ABSTRACT
Recursive estimation methods are routinely used in many applications where process measurements become available continuously and we wish to reestimate or better update on-line the various process or controller parameters as the data become available. Let us consider the linear discrete-time model having the general structure:
A(z1)yn = B(z-')un.k + en (13.1)
where z"1 is the backward shift operator (i.e., yn_i = z"'yn , yn-2= z"2yn> etc.) and A(-) and B(-) are polynomials of z"1. The input variable is un = u(tn) and the output vari-
able is yn = y(tn). The system has a delay of k sampling intervals (k>l). In expanded form the system equation becomes
(1 + a,z"' + a2z"2 + ...+apz"p)yn = (b0 +blzl +b2z"2+...+bqz"cl)u,,-k + en (13.2)
or
Yn = - a,yn.i - a2yn.2 -...- apyn.p + b0un.k + b^,,^., + b2un.k.2+... + bnu,.k.m + en (13.3)
We shall present three recursive estimation methods for the estimation of the process parameters (ab...,ap, b0, bh..., bq) that should be employed according to the statistical characteristics of the error term sequence en's (the stochastic disturbance).
