Page 1 Control Systems Part 3: Laplace Transforms Page 2 Control Systems Part 3: Laplace Transforms Learning objectives ? To state the definition of Laplace transform ? To be able to use Laplace transform table to solve differential equations ? To examine different performance measures in time domain ? To represent system in terms of transfer functions using Laplace transforms. Page 3 Control Systems Part 3: Laplace Transforms Learning objectives ? To state the definition of Laplace transform ? To be able to use Laplace transform table to solve differential equations ? To examine different performance measures in time domain ? To represent system in terms of transfer functions using Laplace transforms. Differential equation and operator representations The linear form of this model is: Introducing a differential operator ?? ? ?: Then Page 4 Control Systems Part 3: Laplace Transforms Learning objectives ? To state the definition of Laplace transform ? To be able to use Laplace transform table to solve differential equations ? To examine different performance measures in time domain ? To represent system in terms of transfer functions using Laplace transforms. Differential equation and operator representations The linear form of this model is: Introducing a differential operator ?? ? ?: Then Definition of Laplace transform Consider a continuous time variable y(t); 0 ? t < ?. The Laplace transform pair associated with y(t) is defined as Page 5 Control Systems Part 3: Laplace Transforms Learning objectives ? To state the definition of Laplace transform ? To be able to use Laplace transform table to solve differential equations ? To examine different performance measures in time domain ? To represent system in terms of transfer functions using Laplace transforms. Differential equation and operator representations The linear form of this model is: Introducing a differential operator ?? ? ?: Then Definition of Laplace transform Consider a continuous time variable y(t); 0 ? t < ?. The Laplace transform pair associated with y(t) is defined as Laplace transform of a derivative term The Laplace transform of the derivative of a function: where y(0 - ) is the initial condition associated with y(t).Read More

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