xfer_inclass - The Transfer Function Unit 3 Modeling in the...

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The Transfer Function Unit 3: Modeling in the Frequency Domain Part 3: Transfer Functions Engineering 5821: Control Systems I Faculty of Engineering & Applied Science Memorial University of Newfoundland January 19, 2009 ENGI 5821 Unit 2, Part 3: Transfer Functions
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The Transfer Function 1 The Transfer Function Definition ENGI 5821 Unit 2, Part 3: Transfer Functions
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Definition Assume we have an LTI system described by a DE,
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Definition Assume we have an LTI system described by a DE, a n d n c ( t ) dt n + a n - 1 d n - 1 c ( t ) dt n - 1 + · · · + a 0 c ( t ) = b m d m r ( t ) dt m + b m - 1 d m - 1 r ( t ) dt m - 1 + · · · + b 0 r ( t )
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Definition Assume we have an LTI system described by a DE, a n d n c ( t ) dt n + a n - 1 d n - 1 c ( t ) dt n - 1 + · · · + a 0 c ( t ) = b m d m r ( t ) dt m + b m - 1 d m - 1 r ( t ) dt m - 1 + · · · + b 0 r ( t ) Take the LT of both sides with the assumption that all initial conditions are zero,
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Definition Assume we have an LTI system described by a DE, a n d n c ( t ) dt n + a n - 1 d n - 1 c ( t ) dt n - 1 + · · · + a 0 c ( t ) = b m d m r ( t ) dt m + b m - 1 d m - 1 r ( t ) dt m - 1 + · · · + b 0 r ( t ) Take the LT of both sides with the assumption that all initial conditions are zero, ( a n s n + a n - 1 s n - 1 + · · · + a 0 ) C ( s ) = ( b m s m + b m - 1 s m - 1 + · · · + b 0 ) R ( s )
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Definition Assume we have an LTI system described by a DE, a n d n c ( t ) dt n + a n - 1 d n - 1 c ( t ) dt n - 1 + · · · + a 0 c ( t ) = b m d m r ( t ) dt m + b m - 1 d m - 1 r ( t ) dt m - 1 + · · · + b 0 r ( t ) Take the LT of both sides with the assumption that all initial
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