Can I graduate now?

Finally finally have the adaptive loop working in the experiment, at least with a single mode. Turns out that the effect on the overall wavefront norm is difficult to see for this disturbance model unless you know its there. Its more clear if you just look the coefficient of the mode being controlled.

But the best way to observe the effectiveness is by comparing the PSDs of the modal coefficient. In the uncontrolled case (classical PI controller only), you can clearly see some color resulting from the disturbance input. In simulation the adaptive loop flattens this out somewhat:



To my surprise, the adaptive loop does an even better job whitening the PSD in the experiment:



Another thing to notice is that I compared the performance using the ideal and identified plants. The adaptive loop uses a model of the closed (classical) loop to estimate the disturbance input. In general we assume that the ideal plant is just an integral controller and a unit delay, since the phase reconstructor is chosen to be the pseudo-inverese of the modal poke matrix. To verify this I also identified a plant using n4sid and a few thousand samples of input/output data, and found the resulting transfer functions very identical. This is nice to know since the plant actually contains some dirty nonlinearities like saturation and rounding, so it looks like those aren't significant for now.

This is all for a single mode. The requirements on the plant in the multiply mode case are more stringent (i.e. a diagonal transfer matrix). Something is also causing this to run quite a bit slower than from an m-file, so that will take some coffee consumption to figure out as well.