Laboratory Exercise No. 4 Laplace and Inverse LaplaceTransformation Using Matlab 1 DOC

Title	Laboratory Exercise No. 4 Laplace and Inverse LaplaceTransformation Using Matlab 1
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Laboratory Exercise No. 4 Laplace and Inverse LaplaceTransformation Using Matlab 1. Objective: The activity aims to introduce some Matlab commands that are useful when treating Laplace transforms.. 2. Intended Learning Outcomes (ILOs): The students shall be able to: 2.1 Understand laplace and inverse laplace transformation using Matlab. 2.2 Gain familiarity with laplace transforms. 3. Discussion: Once a dynamic model has been developed, it can be solved for a variety of conditions that include changes in the input variables or variations in the model parameters. The transient responses of the output responses of the output variables are calculated by numerical integration after specifying both the initial conditions and the inputs as functions of time. Laplace transform is a mathematical tool which can significantly reduce the effort required to solve and analyze linear differential equations. A major benefit is that this transformation converts ordinary differential equations to algebraic equations, which can simplify the mathematical manipulations required to obtain a solution or perform an analysis. Laplace transform is used for solving differential and integral equations. 4. Procedure: 1. To obtain the laplace of f(t) = e2t + t – t2 using the command window, type the commands >> syms t >> exp(2*t) + t + t^2 >> F = laplace(f) Show your output in Part 6 of this laboratory exercise. 2. To obtain the inverse laplace of F(s) = 2s / s2 + 1 using the command window, type the commands >>syms s >>F = 2*s / (s^ 2 + 1) >> f = ilaplace(F) Show your output in Part 6 of this laboratory exercise. 3. Obtain the inverse laplace of G(s) = 2 / s2 + 3s + 1. Show your matlab code and output in Part 6 of this laboratory exercise. 4. To obtain the laplace transform of cosh(3t) + e-t sin(5t) using the command window, type the commands >> syms t >> laplace(cosh(3*t) + exp(-t)*sin(5*t) Show your output in Part 6 of this laboratory exercise. 5. Check the result in Procedure by finding the inverse function with the following codes >>syms s >>ilaplace(ans) Show your output in Part 6 of this laboratory exercise. 6. Obtain the inverse laplace transform of r(s) = s + 2 / s3 + 10s2 + 29s + 20. Show your matlab code and output in Part 6 of this laboratory exercise. 7. To make the expression more readable one can use the commands simplify and pretty. To obtain 1...