8.10.10 [2]

I feel like I'm loosing the script here, so a quick sitrep on what's going on: I currently have 2 different methods written to calculate the optimal FIR disturbance rejection filter. One uses state-space models of the disturbance and plant to generate impulse response sequences. These can be used to form a Weiner-Hopf problem and solved for the optimal coefficients a la earlier work we did on jitter control. The second method uses the models to simulate data directly. Given enough samples, the solution to another (similar) linear equation yields the coefficients.

Theoretically, both of these should give similar results (I think). But so far no luck. Here's a comparison of the output PSD with filters calculated using each method compared to using no filter (F=1).



I used the actual plant disturbance models I identified from the experiment. Using the data approach works pretty well, although its pretty cumbersome, and would be stupid with multiple modes. The method using the impulse responses, however, is just crap, clearly making things worse.

Confusingly, both methods crap out the identical filter with less complicated disturbance models. I think the problem is that the input noise covariance matrix isn't really accounted for in the state-space model of the disturbance. It comes into play in the data driven case since I have to use it to generate the input, but it doesn't show up directly in the impulse response as the moment. It should be easily, however, to incorporate it into the state-space model by multiplying the input matrix.

Thats the plan for the afternoon, as soon as I finish blogging here in a coffee shop.