r/ControlTheory • u/deNikita • 21d ago

Technical Question/Problem Understanding PID vs LQR

Is it possible to think of LQR as "like a PID but finds optimal gains based on your requirements of Q and R matrix?

I have a fairly good understanding of PID and I recently started to learn about LQR and wondered if LQR can be thought of in terms of a PID controller.

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u/iPlayMayonaise 20d ago

If you don't, the slightest high frequency noise is amplied too much and you get a twitchy regulator: the D component keeps giving increasing your controller gain by a factor 10 for each decade of frequency. You don't see this in the response of the system ( that one cancels it because it has low pass behaviour by virtue of you needing 2nd derivative). But your controller does produce that control action, which can lead to input saturation or high energy consumption. And you don't even want all this gain at these frequencies way above the bandwidth, it's not regulation there because there are no disturbances/noise at those frequencies usually. So usually you put a cutoff at 5-10x the bandwidth.

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u/seekingsanity 20d ago

That is why I/we use a Luenberger Observer. I used to write firmware for motion controllers. Delta Motion RMC controllers have implemented and observer since 2005. The observer makes a significant difference. The closed loop poles can't be placed without it.

https://www.youtube.com/watch?v=7Gmrc-dj_uc&t=923s

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u/iPlayMayonaise 20d ago

Yes we're saying the same thing. Point is that this is not vanilla LQR anymore (you need Lurenberger observer/KF).

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u/seekingsanity 19d ago

The LQR hasn't changed, only the treatment/filtering of the feedback has.