Example A.2
MATLAB code for example 2 from Appendix A of the book "Regeltechniek voor het HBO"
Laplace theory for a system with time delay
- Date : 02/03/2022
- Revision : 1.0
Copyright (c) 2022, Studieboeken Specialist Permission is granted to copy, modify and redistribute this file, provided that this header message is retained.
Table of Contents
Here we look at a system with transfer function: 
.
.Determine the unit step response of this system for 
After some calculations we find: 
, 
, 
, , 
=
The factor 
means nothing but: "write everywhere 
instead of t" in the answer (exept in 
of course), and by table lookup we get:
means nothing but: "write everywhere instead of t" in the answer (exept in of course), and by table lookup we get:→ 
.
.So the output equals zero until 
and the final value is 
which can be seen too by substituting 
in 
.
and the final value is which can be seen too by substituting in .Using the graphical method according to section 3.4.4 we get immediately from the output 
:
:
.It can be checked again, that the numerical value at ervery time t equals the preceding expression.