MatrixSolution - MATRIX SOLUTION An example of finding the...

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Tom Penick tomzap@eden.com www.teicontrols.com/notes 5/8/00 MATRIX SOLUTION An example of finding the transfer function of a system represented by a block diagram by forming a matrix of equations. This same system has also been solved using Mason's rule; see the file MasonsRule.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 Find an expression for the transfer function ( 29 ( 29 Cs Rs . Finding expressions for different part of the system: Find an expression for the system after each sum or difference and at the output. R s ( ) s ( ) G 1 G 4 s ( ) s ( ) G 2 s ( ) G 3 Σ C s ( ) x x 3 x C 1 2 s ( ) H 3 s ( ) H 1 s ( ) H 2 Expressions Terms isolated from input component 13 x R CH =- x C HR += 2 1 321 x x xGH 12 0 xx - -= 3 2 x x G CH 2 1 32 0 x Gx CH - 2 4 323 C x G xGG =+ 2 4 0 x G xG GC +
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Tom Penick tomzap@eden.com www.teicontrols.com/notes 5/8/00 Form a matrix equation from the rewritten expressions: 1 23 3 2 11 2 12 4 2 33 1 00 011 0 01 0 10 0 Cx x xR HC R G Hx H Gx G G     -- =
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MatrixSolution - MATRIX SOLUTION An example of finding the...

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