Example H4.3

MATLAB code for example 4.3 from the book "Regeltechniek voor het HBO"

Three examples of second order systems

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
Three examples of second order systems Example 1 : Over criticical damped Example 2 : Critical damped Example 3 : Under critical damped

Example 1 : Over criticical damped

Suppose that the process parameters of formula 4.8 equal: , ,
We now can fit formula 4.8 to the two forms of formula 4.11:
and as we can see:
for one form and for the other form.
This is a so called over critical damped second order system. The unit step response is shown in figure 4.7a and the pole and zero plot in figure 4.8a. The behaviour of such a system can be associated with the behaviour of the fairly rigid suspension of a car. When such car crosses a bump it will not bounce and it takes a relatively long time to reach its new position.

Example 2 : Critical damped

If we change the parameter values in: , , , then fit it again to
the two forms of formula 4.11, it results in:
and as we can see:
for one form and for the other form.
This is a critical damped second order system. The unit step response is shown in figure 4.7b and the pole and zero plot in figure 4.8b. The behaviour of such a system can be associated with the behaviour of the suspension of a car with characteristic that crossing a bump means it will just not bounce and the time to reach its new position is as short as possible.

Example 3 : Under critical damped

And if we change the parameter values in: , , , then fit it again
to the two forms of formula 4.11, it results in:
and as we can see:
for one form and for the other form.
This is an under critical damped second order system. The unit step response is shown in figure 4.7c and the pole and zero plot in figure 4.8c. The behaviour of such a system can be associated with the behaviour of the suspension of a car with characteristic that crossing a bump means it will bounce and the time to reach its new position will be relatively long.