# Controlled position acceleration on the basis of a known process transfer function

JHC is extremly chaotic but here what I've concluded. (and has plenty of time which I don't)
Once he show us object inversing controller. Famous F1*F2=K
(very bad idea, I have already commented it, no disturbance rejection, tragic sensitivity function).
Then he suddenly changed subject to LQR controll, as he said, he just run some software and results just cropped up. He didn't use observer to estimate state (which is strange because he has a PC and observer is easy to calculate). He created mathematical model and assumed that this model (when driving by the same input as object) produces exact states and used them as estimates for LQR algorithm. Well, this is very simplified method and with LQR and easy to controll, slow object could work quite well.
He mixed this two things, inversing and LQR algorithm, so I can't understand whether is he talking about first and last.
P.S. We have the same proverb, "Paper bears everything."
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Mikolaj

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napisa?(a):

You can obtain them by least square approximation methods.
Example: http://home.arcor.de/janch/janch/_news/20070503-mikolaj /
Input: measured points Output: differential equation DE
If you have doubts: Calculate some points from a known DE. Input them to the program and prove the result.
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Jan C. Hoffmann eMail aktuell: snipped-for-privacy@nospam.arcornews.de
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JCH wrote:

I'm not concerned with identifying the derivatives, but with computing them in real time.

Have you accomplished that with real quantized signals and some inevitable noise? How much time delay do the least squares approximation methods impose? How many degrees of lag at Fs/2 is that?
Jerry
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Engineering is the art of making what you want from things you can get.
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napisa?(a):

Sorry, what is Fs/2?
In my view a bad approximation is better than having nothing. An example should explain what I mean. You have just 6 extreme noisy points (red points) and you know they are circle data.
Find the center point (Mittelpunkt x_m, y_m) and radius (Radius r): http://home.arcor.de/janch/janch/_news/20070508-avins /
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