transfer_functions2

transfer_functions2 - Transfer Functions Part 2 1....

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Unformatted text preview: Transfer Functions Part 2 1. Second-order systems 2. Poles and zeros 3. Time delays 4. Simulink example Second-Order Systems General transfer function Overdamped system: > 1 Critically damped system: = 1 Underdamped system: 0 < < 1 t coefficien damping constant time gain state steady 1 2 ) ( ) ( ) ( 2 2 = = = + + = = K s s K s G s U s Y ) 1 )( 1 ( ) ( 2 1 + + = s s K s G 2 ) 1 ( ) ( + = s K s G 1 2 ) ( 2 2 + + = s s K s G Second-Order Example Electrically heated stirred tank Deviation model Laplace transform ) ( ) ( ) ( T T A h Q dt dT C m T T A h T T wC dt dT mC e e e e pe e e e e i p p-- =- +- = ) ' ( ' ) ' ( ) ' ( ' ' ' ' ' T T A h Q dt dT C m T T A h T T wC dt dT mC e e e e pe e e e e i p p-- =- +- = [ ] [ ] [ ] ) ( ' ) ( ) ( ' ) ( ) ( ' ) ( ) ( ' ) ( ) ( ' ' ' ' ' s T s T A h s Q s sT C m s T s T A h s T s T wC s sT mC e e e e pe e e e e i p p-- =- +- = Second-Order Example cont. Rearrange second equation Substitute into first equation & rearrange Transfer function ) ( ' ) ( ) ( ) ( ) ( ' 1 ) ( 1 1 ) ( ' 2 ' 1 1 2 2 ' 1 2 2 s Q s G s T s G s Q s a s a K s T s a s a bs s T i i + = + + + + + + = + + = ) ( ' ) ( ' 1 1 1 ) ( ' s T s Q A h s A h C m s T e...
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This document was uploaded on 02/04/2012.

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transfer_functions2 - Transfer Functions Part 2 1....

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