MasonsRule

# MasonsRule - MASON'S GAIN RULE An example of finding the...

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Tom Penick www.teicontrols.com/notes 5/8/00 MASON'S GAIN RULE An example of finding the transfer function of a system represented by a block diagram using Mason's rule. This problem has also been worked using a matrix solution; see the file MatrixSolution.pdf. The Problem: Given the system: G R s ( ) C s ( ) 1 s ( ) H 3 s ( ) s ( ) H 1 G G 2 s ( ) s ( ) 2 H s ( ) G 3 Σ s ( ) 4 Mason's Gain Rule: jj j M M = M = transfer function or gain of the system M j = gain of one forward path j = an integer representing the forward paths in the system j = 1 – the loops remaining after removing path j . If none remain, then j = 1. = 1 - Σ loop gains + Σ nontouching loop gains taken two at a time - Σ nontouching loop gains taken three at a time + Σ nontouching loop gains taken four at a time - ··· 1) Find the forward paths and their gains: A forward path is a path from R ( s ) to C ( s ) that does not cross the same point more than once. There are two forward paths in this example, so we have a j = 1 and a j = 2. The two paths are: 1 123 M GGG = and 24 MG =

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MasonsRule - MASON'S GAIN RULE An example of finding the...

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