Example H4.8
MATLAB code for example 4.8 from the book "Regeltechniek voor het HBO"
Experimental determination of the transferfunction from the step response
- Date : 31/03/2022
- 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
Determine three parameters from the step response
Suppose in figure 4.25 the step response with step size 4 has a result as shown in figure 4.26. Because of the overshoot we clearly see that this response is part of a (at least dominant) second order process with damping factor 
. The horizontal start of the response in 
underlines the second order behaviour. Figure 4.26 immediately shows the relevant values of the static amplification 
, overshoot D and period time 
of the oscillation:
. The horizontal start of the response in underlines the second order behaviour. Figure 4.26 immediately shows the relevant values of the static amplification , overshoot D and period time of the oscillation:
Calculate the parameters 
From this we can perform all calculations in a certain sequence (see formula sheet in appendix D):
From 
: 
rad/s.
: rad/s.From 
=0.4:
=0.4: 
; as λ is negative → 
.Calculate the parameters β and 
From 
→ 
→ 
(a negative β is physically not possible).(maybe the formula 
had been preferrable in this case; now to late!)
had been preferrable in this case; now to late!)From 
: 
rad/s.
: rad/s.From 
: 
: In summary
We derrived two sets of parameters:
(
) = (6.72, -0.46, 1.57)
) = (6.72, -0.46, 1.57) (
) = (2.5 0.29, 1.64)
) = (2.5 0.29, 1.64)In transfer function (see 4.11):
You can check again the solution by simulating the step response in MATLAB (step size 4 of the input!) and compare the result with figure 4.26. You can do it yourself now, or see the previous examples of this chapter.
In this example we had to do a lot of calculations. To a certain extent that is secondary. What matters is understanding the theory, especially the physical and /or mathematical meaning of the parameters and .
and .