Infoscience

Thesis

Preferential estimation

State estimation is a necessary component of advanced monitoring and control techniques, since these techniques often require information that is too expensive or impossible to obtain from direct measurements. The objective of estimation is the reconstruction of the missing information from both the available measurements and prior knowledge in the form of a dynamic model. Usually, full-state estimation is considered because of the close link between estimation and the state feedback literature. By having an accurate estimate of all states, the entire system can be controlled, provided the system is controllable. However, since in some cases the goal is to control only a subset of the states, knowledge of all states is not required. The objective of this thesis is to estimate accurately a vector of preferred variables, whose dimension is much lower than that of the full state vector, while paying no attention to the accuracy of the estimates of the remaining variables. Such a problem might arise, for example, when optimizing a process by tracking active constraints. Biased estimates are often obtained due to the presence of plant-model mismatch. This mismatch can be regarded as a deterministic disturbance. In addition, the measurements of key variables might be available less frequently than the output measurements. The problem of preferential estimation (PE) is formulated as that of eliminating the bias in the estimates of the preferred variables using their infrequent measurements and a full-order model. Hence, the measurements are handled at two time scales. Such a concept has been studied thoroughly in the literature for the purpose of standard estimation, i.e. estimating all states accurately, for which infrequent measurements of all states are needed. The advantage of PE is to require a smaller number of measurements, despite using the full-order model. The following observer structures are studied in the thesis: Proportional observer. This structure contains a correction term proportional to errors obtained from the frequent measurements of the output variables. The gains corresponding to this term are computed from the infrequent measurements of the preferred variables, thus leading to a calibration-type approach. It is shown that bias can be eliminated in the preferred variables by an appropriate choice of the gains. Due to the observer structure, a different set of gains is required for each disturbance value. Hence, the gains have to be retuned each time the disturbances change or, since the disturbances are not measurable, each time a new measurement of the preferred variables becomes available. Integral observer. In addition to the proportional term based on the frequent measurements of the output variables, this structure contains an integral term based on the infrequent measurements of the preferred variables. Hence, this observer has a dual-rate structure. The presence of the integral term guarantees bias elimination in the preferred variables even for varying disturbances, provided the observer is stable. It is shown that stability can be guaranteed, and a procedure for tuning the observer gains is provided. The design parameters in this procedure can also be determined using a calibration-type approach. To simplify the mathematical developments, PE is formulated for linear time-invariant (LTI) systems. Its performance is investigated both analytically and through simulation. Though the analysis is restricted to LTI systems, the idea extends to more general systems, which is demonstrated via the estimation of biomass and enzyme concentrations in a pilot-scale filamentous fungal fermentation.

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