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KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-lec7

KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-lec7

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1 Chapter 3 Laplace Transforms 1. Standard notation in dynamics and control (shorthand notation) 2. Converts mathematics to algebraic operations 3. Advantageous for block diagram analysis
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2 Chapter 3 Laplace Transforms Important analytical method for solving linear ordinary differential equations. - Application to nonlinear ODEs? Must linearize first. Laplace transforms play a key role in important process control concepts and techniques. - Examples: Transfer functions Frequency response Control system design Stability analysis
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3 Chapter 3 [ ] ( 29 0 ( ) ( ) (3-1) st F s f t f t e dt i - = = L Definition The Laplace transform of a function, f ( t ), is defined as where F ( s ) is the symbol for the Laplace transform, L is the Laplace transform operator, and f ( t ) is some function of time, t . Note : The L operator transforms a time domain function f ( t ) into an s domain function, F ( s ). s is a complex variable : s = a + bj , 1 j - B
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4 Chapter 3 Inverse Laplace Transform, L By definition, the inverse Laplace transform operator, L -1 , converts an s
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