## 4

## Modelling a Control System—Signal Flow Graph

##### 4.1 INTRODUCTION

Block diagrams are very convenient in representing control systems. However, for complicated systems, the block diagram reduction approach for arriving at the transfer function relating the input and output variables is tedious and time consuming. An alternative approach is that of the signal flow graph (SFG) developed by S. J. Mason. A signal flow graph does not require any reduction process because of the availability of a flow graph gain formula which relates the input and output system variables.

**Definition:** A signal flow graph is a graphical representation of the relationship between the variables of a set of linear algebraic equations. It consists of a network in which nodes ...