SFG Algebra

In Signal Flow Graph algebra, the value of a variable a node represents equals the sum of all the signals entering the node. This value is then transmitted through all branches leaving that node.

Parallel branches in the same direction can be replaced with a single branch with a gain equal to the sum of the gains of the original branches.

Similarly, a cascaded connection of unidirectional branches can be replaced with a single branch with a gain equal to the product of the original branch gains.

Feedback systems in signal flow graphs or SFGs follow specific algebraic equations that can be used to derive the closed-loop transfer function.

A block diagram of a control system can be converted into an SFG format. This involves identifying variables, associating each variable to a node, interconnecting nodes with branches, and labeling each branch with the appropriate gain.

Lastly, SFGs can also be constructed from a set of algebraic equations. This process involves step-by-step construction, creating nodes for each variable, and interconnecting them based on the equations.