Slides_LT_35_to_49

# Slides_LT_35_to_49 - Solving Differential Equations using...

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Solving Differential Equations using Laplace and Inverse Laplace Transforms Introduction to the methodology Response of a system to particular inputs – unit impulse input – unit step input – unit ramp input Analyse system in the Laplace domain – without initial condition – with initial condition VFR Dept. of Cybernetics LT. 35

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Introduction to the methodology Systems described by differential equations are solved/analysed in the s -domain through their Laplace transform representation. A general methodology is: From the differential equation given in the time domain. Use the LT to find its (i.e. diff eq) equivalent representation in the s -domain. Generally, this transformation yields the transfer function of the relative system. Solve/analyse the algebraic expressions in the Laplace domain. Transfer back the result into the time domain. The principle remains the same whenever we solve first order or second order differential equations respectively related to first order systems and second order systems. VFR Dept. of Cybernetics LT. 36
VFR LT. 37 Dept. of Cybernetics Example – suppose a system is described by the differential equation where y denotes the output and u the input: (1) – and assume the initial conditions are zero: u y y 2 4 = + ) 0 ( ) 0 ( ) 0 ( ) 0 ( = = = = u u y y & 0

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## This note was uploaded on 11/07/2009 for the course FOFL 4531 taught by Professor Haiza during the Spring '09 term at Carlos Albizu.

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Slides_LT_35_to_49 - Solving Differential Equations using...

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