Example H4.2

Matlab code for example 4.2 from the book "Regeltechniek voor het HBO"

Determine the first order transferfunction from a stepresponse

Date : 10/02/2022
Revision : 1.0

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Determine the first order transferfunction from a stepresponse Assignment Solution

Assignment

The measured step response of a system is shown in figure 4.3a. What transfer function can describe this system?

Solution

Check that the stepresponse starts at t=0 at an angle unequal to zero and that the gradient is more or less like that of an e-power. So it might be a first order system. But until now it is not quite sure that this is true. See for instance the stepresponse of the second order process (two poles!) with a zero in figure 3.9. Only after it is checked that the time that elapses until 63% of the final value is reached (about 3 seconds) also applies to the remainder of the step response (and again to each subsequent remainder; see figure 4.2c), only then it is known for sure that this is a first order system.

Because the step at the input with a value of two leads to an end value at the output of 10 the system apparently also has a constant factor of 5. In that case the transfer function is equal to:

In figure 4.3b you can see the pole and zero plot.

Regardless of our consideration of figure 3.9 it is often concluded that this will be a first order process if there is only the course of the step response according figure 3.9d. It will not be a big mistake. In that case it is officially called a dominant first order process.