Discrete transfer function implementation on hardware explodes to infinity

Question

Felipe 2022-11-5

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https://ww2.mathworks.cn/matlabcentral/answers/1844108-discrete-transfer-function-implementation-on-hardware-explodes-to-infinity

编辑： Bora Eryilmaz 2022-12-7

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.

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Felipe 2022-11-8

TF_Implementation.JPG

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 2022-11-8

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)

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Answer 1

Bora Eryilmaz 2022-12-7

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https://ww2.mathworks.cn/matlabcentral/answers/1844108-discrete-transfer-function-implementation-on-hardware-explodes-to-infinity#answer_1122477

编辑：Bora Eryilmaz 2022-12-7

在 MATLAB Online 中打开

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)