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

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Unformatted text preview: 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 The Transfer Function 1 The Transfer Function Definition ENGI 5821 Unit 2, Part 3: Transfer Functions Definition Assume we have an LTI system described by a DE, 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 c ( t ) = b m d m r ( t ) dt m + b m- 1 d m- 1 r ( t ) dt m- 1 + · · · + b r ( t ) 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 c ( t ) = b m d m r ( t ) dt m + b m- 1 d m- 1 r ( t ) dt m- 1 + · · · + b r ( t ) Take the LT of both sides with the assumption that all initial conditions are zero, 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 c ( t ) = b m d m r ( t ) dt m + b m- 1 d m- 1 r ( t ) dt m- 1 + · · · + b 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 ) C ( s ) = ( b m s m + b m- 1 s m- 1 + · · · + b ) R ( s ) 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 c ( t ) = b m d m r ( t ) dt m + b m- 1 d m- 1 r ( t ) dt m- 1 + · · · + b r ( t )...
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This note was uploaded on 09/07/2009 for the course ENGINEERIN 5821 taught by Professor Andrewvardy, during the Spring '09 term at Memorial University.

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

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