[From Bill Powers (950626.1410 MDT)]
RE: Hans's model.
As Bill Leach suggested, I set x = xopt in Hans's program and ran it.
Since x is computed in two places on every iteration, I tried each
place. In one place it make no difference; in the other (or both), the
Kalman filter blew up. One of the variables (pxx) went negative, which
is not supposed to happen. When the square root was plotted, the program
halted on a floating point error.
Puzzled, I then plotted the difference between x and xopt. According to
Hans (and his equations), this difference should be zero. It is not.
Where xopt is varying as a sine wave, x is varying as a cosine wave with
of about 5 to 8 percent of the amplitude of xopt. This continues to be
true no matter how long I run the _original_ model. This doesn't fit the
picture of the controller as being "perfect."
No doubt the program does not implement exactly the model that Hans
described in words; I haven't tried to track down the difference.
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Best,
Bill P.