Methods are presented for the construction of optimal and suboptimal estimators for inferential control systems. Optimal estimators are constructed with the aid of Kalman filtering techniques applied to linear systems driven by integrated white noise disturbances. The description of the disturbances as integrated white noise leads to optimal dynamic estimators which reduce to optimal static estimators for sustained disturbances. Suboptimal estimators are constructed by prespecifying the structure of the estimator and choosing estimator parameters so as to minimize the mean square error in estimation.
Optimal and suboptimal estimators are compared by using them in an inferential control system which attempts to control the product composition of a simulated multicomponent distillation column. There is little difference in performance between optimal and suboptimal estimators which use temperature and flow measurements to estimate product composition. However, the inferential control system using a simple suboptimal estimator is significantly superior to the policy of maintaining a selected tray temperature constant through a standard feedback control system. The inferential control system is also superior to composition feedback control systems where the measurement delay is greater than 5 min.