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The signal flow diagram for a certain feedback control system is shown in the figure. Now consider the following set of equations for the nodes 1. x2 = a1x1 + a9x3 2. x3 = a2x2 + a8x4 3. x4 = a3x3 + a5x2 4. x5 = a4x4 + a6x2 Which of the following is correct?

The signal flow diagram for a certain feedback control system is shown in the figure. Now consider the following set of equations for the nodes 1. x2 = a1x1 + a9x3 2. x3 = a2x2 + a8x4 3. x4 = a3x3 + a5x2 4. x5 = a4x4 + a6x2 Which of the following is correct? Correct Answer 1, 2 and 4

Concept:

Terminology:

Node: A node in SFG represents a variable in the system I.e. number of nodes is equal to no of variables.

Input node: The node that has only incoming branch

Output node: The node that has only outgoing branch

Forward path: The path that connects the input node with the output node such that no node is repeated.

Loop: A loop is a close path that starts and ends at the same node such that no node is repeated.

Analysis:

We just need to observe the incoming branch at the respective node.

From the above concept:

x2 = a1x1 + a9x3

x3 = a2x2 + a8x4

x4 = a3x3 + a7x4

x5 = a4x4 + a6x2

Only (3) is incorrect.

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