Lab # 03
Control Systems
Objective:
The main objective of this lab is to make the students understand how we can
calculate the Laplace transform and inverse Laplace transform. While calculating the
inverse Laplace transform we often need to solve the partial fractions. Matlab has a
command to obtain the partial fraction expansion of a function in the form B(s)/A(s).
LAPLACE TRANSFORM
To find the Laplace transform of a function f(t) we know that:
∫
∞
−
=
0
)()]([ dtetftfL st
In Matlab we can use just one command laplace(f(t)) to calculate the Laplace
transform.
Example
>> syms t //define a symbolic object
>> y=t
y =
t
>> laplace(t)
ans =
1/s^2
Lab Task 1: Find the Laplace transform of the following functions.
1. g(t)= )sin( t
ω
2. g(t)=
)20sin( t
3. g(t)=
2
t
4. g(t)=
at
e
5.
t
tetg 5
5)( −
=
6.
)2sin(2)( 2tetg t−
=
DEFINING A TRANSFER FUNCTION
To define a transfer function in Matlab we can use the command tf to declare a
transfer function.
(Note: tf stands for transfer function)
>> syms s
>> A=[1 1 0] //where 1,1 and 0 are the coefficients of the denominator
A =
1 1 0
