Electrical Engineering (EE) Exam  >  Electrical Engineering (EE) Notes  >  Control Systems  >  Signal Flow Graphs (with Examples)

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE) PDF Download

Introduction

Block diagram reduction is the excellent method for determining the transfer function of the control system. However, in a complicated system, it is very difficult and time-consuming process that is why an alternate method, i.e., SFG was developed by S.J Mason which relates the input and output system variables graphically. In the signal flow graph, the transfer function is referred to as transmittance.

Characteristics of SFG

SFG is a graphical representation of the relationship between the variables of a set of linear algebraic equations. It doesn't require any reduction technique or process.

  • It represents a network in which nodes are used for the representation of system variable which is connected by direct branches.
  • SFG is a diagram which represents a set of equations. It consists of nodes and branches such that each branch of SFG having an arrow which represents the flow of the signal.
  • It is only applicable to the linear system.

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

Question for Signal Flow Graphs (with Examples)
Try yourself:What is the Signal Flow Graph (SFG) in the context of control systems?
 
View Solution

Terms used in SFG

Node: It represents the system variable which equals to the sum of all signals. Outgoing signal from the node does not affect the value of node variables.

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

Branch: Branch is defined as a path from one node to another node, in the direction indicated by the branch arrow.

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

Node as a summing point:
x1 = Summing point
x1 =  x2+x3+x4

Node as a transmitting (outgoing) point:
x1 = x5+x6

Input node or source: It is the node which have only outgoing branches.
Output node or sink: It is a node which has only incoming branches.
Forward Path: It is a path from an input node to an output node in the direction of branch arrow.
Loop: It is a path that starts and ends at the same node.


Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

Non-touching loop: Loop is said to be non-touching if they do not have any common node.

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

Forward path gain: A product of all branches gain along the forward path is called Forward path gain.

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

Loop Gain: Loop gain is the product of branch gain which travels in the loop.
Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)


Construction of SFG and Mason Gain Formula

The SFG of a system is constructed by the following equations -

Example
Consider a system described by following sets of equations

x= a22x1 + a32x3 + a42x4 + a52x5

x3 = a23x2

x4 = a34x3 + a44x4

x5 = a35x3 + a45x4

Where x1 is input and x5 is output.

Step 1 - First step is to draw all the nodes.

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

Step 2 - Draw the SFG for equation (1)

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

Step 3 - Draw the SFG for equation (2)

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

Step 4 - Draw the SFG for equation (3)

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

Step 5 - Draw the SFG for equation (4)

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

Step 6 - Now draw the complete signal flow graph with the help of the above graph.

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

Question for Signal Flow Graphs (with Examples)
Try yourself:Which of the following steps correctly describes the construction of a Signal Flow Graph (SFG) for a system?
 
View Solution

The document Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Control Systems.
All you need of Electrical Engineering (EE) at this link: Electrical Engineering (EE)
53 videos|73 docs|40 tests

Top Courses for Electrical Engineering (EE)

53 videos|73 docs|40 tests
Download as PDF
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

MCQs

,

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

,

study material

,

Previous Year Questions with Solutions

,

Important questions

,

ppt

,

video lectures

,

pdf

,

Free

,

Sample Paper

,

Summary

,

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

,

Signal Flow Graphs (with Examples) | Control Systems - Electrical Engineering (EE)

,

shortcuts and tricks

,

Exam

,

mock tests for examination

,

Extra Questions

,

past year papers

,

Objective type Questions

,

Semester Notes

,

Viva Questions

,

practice quizzes

;