Construction of Signal Flow Graph from Linear Equation
Let us consider a system which is described by a set of linear equations
[Tex]x_2=a_{12}x_1+a_{12}x_3+a_{12}x_4 \newline x_3=a_{23}x_2 \newline x_4=a_{24}x_2+a_{32}x_3+a_{44}x_4 \newline x_5=a_{25}x_2+a_{45}x_4 [/Tex]
Where the input node is x1 and output node is x5
Now constructing the SFG
Step 1: First placing the nodes
Step 2: Graph from 1st Equation
Step 3: Graph from 1st and 2nd equation
Step 4: Graph from 1st, 2nd and 3rd equation
Step 5: Combing all the four equations we get the final signal flow graph
Conversion of Block Diagrams into Signal Flow Graphs
In this article, we will discuss the method of converting the block diagram into a signal flow graph in a control system. We will first discuss about signal flow graph and its terminologies. We also discuss the construction of signal flow graphs from linear equations. We will then discuss about block diagram and its components. We will then discuss the steps for conversion and then see an example. We will discuss the Mason gain formula and its example. Later in the article, we will discuss the advantages, disadvantages, and applications of this method.
Table of Content
- What is a signal flow graph?
- Construction of Signal Flow Graph from linear equation
- What is Block Diagram?
- Steps to draw signal flow graph from block diagram
- Mason’s Gain Formula
- Solved Example
- Application