Hi Bill,
I read the doc page arx, left, and came back to it and the words still don't make sense. Not to mention the mixed notation with discrete- and continuous-time, i.e., A(z)*y(t) (maybe that's standard in the System ID world). This section of the doc page is not helpful.
Things are further confusing because the screen output of B(z) as shown above is NOT the same as B(z) (or B(q)) as shown in the ARX structure definition of the model. For your example, the B(z) in the math model is really first order
B(z) = 1.222 + 0.8787 z^-1
and then the b parameter of sys, i.e., sys.b, should be the standard Matlab representation of B(z^-1)*z^(-nk) in ascending powers of z^-1.
sys.b = [0 0 1.222 0.8787]
Based on your example and a few that I tried, it seems that na and nb are really supposed to be the number of unknown coefficients in A(z) and B(z) (as defined for the model) respectively. Keeping in mind that A(z) is assumed to always have a leading coefficient of 1, at least based on my reading of the doc, then na is the same as the order of A(z). But that's not the case for nb. Maybe they really mean nb = order(B(z)) + 1, which you identified above as a possbility (keeping in mind that B(z) here is not the same as the B(z) in the screen output. But if that's what is meant, the doc is doing a really poor job of explaining that, and phrases like "Because sys.b + 1 is a ..." make no sense whatsoever.
And I don't understand what the Name-Value parameter InputDelay is. Is that supposed to be a delay on the input disturbance, e? I assume that is the case because any delays on the input u would be captured by nk, but the doc does not explictily say to which input (u or e) InputDelay is applied.
