Automatic Control Laplace Transformation

# Automatic Control Laplace Transformation

## Automatic Control Laplace Transformation

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##### Presentation Transcript

1. Automatic ControlLaplace Transformation Dr. Aly Mousaad Aly Department of Mechanical Engineering Faculty of Engineering, Alexandria University

2. 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)

3. 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.

4. Unit step function

5. Exponential function

6. Frequency shift

7. Sine and cosine functions Exercise: show that and

8. Impulse function

9. Unit ramp (integration by parts) similarly

10. Differentiated function

11. Integrated function 2nd shifting theorem

12. Solution of differential equations using Laplace Transformation Transformed Equation Differential Equation Laplace Transformation Algebraic Manipulation Particular Integral Complementary function Transformed Solution Solution Inverse Laplace

13. Example Transformed Equation Transformed Solution