Why is this simple Simulink System unstable for low sampling frequencies?

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Dominik Hiltbrunner
Dominik Hiltbrunner on 7 Jul 2020
Hello Community!
I have a simple Simulink System which appears to be unstable for low sampling rates.
The model looks like this (.slx file was created in 2020a release and is attached to this thread)
  • The model is simulated with fixed time steps (no continuous states)
  • The sampling frequency is an integer multiple of audio sampling frequency, e.g. 44100 * 64
  • The z-transfer-function Y(z)/U(z) in the middle is calculated depending on the sampling rate. It is a first-order system in the s-domain that is converted as follows:
clc; clear; close all;
s = tf('s');
fs_sim = 44100*64;
T = 1/(s*1.1e-9+0.0002288);
model = 'tustin';
[N4 D4] = tfdata(c2d(T, 1/fs_sim, model),'v')
Now I observe the following behaviour:
For high sampling rates, e.g.
fs_sim = 44100*128;
the model does what it is supposed to do.
For low sampling rates, e.g.
fs_sim = 44100*64;
the system becomes unstable.
Can someone explain why this happens?
Thanks for any advice!

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