Signal Flow Graphs

Signal-flow graphs serve as an alternative to block diagrams to represent control systems. They consist of branches, symbolizing systems, and nodes, symbolizing signals.

The direction of the signal flow is indicated by an arrow, with the transfer function written adjacent to it.

Each signal in a signal-flow graph sums the signals flowing into it, which differs from block diagrams where the negative sign is associated with a summing junction.

To convert block diagrams to signal-flow graphs, first, the signal nodes are drawn for the system.

Following this, the nodes are interconnected with branches representing the system.

Consider a block diagram with multiple feedback loops. The process begins with creating signal nodes, which are interconnected to illustrate the direction of signal flow, each identified by its specific transfer function.

In the resulting signal-flow graph, negative signs at summing junctions in the block diagram translate to negative transfer functions.

The final step simplifies the graph by eliminating signals with a single flow in and out, creating a more streamlined representation.