GATE EE 2025 Set 1 — Question 65
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0MediumGain & Phase MarginStability AnalysisControl SystemsP, PI & PID ControllersCompensators & Controllers
Control Systems → Compensators & Controllers → Gain & Phase Margin
Last updated
Question
A controller of the form is to be designed for the plant as shown in the figure. The value of that yields a phase margin of at the gain cross-over frequency of is ________________ (round off to one decimal place).
Correct answer
0.1 to 0.1
Solution
The open-loop transfer function is .The phase of the open-loop system is:
At the gain cross-over frequency :
The phase margin () is defined as:
Given :
.Verification of gain condition :
.
The condition is satisfied.
At the gain cross-over frequency :
The phase margin () is defined as:
Given :
.Verification of gain condition :
.
The condition is satisfied.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE EE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Compensators & Controllers
2026 Set 1 Q13The Laplace transform of the step response of a system is given by…2026 Set 1 Q29The asymptotic Bode magnitude plot of a system is shown. [figure] Which one of the following…2026 Set 1 Q52A system is characterized by the following state equation and output equation (: input,…2026 Set 1 Q53A system is represented in state-space form as follows: (: input, : state vector,…2025 Set 1 Q22Selected data points of the step response of a stable first-order linear time-invariant (LTI)…