Studies in the synthesis of control structures for chemical processes: Part III: Optimal selection of secondary measurements within the framework of state estimation in the presence of persistent unknown disturbances

When primary control objectives cannot be measured directly, secondary measurements have to be selected and used in conjunction with estimators to infer the value of the unmeasurable variables. Unmeasured process disturbances (state excitation noise) are assumed to be of major importance, dominating the errors caused by measurement noise. Since the white noise assumption is generally insufficient for the persistent disturbances commonly occuring in the Chemical Engineering, environment, a nonstationary noise model has been employed, and is shown to yield superior estimations under these circumstances. New necessary and sufficient conditions have been developed for the observability of the dynamic system augmented to include the noise model. A variety of new measurement selection criteria is presented here, with the goal of minimizing estimation error. One class of criteria aims at minimizing the transient estimation error when a static estimator is used. The other class minimizes the measurement error caused by the unobservable subspace. The design of state reconstruction procedures (which are able to handle persistent unmeasured process disturbances) is explained in a stochastic and a deterministic framework. Finally, the synthesis of reduced order control schemes is discussed. The power of the selection criteria and the superiority of a Kalman filter design employing a nonstationary noise model is demonstrated in many examples.