Laplace Transform in Linear Control Systems, Slides of Linear Control Systems

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Linear Control System (EE-322)

Lecture 02

Dr S M Wasif [email protected]

Department of Electrical Engineering Hafiz Hayat Campus, University of Gujrat

May 12, 2022

Outline

(^1) Laplace Transform Laplace Transform Laplace Transform using MATLAB Theorems of the Laplace Transform Partial-Fraction Expansion Differential Equation Solution using Laplace Transform

Laplace Transform

Example: Find the Laplace transform of

f (t) = Ae−at^ u(t)

Example: Find the inverse Laplace transform of

F (s) = (^) (s+3)^12

Outline

(^1) Laplace Transform Laplace Transform Laplace Transform using MATLAB Theorems of the Laplace Transform Partial-Fraction Expansion Differential Equation Solution using Laplace Transform

Outline

(^1) Laplace Transform Laplace Transform Laplace Transform using MATLAB Theorems of the Laplace Transform Partial-Fraction Expansion Differential Equation Solution using Laplace Transform

Theorems of the Laplace Transform

Partial-Fraction Expansion

Convert the function to a sum of simpler terms.

F (s) = N(s)/D(s)

Case 1. Roots of the denominator of F (s) are real and distinct. Case 2. Roots of the denominator of F (s) are real and repeated. Case 3. Roots of the denominator of F (s) are complex or imaginary

Outline

(^1) Laplace Transform Laplace Transform Laplace Transform using MATLAB Theorems of the Laplace Transform Partial-Fraction Expansion Differential Equation Solution using Laplace Transform