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## Automatic Control Laplace Transformation

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**Automatic ControlLaplace Transformation**Dr. Aly Mousaad Aly Department of Mechanical Engineering Faculty of Engineering, Alexandria University**Laplace Transformation**The Laplace transform of a function f(t), defined for all real numbers t ≥ 0, is the function F(s), defined by: L F(s)**Why s-domain?**• We can transform an ordinary differential equation into an algebraic equation which is easy to solve. • It is also easy to analyze and design interconnected (series, feedback etc.) systems.**Sine and cosine functions**Exercise: show that and**Unit ramp**(integration by parts) similarly**Integrated function**2nd shifting theorem**Solution of differential equations using Laplace**Transformation Transformed Equation Differential Equation Laplace Transformation Algebraic Manipulation Particular Integral Complementary function Transformed Solution Solution Inverse Laplace**Example**Transformed Equation Transformed Solution