Discrete transfer function implementation on hardware explodes to infinity

Hi,

I have a very simple transfer function model that works well in Matlab/Simulink. However, when I try to implement it on my actual hardware, the output quickly explodes to infinity.

I'm trying to deploy this model to a PLC running Twincat. Twincat has its own implementation of transfer functions which I have faith it is bug free. I have double checked my calls and I don't believe there is anything wrong (famous last words!).

Could this numeric instability be due to the way that matlab/simulink implements the calculation versus the way that Twincat does it?

Or could it be something related to the type/order of the model? Would state space offer any advantage in terms of numeric stability?

Thanks

#Matlab code

sys = tf([0 0.0611], [1 2.05 0])

sys =

0.0611

------------

s^2 + 2.05 s

Continuous-time transfer function.

sysd = c2d(sys, 0.002)

sysd =

1.22e-07 z + 1.219e-07

----------------------

z^2 - 1.996 z + 0.9959

Sample time: 0.002 seconds

Discrete-time transfer function.

[John D'Errico]

You may have faith, but faith is too often poorly rewarded. What you don't say, or possibly don't know, is if the implementation that you are using does its work in fewer significant digits. For example, is that code runniing in effectively a lower precision arithmetic?

Knowledge is always better than simple faith.

[Felipe]

Hi John, thanks for your answer.

Beckhoff's Twincat Tc_ControllerToolbox, isn't some obscure open source repo off the internet. I paid for the license, I should trust it works. The same way you and I and everybody else using Matlab trust it works.

Twincat's implementation of TF's runs with long reals, it's plenty of resolution.

[Mathieu NOE]

hello @Felipe

which IIR topology are you using ?

Biquad implementation is more numerically stable than Direct Forms

Digital biquad filter - Wikipedia

[Felipe]

Hi Mathie, thanks for your reply!

I did not know that. The transfer function I'm trying to implement has 2 poles and 2 zeros. The API I'm using, implements the model in this form:

[Mathieu NOE]

That sounds ok to me

make sure the a and b coefficients are passed in the right order (usual error is when copy paste from ascending vs descending power of z formalism)

Answer 1

[Bora Eryilmaz]

Your discrete transfer function has poles (almost) right on the unit circle:

sys = tf([0 0.0611], [1 2.05 0]);
sysd = c2d(sys, 0.002);
pzmap(sysd)

Any slight perturbation of your model coefficients when it is implemented using fixed-point numbers on the PLC would likely make your transfer function unstable.

Also, your model has an integrator (1/s term). So its simulation would go to infinity anyway.

step(sys)