Control Systems

1
Control Systems
Welcome to
ME30029 / ME50151
Chapter 3. Laplace Transforms

• Dr. M. Necip SahinkayaDepartment of Mechanical
  Engineering
• University of Bath

2
Chapter Content

• Laplace Transform Definition
• Properties
• Inverse Laplace Transform
• Non-Zero Initial Conditions
• Dead Time
• Piece-Wise Continuous Inputs
• Final and Initial Value Problems

3
Laplace Transform
Definition
4
Step and Ramp Functions
5
Pulse / Impulse Function
6
Properties of Laplace Transforms

• Linearity
• Derivatives
• Integral

7
Laplace Transform Table
8
Inverse Laplace Transform Example
9
Time Reasponse
10
Non-Zero Initial Conditions
Consider the change in output due to change in
input by taking zero initial conditions, then add
to the datum level of output due to the datum
level of input.
11
Dead Time (Transport Lag)
Heavyside function
Laplace Transform
12
Piece-Wise Continuous Inputs
13
Piece-Wise Continuous Inputs Example
14
Final and Initial Value Theorem

• Final Value
• Initial Value

15
The End

• End of Section 3.
• gtgtLaplace Transforms

Thank you
Dr. M. Necip Sahinkaya Department of Mechanical
Engineering University of Bath