transfer_functions

transfer_functions - Transfer Functions 1. Transfer...

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Unformatted text preview: Transfer Functions 1. Transfer functions 2. Standard process inputs 3. First-order systems 4. Simulink example 5. Integrating systems 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 +- = ) ( Q Q T T T T i i = = = ) ( ) ( ) ( [ ] ( 29...
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This document was uploaded on 02/04/2012.

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transfer_functions - Transfer Functions 1. Transfer...

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