Modeling-2

Modeling-2 - Laplace Transform Review (Tutorial 1) Laplace...

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aplace Transform Review (Tutorial 1) 1. For the following transfer functions, find the equivalent Laplace Transform Review (Tutorial 1) differential equation: (problem 8.c) 2 () 2 Xs s 2. (skill assessment) Find inverse Laplace transform of 32 89 1 5 F s s ss  2 10 (2 ) (3 ) s 21 (c) 2010 Farrokh Sharifi
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aplace Transform Review (Tutorial 1) 1) Solution Laplace Transform Review (Tutorial 1) 2) Solution 22 (c) 2010 Farrokh Sharifi
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aplace Transform Review (Tutorial 1) 2) Solution cont. Laplace Transform Review (Tutorial 1) 23 (c) 2010 Farrokh Sharifi
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ransfer Function A function that algebraically relates a system’s output to its Transfer Function input Allows separation of the input, system, and output into three separateand distinct parts (unlike the DE) Allows us to algebraically combine mathematical r presentations f bsystems ield tal stem ep ese tat o s o subsyste s to yed a tota syste representation 24 (c) 2010 Farrokh Sharifi
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ransfer Function Starting with a general nth-order, linear, time-invariant differential Transfer Function equation representing the system: Taking the Laplace transform of both sides: Assume all initial conditions are zero (or add them if given): Form the ratio of output transform, C(s) , and input transform, R(s) : 25 (c) 2010 Farrokh Sharifi
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ransfer Function Separates the output, C(s) , the input, R(s) , and the system Transfer Function This ratio, G(s) , is called the transfer function G(s) is evaluated with zero initial conditions Input Output Transfer Function 26 (c) 2010 Farrokh Sharifi
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ransfer Function Example :find the transfer function represented by
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Modeling-2 - Laplace Transform Review (Tutorial 1) Laplace...

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