KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec11

KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec11

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Unformatted text preview: 1 Chapter 4 Important Properties of Laplace Transforms 1. Final Value Theorem It can be used to find the steady-state value of a closed loop system (providing that a steady-state value exists. Statement of FVT: ( 29 ( 29 lim lim t s sY s y t . . = providing that the limit exists (is finite) for all where Re ( s ) denotes the real part of complex variable, s . ( 29 Re 0, s . 2. Initial Value Theorem 2 Chapter 4 Example: Suppose, ( 29 ( 29 5 2 (3-34) 5 4 s Y s s s + = + Then, ( 29 ( 29 5 2 lim 0.5 lim 5 4 t s s y y t s . . + @ = = = + 3. Time Delay Time delays occur due to fluid flow, time required to do an analysis (e.g., gas chromatograph). The delayed signal can be represented as ( 29 time delay y t- = Also, ( 29 ( 29 s y t e Y s-- = L 3 Chapter 4 Transfer Functions Convenient representation of a linear , dynamic model. A transfer function (TF) relates one input and one output: ( 29 ( 29 ( 29 ( 29 system x t y t X s Y s . The following terminology is used: x input forcing function cause y output response effect 4 Chapter 4 Definition of the transfer function:...
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KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec11

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