Modelling Hydraulic Systems

I think an accurate model is always useful. The more accurate the model and the less intuitive feel one has the more useful the model is. I can tell how accuate a model is by looking the mean squared error between the estimated and actual response. In the link to the system ID you can see the error was 0.102183. That is the sum of squared errors. If I divide that by 1500 samples I get a means square error that is very small. It is easy to see estimated velocity is matching the actual velocity very well. I know I can use the gain, damping factor and natural frequency to plug into my gain calculation equations and the results will be very good. Since I am measuring the position with a Temposonic rod with a resolution of about 0.001 inches every millisecond you would think my speed measurements would be very coarse. It makes one wonder what is more accuate, calculating the speed from the Tempsonic rod or using the model to estimate the speed. Which would you rather use for calculating the derivative gain term of the control output, the model velocity or the velocity calculated from the Temposonic rod?

Peter Nachtwey

True, but the less of an intuitive feel I have for the system, the less I trust my ability to make an accurate model. When I have to approach a system this way -- by modeling it, then developing an intuitive understanding from the model -- I make darn sure that I do tests (like your MSE error between estimated and actual response) to verify my model before I go building systems that may be blunders.

Do you mean your derivative _gain_ term or the derivative term itself. Using a model to calculate a velocity is all well and good if the model is accurate, but when reality diverges from the model you can be applying some really wrong control signals if you depend too much on the model.

I'm not putting down using a well-constructed observer here -- just pointing out that you need to take care that it is, indeed, well-constructed and not just a flight of your own imagination.

On Mon, 01 Oct 2007 09:53:17 -0700, Tim Wescott proclaimed to the world:

This pretty well states a lot of my uneasy feelings about models. I fear that a student that uses models supplied them without any intuitive feel, has no way to know if the model is giving them junk or something useful. Without any experience seeing the control system built and running, how do they get the intuitive understanding?

"Paul M" schrieb im Newsbeitrag news: snipped-for-privacy@4ax.com...

... by using models. See also how to get the necessary process transfer function:

I meant the derivative term but I also use the model to calculate the derivative gain.

Obviously the model needs some feedback to keep from going astray. As you pointed out below the result is an well-constructed observer or possibly Kalman or H-infinity filter. The difference between them is small especially if you are talking about steady state filters.

That applies to Kalman filters and H-infinity filters too doesn't it? I have seen the terms Kalman and H Infinity filter used on this and other forums but it is all just big talk unless one can get past the basics and both filters start with the system transition matrix.

I wonder if the astronaut landing on the moon would have had an intuitive feel for landing without models and simulators.

Peter Nachtwey

Unless I'm sadly mistaken a Kalman or H-infinity filter, when used in a control system, is nothing more than a formally constructed time-varying observer. If you don't like (or don't need) the time-varying part, then a steady-state Kalman or H-infinity filter (if done right) pretty much meets the criterion for "well constructed observer".

AFAIK, yes.

Probably not. But the folks working on those models and simulations put a whole lot more effort into them than usually goes into a model for an industrial system. Certainly, if you are _really_ careful with your math then you can squeeze some valid intuition out of it -- but it doesn't just happen automatically.