ABSTRACT
All the machinery is now available for self-tuning: connect a parameter estimator to an MV controller by solving the Diophantine identity of Equation 33.47. Note that MV controller design requires knowledge of k, A, B, and C. In difference equation terms the CARMA plant model is
y(t) = −a1y(t − 1)− · · ·+ b0u(t − k)+ · · ·+ e(t)+ c1e(t − 1)+ · · · ,
but the standard estimators can estimate only A,B; the driving noise e(t) is not measurable and, hence, cannot be placed into the x-vector to estimate C. There are methods (such as extended least squares) for estimating C, but these tend to be unreliable in practice. However, it transpires we can obtain self-tuned MV (giving a self-tuning regulator) by using a standard LS estimator without needing knowledge of C (in effect, assuming C = 1)!
