Modern Control System Theory and Design, 2nd Edition

2.15  REDUCTION OF THE SIGNAL-FLOW GRAPH

Several preliminary simplifications can be made to the complex signal-flow graphs of a system by means of the following signal-flow graph algebra.

(a)  Addition

1. The signal-flow graph in Figure 2.13a represents the linear equation

2. The signal-flow graph in Figure 2.13b represents the linear equation

Figure 2.13   Signal-flow graph algebra.

(b)  Multiplication. The signal-flow graph in Figure 2.13c represents the linear equation

(c)  Feedback loops

1. The signal-flow graph in Figure 2.13d represents the linear equation

2. The signal-flow graph in Figure 2.13e represents the linear equation

It is possible to apply the preceding signal-flow graph algebra to a complicated graph and reduce it to one containing only a source and a sink. This process requires repeated applications until the final desired form is obtainable. An interesting property ...