Solved Example
Convert the block diagram into signal flow graph and find the overall transfer function
The signal flow diagram of the given block diagram is
The forward paths are
[Tex]P_1=G_1G_3G_4 \:\:\:\:\:P_2=-G_1G_2 [/Tex]
The loop gains are
[Tex]L_1=G_3G_4(-1) \newline L_2=G_1G_3H_1(-1) \newline L_3=G_1G_3H_1(-1) \newline L_4=G_1(-G_2)(-1)G_3H_1(-1) \newline L_5=G_1(-G_2)(-1)G_3H_1(-1) [/Tex]
As we can see that all loops are touching path [Tex]P_1\:and \:P_2 [/Tex] . therefore the path factors will be unity.
[Tex]\Delta=1-(L_1+L_2+L_3+L_4+L_5) \newline= 1+G_3G_4+2G_1G_3H_1+2G_1G_2G_3H_1 [/Tex]
using mason’s gain formula we get,
[Tex]\frac{C}{R}=\frac{P_1\Delta_1+P_2\Delta_2}{\Delta}=\frac{G_1G_3G_4-G_1G_2}{1+G_3G_4+2G_1G_3H_1+2G_1G_2G_3H_1} [/Tex]
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