Question

Signal flow graph is used to find:

• A. Poles of the system
• B. Transfer function of the system
• C. Stability of the system
• D. Controllability of the system

Hint:

Signal Flow Graph + Mason’s Formula = Direct way to compute transfer function.

Answer 1

The Correct Option is B

Concept: A Signal Flow Graph (SFG) is a graphical representation of a system of linear equations. It is widely used in control systems to determine the relationship between input and output using Mason’s Gain Formula.

Step 1: Understanding Signal Flow Graph A signal flow graph consists of:
• Nodes representing system variables
• Directed branches representing functional relationships

Step 2: Mason’s Gain Formula The transfer function is obtained as: \[ T = \frac{\text{Output}}{\text{Input}} = \frac{\sum P_k \Delta_k}{\Delta} \] Where:
• $P_k$ = Forward path gain
• $\Delta$ = Determinant of graph
• $\Delta_k$ = Cofactor of $k$th path

Step 3: Analyze options
• Poles → obtained from transfer function, not directly SFG
• Transfer function → directly obtained using Mason’s formula
• Stability → derived from poles
• Controllability → state-space concept \[ \therefore \text{Correct answer is (B)} \]