GATE EC 2025 Set 1 — Question 56
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MSQ+2 / -0MediumBlock Diagram ReductionSystem ModellingControl SystemsSignal Flow & Mason's Gain
Control Systems → System Modelling → Block Diagram Reduction
Last updated
Question
Consider a system represented by the block diagram shown below. Which of the following signal flow graphs represent(s) this system? Choose the correct option(s).
Correct answer
(B) [figure]
Solution
To identify the correct signal flow graph (SFG), we first analyze the given block diagram to determine the system's transfer function.
1.Analyze the Block Diagram:
- The input is .
- The first summing point produces an error signal , where is the feedback signal.
- The signal splits into two parallel paths: one through and another through .
- The feedback signal is taken from the output of before it is summed with the output of . Thus, .
- The output is the sum of the outputs of the two parallel paths: .
- From and , we have:
- Substituting into the expression for :
3.Evaluate the SFGs:
- Option (B): There are two forward paths from to : and . There is one feedback loop starting from the node after and returning to the node before it. Using Mason's Gain Formula:
- Options (A) and (D): These represent feedback taken from the output or the final summing point, which would result in .
- Option (C): This represents positive feedback, resulting in .
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 System Modelling
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 …