530_343lecture12

530_343lecture12 - ME 530.343: Design and Analysis of...

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Unformatted text preview: ME 530.343: Design and Analysis of Dynamic Systems Spring 2009 Lecture 12 - Transfer Functions and Block Diagrams Week of March 2, 2009 Todays Objectives Transfer Functions Transform Block Diagrams Simulink in MATLAB Transfer Functions example: X ( s ) = 1 ms 2 + bs + k F ( s ) let H ( s ) = 1 ms 2 + bs + k X ( s ) = H ( s ) F ( s ) H ( s ) is a transfer function Block Diagrams To represent X ( s ) = H ( s ) F ( s ), use: Say you have: Y ( s ) = X ( s ) + D ( s ) arrows: signals ( F ( s ), X ( s ), D ( s ), Y ( s )) blocks: transfer functions H ( s ) summing junction: add or subtract signals Multiple Transfer Functions X ( s ) F ( s ) = J ( s ), where J ( s ) = H ( s ) G ( s ) 1 Feedback system X ( s ) = G ( s ) E ( s ) E ( s ) = F ( s )- U ( s ) U ( s ) = H ( s ) X ( s ) What is the equivalent transfer function for the entire feedback loop? E ( s ) = F ( s )- H ( s ) X ( s ) X ( s ) = G ( s )[ F ( s )- H ( s ) X ( s )] X ( s ) = G ( s ) F ( s )- G ( s ) H ( s ) X ( s ) X ( s )[1 + G ( s ) H ( s )] = G ( s ) F ( s ) X ( s ) F ( s ) = J ( s ) = G ( s ) 1+ G ( s ) H ( s ) Example: Servo motor system L di dt + Ri + e b = e i (electrical circuit) e b = K v d dt (back emf)...
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530_343lecture12 - ME 530.343: Design and Analysis of...

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