electrical4u.com logo Home MCQ Engineering Calculators Videos Basic Electrical Circuit Theories Electrical Laws Materials Batteries Illumination Generation Transmission Distribution Switchgear Protection Measurement Control System Utilities Safety Transformer Motor Generator Electrical Drives Electronics Devices Power Electronics Digital Electronics Biomedical Instrumentation

Signal Flow Graph of Control System

Published on 24/2/2012 & updated on 8/8/2018
Signal flow graph of control system is further simplification of block diagram of control system. Here, the blocks of transfer function, summing symbols and take off points are eliminated by branches and nodes.
The transfer function is referred as transmittance in signal flow graph. Let us take an example of equation y = Kx. This equation can be represented with block diagram as below signal-flow-diagram The same equation can be represented by signal flow graph, where x is input variable node, y is output variable node and a is the transmittance of the branch connecting directly these two nodes.

simple signal flow graph

Rules for Drawing Signal Flow Graph

  1. The signal always travels along the branch towards the direction of indicated arrow in the branch.
  2. The output signal of the branch is the product of transmittance and input signal of that branch.
  3. Input signal at a node is summation of all the signals entering at that node.
  4. Signals propagate through all the branches, leaving a node.
signal flow graph

Related pages
Signal Flow Graph of Control System

Simple Process of Calculating Expression of Transfer Function for Signal Flow Graph

signal flow graph

If P is the forward path transmittance between extreme input and output of a signal flow graph. L1, L2…………………. loop transmittance of first, second,.….. loop of the graph. Then for first signal flow graph of control system, the overall transmittance between extreme input and output is signal flow graph Then for second signal flow graph of control system, the overall transmittance between extreme input and output is signal flow graph Here in the figure above, there are two parallel forward paths. Hence, overall transmittance of that signal flow graph of control system will be simple arithmetic sum of forward transmittance of these two parallel paths.

As the each of the parallel paths having one loop associated with it, the forward transmittances of these parallel paths are Therefore overall transmittance of the signal flow graph is

Mason's Gain Formula

The overall transmittance or gain of signal flow graph of control system is given by Mason’s Gain Formula and as per the formula the overall transmittance is Where, Pk is the forward path transmittance of kth in path from a specified input is known to an output node. In arresting Pk no node should be encountered more than once. Δ is the graph determinant which involves closed loop transmittance and mutual interactions between non-touching loops.
Δ = 1 - (sum of all individual loop transmittances) + (sum of loop transmittance products of all possible pair of non-touching loops) - (sum of loop transmittance products of all possible triplets of non-touching loops) + (……) - (……) Δ k is the factor associated with the concerned path and involves all closed loop in the graph which are isolated from the forward path under consideration. The path factor Δk for the kth path is equal to the value of grab determinant of its signal flow graph which exist after erasing the Kth path from the graph. By using this formula one can easily determine the overall transfer function of control system by converting a block diagram of control system (if given in that form) to its equivalent signal flow graph. Let us illustrate the below given block diagram.




Please Rate this Article
4.33
⚑ 3 total
5
4
3
2
1


New Articles
More Articles on Control System
LaplaceFourier
Articles Categories
Home
Basic Electrical
Electric Transformer
Electric Generator
Electric Motor
Electrical MCQ
Engineering Calculators
Video Lectures
Electrical Generation
Electric Transmission
Switchgear
Electric Protection
Electrical Measurement
Electronics Devices
Power Electronics
Digital Electronics