Overly Ambitious

Now that the FIR filter is basically working for the single channel experiment, I think its a good time to set some targets for the next four weeks. The clear next step is to start working on a multichannel version using more modes. Theoretically there isn't that much difference here, but I suspect there will be practical problems with actuator saturation and other shittyness that will slow things down.

I think a reasonable goal is a 10 channel adaptive/optimal filter in 4 weeks. Here are some things that will need to happen:

1. Characterize closed-loop transfer matrix. How similar are the diagonal terms? How significant are the off diagonals? What's the best scalar transfer function approximation?

2. Get the adaptive controller working given an identified or ideal transfer matrix.

3. Write a script to compute the optimal multichannel FIR and IIR filters.

4. Get target camera working to compute Strehl ratios.

5. Find/write/steal a simulink block that can implement multichannel transfer functions. The pole at 1 in the pure integrator I'm using now might (will) lead to saturation when more modes are controlled.

6. Questions: How to the PSD's of the output channels compare? How does changing the number of modes alter steady-state performance?

A lot of this will require running many experiments or simulations, so there should be plenty of down time to pursue some theoretical stuff for the SISO case. Basically, I'd like to write m-files that do the following:

1. Compute the optimal IIR filter. How does performance compare to the FIR case?

2. Compute the optimal FIR gains using and RLS array algorithm.

3. Compute the optimal FIR gains using an RLS lattice filter.

4. Do something about implementing a Laguerre filter.

SInce these will all be m-files, I don't expect to implement these in the actual experiment right away. Mainly, I want to get some idea of the theoretical performance benefits by using increasingly complicated methods. Obviously I want to do all of this for the multichannel case one day, but the details of that are so complicated my head might explode first. We'll see.