Modeling 1

# Modeling 1 - Modeling Chapter 2 Laplace Transform Review...

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Modeling Chapter 2

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aplace Transform Review Laplace Transform Review hy? Why? Many engineering systems are represented mathematically by differential equations. Differential equations are difficult to model as a block diagram. ut e refer stem presentation y lock iagram But we prefer system representation by block diagram where there are distinct inputs-outputs and separate parts. utput System G(s) Input output R ( s ) C ( s ) Laplace Transform 2
Laplace Transform Review Example of Modeling ( acceleromter within rocket-propelled sled, 6345 mph, - US Air Force ) bk yyy M x M M   (c) 2010 Farrokh Sharifi 3

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aplace Transform Review Laplace Transform Review hen? When? When coefficients of differential equations (model parameters) are LINEAR, TIME-INVARIANT (LTI). 11 10 () nn mm nm dct d ct drt d rt aa a c t b b b r t dt dt dt dt    Many systems are not LTI but can be simplified to LTI stems systems. In this course we will focus on LTI systems. utput Input output 4 (c) 2010 Farrokh Sharifi
aplace Transform Review Laplace Transform Review he aplace ransform efined The Laplace Transform is defined as: where , is called the Laplace transform f jw s   ) ( s F ) ( t f of . Question: what does the notation in the lower limit mean? e? The Inverse Laplace Transform which allows to find iven given is: where: ) ( t f ) ( s F 5 (c) 2010 Farrokh Sharifi

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Laplace Transform Review e n erive ble r We can derive a table for conventional functions: amp l e d l f f t Example : find the Laplace Transform of ) ( ) ( t u Ae t f at 6 (c) 2010 Farrokh Sharifi
Laplace Transform Review Laplace Transform Theorems: 1 0 1 (0 ) (0 ) 0 ) ff df  0 () t f dt   7

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aplace Transform Review Laplace Transform Review xample ind e verse aplace ansform f Example : Find the inverse Laplace transform of: ased n ble e verse f e aplace ansfer 2 1 ) 3 ( 1 ) ( s s F Based on table 2.1, the inverse of the Laplace transfer function is .
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## This note was uploaded on 02/20/2011 for the course MEC 709 taught by Professor Sharifi during the Fall '11 term at Ryerson.

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Modeling 1 - Modeling Chapter 2 Laplace Transform Review...

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