Slides_LT_35_to_49

Slides_LT_35_to_49 - Solving Differential Equations using...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 15

Slides_LT_35_to_49 - Solving Differential Equations using...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online