Discrete Time Speed and Torque load observer produces unexpected oscillation in the estimation of the torque load.

Hi everyone,

I tried creating a continuous and a discrete time speed and torque load observer, for a simple mechanical system.

The dynamic equation of the system is:

, where .

The speed observer scheme is the following (first is the continuous, while second is discrete):

The speed estimation and torque load estimation for the continuous observer works well. The discrete estimates speed well but shows a very strange oscillation in torque load estimation in the very first instants, as shown in the following image:

The reason why i don't understand such behaviour is that in the continuous model it works perfectly and with same performance, but in the discrete domain, it doesn't. Any ideas of what could be the issue?

I uploaded both the .m file for parameters and the simulink file for you to try and see what could be the problem.

Thank you in advance for your time,

Claudio

[Mathieu NOE]

hello

I have R2020b - can you share a slx version compatible with my release ? tx

[Claudio Di Pietro]

Here it is :)

[Mathieu NOE]

Ok so I tried a couple of things

fixed step solver - maybe not critical as we have anyway a discrete system to simulate so fixed step would be choosen by "automatic slover" option

pid without filtering on the derivative output - this can create lag and oscillations

played with PID gains - see best combination below (IMHO)

anyway, a discrete model will always "lag" behind the true continuous system, so there can be some differences in transient behavior , usually the discrete version is not as good as the continuous system in terms of transients

yiu can also try to increase the sampling rate if you can to get closer to the continousmodel performance;

I could not get any better than this (zoom on first samples) with original sampling rate :

attached are the two files with my settings

[Claudio Di Pietro]

Thank you so much Mathieu!

I have close to no expertise in PID tuning and i followed some iterative techniques i have found online, but your gains work much better. Is there any procedure or algorithm you would suggest for PID tuning? In case you have no time to give me this info, can you tell me books or papers where I could find this?

Thanks again Mathieu your help is great and I really can't tell you how much I appreciate it.

[Mathieu NOE]

hello Claudio

I have to admit I tweaked the gains purelly manually here; my first thought in your model is that there are already two integrators in the loop so no need to have PID integrator gain

so I started with only P gain and tried to maximise it until it get's unstable , then reduce back to half ;

then add a bit of damping , starting with very low value and get up to the optimal point where we have no oscillations and shortest transients;

now , there is an "auto tuning" function in simulink but I think that requires a specific toolbox

In the file exchange section you can see many submissions about PID tuning; the best I found is the "VTiger" method (zip attached); but it works in matlab script , not with simulink file, but it's easy to do it in your case;

there are many publications about PID tuning on MathWorks website

all the best

[Claudio Di Pietro]

Mathieu you are a lifesaver. Thank you very much.

Best regards

[Mathieu NOE]

My pleasure !