laplace_transform

laplace_transform - Transfer Functions 1. The Laplace...

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Unformatted text preview: Transfer Functions 1. The Laplace transform 2. Solution of linear differential equations 3. Transient response example 4. Simulink example The Laplace Transform Definition Time ( t ) is replaced by a new independent variable ( s ) We call s the Laplace transform variable The Laplace domain Often more convenient to work in Laplace domain than time domain Time domain ordinary differential equations in t Laplace domain algebraic equations in s General solution approach Formulate model in time domain Convert model to Laplace domain Solve problem in Laplace domain Invert solution back to time domain - = = ) ( )] ( [ ) ( dt e t f t f L s F st Laplace Transform of Selected Functions Constant function: f ( t ) = a Exponential function: f ( t ) = e- bt Derivatives and integrals s a s a e s a dt ae a L s F st st = -- =- = = = -- ) ( ) ( [ ] +- +- --- + = +- = = = = ) ( ) ( 1 1 ) ( ) ( b s e s b dt e dt e e e L s F t s b t s b st bt bt ) ( 1 * *) ( * *) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (...
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laplace_transform - Transfer Functions 1. The Laplace...

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