For further research, I need to estimate a friction torque of Permanent Magnet DC machine. I have deisgned linear Kalman filter (LKF), where u=applied voltage, y1=measured speed, y2=measured current, x1=y1, x2=y2 and x3=load torque. It is assumed that dx3/dt aproximately equals zero.
Design of LKF is quite simple, and I tuned LKF for data measured from real PMDC drive. But how do I know that observed (or estimated) friction torque is good? Should I compare it with theoretical values?
Dear Karol,
first by the LKF you probably mean just an ordinary Kalman filter -- it was already designed for linear models. For non-linear ones, there is a variety of different Kalman filters like extended one, unscented etc. Second, as the reference for state estimation evaluation you can either use a model and simulate, say, the friction torque or perform an experiment where you would be able to measure the relevant state. Of course, the latter is the best you can do.
Dear Pavol, thank you for you answer. Of course, I have meant ordinary Kalman filter. I can design EKF, but I was wondering if LKF can do the thing.
I agree with you that rather to model a drive with friction torque (it isn't an easy task) it is better to measure friction torque in order to further comparison with estimated one. How can I do it without torque transducer?
Dear Karol,
do you have access to actual torque values or to actual current values?
Dear Matthias,
yes I have acces to the actual current values (from current sensor).
If we assume, that Tact = Kt_est iact, where Kt_est is torque constant of machine (measured) I also have acces to the actual torque values.
I don't have torque transducer to measure actual torque values.
Dear Karol, is the quality of the current signals sufficient to use the estimation you give for the actual torques?
If this is the case, then my next question would be whether you can compare the estimated actual torque with a model of the expected torque for the given situation, thus extracting a difference. If the model includes friction torques, then the difference would hopefully consist mostly of externally applied torques, i.e. non-modeled "disturbances" on the rotational motion. If the model does not include friction, then the difference would comprise friction and external torques.
When modeling friction torques, you might consider a constant as well as a speed-proportional component of friction. Is temperature variation going to be of interest for you?
Dear Matthias,
thank you for your answers. I can't further continue in our discussion today. But at least: I think that quality of current signals is sufficient.
I will compare actual measured torque with the actual modelled torque from model which doesn't include friction (it is a great and simple idea - thanks).
I would like to consider both constant and a speed -proportional component of friction. We assume that temperature variation and its influence is neglected (for simplicity).
Dear Karol,
In my lab we have a setup with which we can measure the friction torque as function of the speed, voltage, current etc. In the motor-gearbox combinations I use, we found that the friction can quite accurately be modeled by three components:
- a constant, speed opposing friction torque
- a current-proportional speed opposing friction torque and
- a small speed-dependent friction torque
Since this second term was one of the largest contributors to the total friction, you might consider such a term in your model.
I measured the "friction torque" of a few motors with very simple inexpensive equipment: Prolong the axel at the rear bearing, put a small bearing on it can be 8mm inside 22 outside (skate board type). You put that bearing in some cradle. Use the thread in the normal axel side to put an threaded rod in it. Put the other end in a drill mandarin. Fix a wooden lath to the stator. Rotate the drill, use a small weight with a chord to measure torque, and distance to equilibrium point. To avoid the chord mass error weigh the weight + chord to be more accurate. Use the frequency to know the speed.
The experiment is close to set ups where equilibration is done, some safety has to be taken into account: for example avoid that the motor would fall from the table if it jumps out of the cradle, or if something breaks.
Hysteresis (and Foucault) iron losses are experienced as "mechanical losses". hysteresis losses appear as a constant torque. I leaned that the hysteresis losses of the iron dominate above the mechanical bearing losses, except if rubber sealed bearings are used. Too much grease in the bearings is recognized as a temperature dependent friction torque.
Dear contributors to this question. Thank you for all your answers. We have done one step closer in question "how to find a friction torque value" by using a torque transducer, which we have obtained today in our lab :) now we can compare Kalman filter's results with the actual torque value. I found this comparison sufficient. But your comments to this issue are still welcomed.
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