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transfer_functions

# transfer_functions - Transfer Functions 1 2 3 4 5 Transfer...

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Transfer Functions 1. Transfer functions 2. Standard process inputs 3. First-order systems 4. Simulink example 5. Integrating systems

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Transfer Functions The transfer function » Represent relation between input U ( s ) & output Y ( s ) in the Laplace domain » Usually denoted as G ( s ) » Y ( s ) = G( s ) U ( s ) » Only applicable to linear models! Deviation variables » Defined as difference between variable and its steady-state value » Transfer functions always specified in terms of deviation variables » Y’ ( s ) = G ( s ) U ’( s ) » Usually often omit primes for notational simplicity G ( s ) Transfer function Input Output U ( s ) Y ( s ) )] ( ' [ ) ( ' ) ( ) ( ' )] ( ' [ ) ( ' ) ( ) ( ' t y L s Y y t y t y t u L s U u t u t u = - = = - =
Transfer Function Example Stirred tank heater Steady-state equation: Initial conditions: Subtract steady-state equation Q T T wC dt dT VC i p p + - = ) ( ρ Q T T wC i p + - = ) ( 0 Q Q T T T T i i = = = ) 0 ( ) 0 ( ) 0 ( [ ] ( 29 ( 29 model Deviation ' ' ' ) ( ) ( 0 ' + - = - + - - - = - Q T T wC dt dT VC Q Q T T T T wC dt dT VC i p p i i p p ρ ρ

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Transfer Function Example cont.
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