4 ms·
In a world where one can do so much computation, I would really like to see more adaptive control techniques. The I in PID is the only adaptive part. You can t
by gugagore 5y ago
In a world where one can do so much computation, I would really like to see more adaptive control techniques.
The I in PID is the only adaptive part. You can think of it as an estimator of an additive term that arises from e.g. friction or forces due to gravity.
But what about estimating e.g. a multiplicative term? It seems we should be able to do much better than PID, but without needing to commit all the way to a model-based method or reinforcement learning.
I wish there were some materials for how to move just beyond PID, but textbook treatments of LQR or MPC cannot even handle the I in PID.
- salty_biscuits 5y agoYou can always add an extra variable to your state space model to handle an integrated qty...
- pidtuner 5y agoThe problem with many adaptive control techniques is that is very difficult to prove the closed loop stability and performance margins, because such systems are highly nonlinear and we do not have yet the mathematics to provide simple guarantees (for example, I would not get into an aircraft where the control systems have not been rigorously, mathematically, designed) The integral problem of LQR and MPC is indeed not the first topic discussed on textbooks, but there has been a solution for that for year, called "disturbance model". You you can have an "adaptive MPC" following some design procedures. Check out this reference: https://folk.ntnu.no/skoge/prost/proceedings/ifac2014/media/files/2032.pdf https://folk.ntnu.no/skoge/prost/proceedings/ifac2014/media/...
- gugagore 5y agoThanks for the reference. I agree that the solution to getting I action is to model the disturbance, and augment the state. The system certainly becomes uncontrollable in the augmented state space. I've run into a conceptual problem when using this approach with [infinite-horizon] LQR to try to recover what looks like a PID controller, which IIRC is due to the control u not necessarily converging to 0. This is expected, to counteract a constant disturbance, but it means that the sum doesn't converge. I only skimmed the reference, but I did not find a discussion of this issue.
- pidtuner 5y agoThe trick is that, even though the augmented state is uncontrollable, you still use it in the predictions, so the MPC algorithm can still compensate for it. Take a look at the before-last graph in the paper, see how that technique improves predictions after learning the real-time disturbances.
- gugagore 5y agoThat's not what I was concerned about. The subspace that's uncontrollable is the disturbance components of the state, which I don't care to control anyway.
- pidtuner 5y agoNot to control, but to compensate. This is what the I action in the PID does, compensate for un-modeled disturbances