laplace_inclass - The Laplace Transform Unit 2: Modeling in...

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Unformatted text preview: The Laplace Transform Unit 2: Modeling in the Frequency Domain Part 2: The Laplace Transform Engineering 5821: Control Systems I Faculty of Engineering & Applied Science Memorial University of Newfoundland January 22, 2009 ENGI 5821 Unit 2, Part 2: The Laplace Transform The Laplace Transform 1 The Laplace Transform The need for Laplace The Laplace Transform The Inverse Laplace Transform The Laplace Transform Pair Table Laplace Transform Theorems (Part 1) Laplace Transform Theorems (Part 2) Partial-Fraction Expansion ENGI 5821 Unit 2, Part 2: The Laplace Transform The Laplace Transform The need for Laplace The Laplace Transform The Inverse Laplace Transform The Laplace Transform Pair Table Laplace Transform Theorems (Part 1) Laplace Transform Theorems (Part 2) Partial-Fraction Expansion The need for Laplace In the previous section we saw that the responses to a series RL circuit (which could be any other linear system) was composed of constants, decaying exponentials, and sinusoids. ENGI 5821 Unit 2, Part 2: The Laplace Transform The Laplace Transform The need for Laplace The Laplace Transform The Inverse Laplace Transform The Laplace Transform Pair Table Laplace Transform Theorems (Part 1) Laplace Transform Theorems (Part 2) Partial-Fraction Expansion The need for Laplace In the previous section we saw that the responses to a series RL circuit (which could be any other linear system) was composed of constants, decaying exponentials, and sinusoids. The complex frequency representation can handle all of these by utilizing the following representation with different values for s : ENGI 5821 Unit 2, Part 2: The Laplace Transform The Laplace Transform The need for Laplace The Laplace Transform The Inverse Laplace Transform The Laplace Transform Pair Table Laplace Transform Theorems (Part 1) Laplace Transform Theorems (Part 2) Partial-Fraction Expansion The need for Laplace In the previous section we saw that the responses to a series RL circuit (which could be any other linear system) was composed of constants, decaying exponentials, and sinusoids. The complex frequency representation can handle all of these by utilizing the following representation with different values for s : x ( t ) = <{ Xe st } ENGI 5821 Unit 2, Part 2: The Laplace Transform The Laplace Transform The need for Laplace The Laplace Transform The Inverse Laplace Transform The Laplace Transform Pair Table Laplace Transform Theorems (Part 1) Laplace Transform Theorems (Part 2) Partial-Fraction Expansion The need for Laplace In the previous section we saw that the responses to a series RL circuit (which could be any other linear system) was composed of constants, decaying exponentials, and sinusoids. The complex frequency representation can handle all of these by utilizing the following representation with different values for s : x ( t ) = <{ Xe st } However, if the input is not of this form it is more difficult to solve for the systems response....
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laplace_inclass - The Laplace Transform Unit 2: Modeling in...

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