SIGNAL FLOW GRAPH THEORY - TRANSFER FUNCTION DETERMINATION IN CONTROL SYSTEM
A signal flow graph is a graphical representation of the relationship between the variables of a set of linear algebraic equations.
A signal flow graph is a diagram which represents a set of simultaneous equations.
It consists of line network in which various nodes are connected by means of directed lines called branches.
Signal flow graphs are particularly useful for feedback control systems because feedback theory is primarily concerned with the flow and processing of signals in systems.
Need for Signal flow graph:
Block diagrams are very successful for representing control systems, but for complicated systems, the block diagram reduction process is tedious and time consuming.
So signal flow graphs are needed which does not require any reduction process because of availability of a flow graph formula, which relates the input and output system variables.
Properties of Signal flow graph
A branch indicates the functional dependence of one signal upon another. A signal passes only in the direction specified by the arrow of the branch.
A node adds all signals of all incoming branches and transmit this sum to all outgoing branches. This is known as additive rule.
A mixed node which has both incoming and outgoing branches may be treated as an output node by adding an outgoing branch of unity gain.
For a system, a signal flow graph is not unique.
Rules for drawing signal flow graph
The signal always travels along the branch towards the direction of indicated arrow in the branch.
The output signal of the branch is the product of transmittance and input signal of the branch.
Input signal at a node is summation of all the signals entering at that node.
Signals propagate through all of the branches.
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