[Hans Blom, 950918d]
(Rick Marken (950917.1250))
The stored value of dold contributes to the increased accuracy
of the prediction. I had a feeling that the reason this was true
was because the disturbances we are using have nice, smooth
changes over time.
Right! Predictability must exist for something to be able to be
predicted. In fact, it is the only prerequisite ;-). Smoothness (low
frequency of variation) helps a lot, because it makes prediction
dependent only on a few of the most recent samples, i.e.
s[i] := c1 * s[i-1] + c2 * s[i-2]
already works well, as in my most recent model-based controller which
modelled the disturbance. A more general method is
s[i] := c1 * s[i-1] + c2 * s[i-2] + ... + cN * s[i-N]
which will work with any type of regular signal, provided N is large
enough to encompass the periodicity of the regularity. This also
works with any square wave disturbance...
I tested this hypothesis by running Hans' model against the
control model when the disturbance was a square wave rather than
a relatively narrow band random disturbance. When I did this,
the control model did much better than Hans' model.
I did stipulate somewhen that my predictive controller would do
nicely with the MAINDIST disturbances, which are nice and smooth :-).
That does not mean, of course, that your REGULAR (periodic) square
wave could not be predicted. It just takes a longer memory (at least
one period worth of samples). The basic method does not change: to
base a prediction on a previous batch of values.
Indeed, the rms error for the control model (with square wave
disturbance) is about half that for Hans' model.
Did you also compare the performances of both controllers with a
square wave REFERENCE signal? What was the result?
The difference in the way the PCT and Hans' model dealt with
square wave disturbances suggested a way to test the two models;
just compare the performance of the two models with that of a
human working against a square wave disturbance
Are you serious? These models are far too simple to say anything
about humans. Maybe they show what is necessary, but certainly not
what is sufficient.