Laplace Transforms Part 3 (Control Systems) Electrical Engineering (EE) Notes | EduRev

Electrical Engineering (EE) : Laplace Transforms Part 3 (Control Systems) Electrical Engineering (EE) Notes | EduRev

 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). 
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