Sugar Momma

Like every good grad student I'm always looking for ways to get more money. One way of approaching that is to look at the current buzzwords that are flying out of research journals, and finding ways to use your own research in those areas.

Networked control systems seem to be a popular research topic in the control engineering world these days, and one of the major headaches there seems to be the uncertain time delay that results from unreliable data networks. I haven't read enough to know how this is dealt with in practice, but I would guess some kind of ZOH handwaving is used to duct tape the problem.

The AO problem deals with time delays explicitly by predicting future outputs. This is possible since wavefronts exhibit some correlation so we can usually do better than pure guessing on average. Adaptive controllers work even better because the nature of the correlation is uncertain or changes over time.

NCS problems also have time delays, but the problem is exacerbated because the delay itself is unknown. On the other hand, would it be outrageous to assume that the delays might be correlated? If that's true, could you design an adaptive controller/observer that provided an estimate that performed better than ZOH?

In other words, could you consider random delays as simply changes to the PSD of the measured signal? If so, then an adaptive controller might have some promise.

Hmm, this could all be nonsense on second thought.

An Update

I finally charmed enough professors into being on my Ph.D committee. The motley crew consists of 3 controls people from MAE and one optimization prof from EE. I deliberately avoided having anyone with too much background in optics to avoid any potentially embarrassing questions, and I really want to emphasize that this is more a controls project than an optics one.

Since it looks like I'll actually be able to do my Quals this quarter, experiments have basically been nonexistent while I work on my prospectus. I'm trying go heavy on the detail to make things easier when its time to write the big boy, and right now I anticipate it'll clock in around 40-5o pages. Bigger than the average prospectus maybe, but I have been plugging away at this for some time after all. Its actually nice to review over everything at one time and see how much I've done...and how much I still have to do.

Graduation in 2010? Maybe not so far fetched after all.

FIR, LMS, RLS, WTF?

Now that my hardware setup is approaching something near its final form, I think its time to start thinking about what I'd like to accomplish here come check out time. Thus, I present...

A 7 point plan for dissertation ass kicking:

1. Finish configuring the SLM to generate disturbances. If that fails, use a DM or other active optical element. These disturbances should originate, using various simulation parameters, from the HEL simulation.

2. Try basic classical AO controllers with said disturbances. Characterize bandwidth properties and relationship to number of modes used.

3. Try "blind" optimization algorithms using target camera information only. Ideally, the cost function used would be somehow related to the Strehl ratio, and could be measured using a photodiode if desired (e.g. intensity). Some interesting first-order algorithms to try include: simple gradient descent, quasi-newton, gradient mapping, and (not first-order) interior point methods.

4. With dynamic disturbances, try to identify a FIR controller using LMS offline. In real time, use a basic RLS fixed-order controllers.

5. Lattice based, order-recursive FIR controllers

6. RLS Laguerre, order-recursive IIR controllers

7. Try RLS adaptation using some other set of orthogonal transfer functions. Maybe something could be done here using Q-parametrization.

That last one might be off in la-la land, but if there's time it could be interesting. S. Boyd's book on Linear Controller Design might have some interesting material related to that.