant when adjusting one gain cannot meet the steady-state and transient specifications together.
10 previous-year questions · 18 marks · 6 practice questions
State-space models
State-space models describe an LTI system by n first-order differential equations in a state vector, ẋ = Ax + Bu and y = Cx + Du, instead of by a single input-output transfer function.
16 previous-year questions · 30 marks · 6 practice questions
- GATE IN only
Actuators, time delay and industrial control
Real plants add dead time to their loops, and every controller output reaches the process through a valve or motor whose characteristic and transfer function shape the loop.
2 previous-year questions · 2 marks · 7 practice questions
QUESTIONS BY TOPIC AND YEAR
120 questions, by topic and year
How many questions each topic had in the EC, EE and IN papers of each year. This shows what was asked, not what will be asked. We placed each question under a topic ourselves; the exam paper does not label topics. Every question links back to its paper.
| Topic | 2018 | 2020 | 2022 | 2023 | 2024 | 2025 | 2026 | Total |
|---|---|---|---|---|---|---|---|---|
| Block diagrams & SFG | 1 | 2 | 2 | 2 | 1 | 1 | 1 | 10 |
| Time response | 4 | 4 | 4 | 1 | 5 | 2 | 2 | 22 |
| Routh–Hurwitz | 3 | 3 | 3 | 1 | 1 | 3 | 1 | 15 |
| Root locus | · | 2 | 1 | · | 2 | 2 | · | 7 |
| Bode & margins | 5 | 4 | 5 | 6 | 4 | 1 | 2 | 27 |
| Nyquist | 2 | 3 | 2 | 2 | · | 2 | · | 11 |
| Compensators & PID | · | 1 | · | 3 | 1 | 4 | 1 | 10 |
| State space | 3 | 2 | 1 | 2 | 2 | 2 | 4 | 16 |
| Process control (IN) | · | · | 1 | · | 1 | · | · | 2 |
GATE ECE question papers with solutions: 2026, 2025, 2024, 2023, 2022, 2020, 2018
GATE EE question papers with solutions: 2026, 2025, 2024, 2023, 2022, 2020, 2018
GATE IN question papers with solutions: 2026, 2025, 2024, 2023, 2022, 2020, 2018
The 2019 and 2021 papers are not included yet: the copies we host are image scans without the official key.
Control Systems formulas by topic
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THE OFFICIAL SYLLABUS
What each paper lists under Control Systems
From the GATE 2027 syllabus PDFs. IN lists more than EC and EE: actuators, process controllers, time-delay systems, DCS and PLC. That is why one topic here is marked IN only.
GATE EC
Basic control system components; Feedback principle; Transfer function; Block diagram representation; Signal flow graph; Transient and steady-state analysis of LTI systems; Frequency response; Routh-Hurwitz and Nyquist stability criteria; Bode and root-locus plots; compensators, PID controller; State variable model and solution of state equation of LTI systems.
GATE EE
Mathematical modelling and representation of systems, Feedback principle, transfer function, Block diagrams and Signal flow graphs, Transient and Steady‐state analysis of linear time invariant systems, Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci, Lag, Lead and Lead‐Lag compensators; P, PI and PID controllers; State space model, Solution of state equations of LTI systems.
GATE IN
Feedback principles, role of sensing in feedback, signal flow graphs, transient response, steady state error, Bode plot, phase and gain margins, Routh and Nyquist criteria, root loci, state-space representation of systems; time-delay systems. Actuators for control system: control valves, servo valves, servo motors, stepper motors; on-off, P, PI, PID, cascade, feed forward, and ratio controllers, tuning of PID controllers; design of lead, lag and lead-lag compensators; basic concept of supervisory control, basics of distributed control system (DCS) and programmable logic controller (PLC).
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