Example A.3
MATLAB code for example 3 from Appendix A of the book "Regeltechniek voor het HBO"
Laplace theory
- Date : 02/03/2022
- Revision : 1.0
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Table of Contents
The differential equation in the block diagram of figure A2a is in the block diagram of figure A2b shown as a transfer function in s-notation.
The following applies:
.
can be found by transforming the differential equation (all initial conditions zero): 
Simplification gives: 
=
=and:
If we want to determine the output we get: 
Because this expression for is not present in the standard overview, we must reduce it to expressions that do belong to the overview as follows:
is not present in the standard overview, we must reduce it to expressions that do belong to the overview as follows:
Then it turns out: 
and 
and After back transformation we get: 
(we'll add the factor 
to avoid having to state that this only applies from 
(we'll add the factor to avoid having to state that this only applies from If we use the graphical method according to section 3.4.4 (poles in 0 and 
and 
we get: 
.
and we get: .