CS545_Lecture_4 - CS545Contents IV Frequency Domain...

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CS545—Contents IV Frequency Domain Representations Laplace Transform Most important Laplace Transforms Transfer functions Block-Diagram Algebra Examples Matlab/Simulink Introduction How to get started The most relevant blocks and settings of Simulink Reading Assignment for Next Class See http://www-clmc.usc.edu/~cs545
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The Laplace Transform Properties of Frequency Domain Representations A convenient method so solve (linear!) differential equations (even without a computer …) by converting them to algebraic equations Makes system analysis easy, even for very big systems Simple mathematics Only applicable for linear time invariant systems! The Core of Frequency Domain Analysis: The Laplace Transform L f t ( ) ( ) = f s ( ) = f t ( ) e st dt 0 where s = σ + j ω and j = 1 Robot ??
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L x t ( ) ( ) = x s ( ) L u t ( ) ( ) = u s ( ) L ˙ x t ( ) ( ) = sx s ( ) x 0 ( ) (commonly, x 0 ( ) = 0 , accomplished by coordinate transformations) L ˙ ˙ x t ( ) ( ) = s 2 x s ( ) (and analogues for higher derivatives) L x t ( ) dt ( ) = 1 s x s ( ) Most Important Laplace Transforms L ax t ( ) ( ) = aL x t ( ) ( ) where a is a constant
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Transfer Functions The Transfer Function describes the Input-Output Relationship of a
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CS545_Lecture_4 - CS545Contents IV Frequency Domain...

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