Inb4SID

I'm trying to gradually ween myself (and my advisor) off tinkering with my experiment and start working on actual controls. Before I can get to controller design I have to do some work on system ID; stuff more complicated than simple ARX models of the DM. Its been so long since I've actually taken any classes in this stuff that this means a lot of reading in the weeks ahead.

The reason for focusing on system ID is that one way to reject disturbances is to characterize the disturbance input as the output of an LTI filter with white noise input. Once you have that you can internalize the model in the controller and use it to reject disturbances "optimally." This is explicitly what an adaptive controller does, but doing the ID in a separate step has its advantages.

The immediate question was did the experiment have enough accuracy in reading and applying wavefronts to do this? To do this I cooked up a little Simulink file that runs white noise through a FIR filter and applies the resulting modal commands. The game is to read the wavefronts from this and reconstruct these filtered commands. With those and knowledge of the inputs, it should be possible to identify the FIR coefficients if the reconstruction is accurate enough.

To my amazement this actually worked out well; the reconstruction of the filtered commands was accurate enough to do a good job of estimating the filter with batch least-squares. The modes also seemed orthogonal enough that I could determine identify separate filters if a different one was applied to different modal channels.

For shits and giggles I stuck the RLS block in the Simulink model and was able to get it to converge to the SS error pretty quickly. You can see this in action by changing the filter coefficient half way through the experiment and watching it re-converge.

This is good news. Eventually I'm going to unleash a subspace ID algorithm on this biotch to identify even more complicated state space, MIMO models, but since I know nothing about that stuff its going to be a while before I catch up on all the reading. In the mean time there's plenty to play around with here. I'd like to see how well I can identify a multichannel FIR filter, particularly if only a limited number of modes are used in the ID. Also, I think I'd be good for the soul to try to code an RLS filter myself.