Signal Flow Graph (SFG) is a graphical representation of the relationships among variables in a control system, where system variables are represented by nodes and the mathematical relationships between them are represented by directed branches with associated gains. The direction of each branch indicates the flow of a signal from one node to another, while a branch gain specifies how the signal is modified. Signal flow graphs provide a convenient way to analyze complex control systems containing feedback loops, forward paths, and interconnected subsystems. The overall transfer function of an SFG can be determined using Mason’s Gain Formula, making it an important tool for analyzing and simplifying linear control systems.
Signal Flow Graph Simulation
Change G₁, G₂ and H to observe how the forward path, feedback loop and overall transfer function change.
T = Σ(PₖΔₖ) / Δ
Forward path: P₁ = G₁G₂
Loop gain: L₁ = −G₁G₂H
Determinant: Δ = 1 − L₁
Therefore: Y/R = G₁G₂ / (1 + G₁G₂H)