GATE EC 2017 Set 1 — Question 49
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumNyquist CriterionStability AnalysisControl Systems
Control Systems → Stability Analysis → Nyquist Criterion
Last updated
Question
The Nyquist plot of the transfer function does not encircle the point for but does encircle the point for . Then the closed loop system (having unity gain feedback) is
Correct answer
(B) stable for K = 10 and unstable for K = 100
Solution
The open-loop transfer function is given by .
For the system to be stable, we must have . Since , stability requires (no encirclements).
1.Determine Open-Loop Stability:
The open-loop poles are the roots of .2.Apply Nyquist Stability Criterion:
The number of closed-loop poles in the RHP is given by , where is the number of clockwise encirclements of the critical point by the Nyquist plot.For the system to be stable, we must have . Since , stability requires (no encirclements).
3.Analyze for given K values:
- For : The problem states the plot does not encircle . Thus, . . The system is stable.
- For : The problem states the plot encircles . Thus, . . The system is unstable.
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 EC 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 Stability Analysis
2026 Set 1 Q11Consider the differential equation , with…2026 Set 1 Q19A control system is shown in the Figure. Which option represents the correct transfer function of…2026 Set 1 Q40For the control system shown in the Figure, the transfer function of a plant,…2026 Set 1 Q41The state and output equations for a control system are:…2026 Set 1 Q59Consider the unity negative feedback control system shown in the Figure. The value of gain …