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GATE 2025 EC – Question 56

Control Systems · Transfer Function, Block Diagram and Signal Flow Graph · 2 marks · Multiple select

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).

Diagram for GATE 2025 EC question 56
  1. Signal flow graph (A)
  2. Signal flow graph (B)
  3. Signal flow graph (C)
  4. Signal flow graph (D)

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Show answer and explanation

Correct answer: (B) Signal flow graph (B)

Explanation

Let $e=R-y_1$ be the first summer output. Then $y_1=G_1e$ (the signal after $G_1$, which is also fed back), and the output summer gives $Y=y_1+G_2e$. As a signal flow graph: $R\to e$ (gain 1), $e\to y_1$ (gain $G_1$), $y_1\to e$ (gain $-1$), $e\to Y$-node (gain $G_2$), $y_1\to Y$-node (gain 1), $Y$-node $\to Y$ (gain 1). This is graph (B): the $-1$ feedback comes from the node after $G_1$ and $G_2$ bypasses it. In (A) and (C) the feedback comes from the summed output; in (D) it comes from after the summing node.