Estimation and prediction of convection-diffusion-reaction systems from point measurement

Different procedures with respect to estimation and prediction of systems characterized by convection, diffusion and reactions on the basis of point measurement data, have been studied. Two applications of these convection-diffusion-reaction (CDR) systems have been used as a case study of the proposed estimation and prediction methods. One is a climate room for bulk storage of agricultural produce (Case A) and the other is a UV disinfection process used in water treatment, food industry and greenhouse cultivation (Case B).
An essential step in the implementation of estimation and prediction for these types of systems is model reduction. The proposed procedures not only differ by the nature of the estimation and prediction method, but also with respect to early or late model reduction. In the context of this thesis, early model reduction encompasses approximation of the infinite-dimensional system to finite-dimensional form before estimation and prediction is worked out, whereas in late model reduction, the approximation step is applied after synthesis of an infinite-dimensional estimator (observer) or predictor.
The first contribution of this thesis is an identification approach with output-error (OE) modelling techniques that links important physical parameters in a reduced order model to the OE parameters. This technique is illustrated by Case A, using real experimental data. Local parametric sensitivity analysis shows how physical parameters affect the dominant time constant in an identified, first order output-error model.
The second contribution is a realization approach from a discrete-time linear finite-dimensional system affine in parameters to linear regressive form. The resulting linear regression form allows the formulation of a convex parameter estimation and prediction problem. Such an approach is attractive for reduced order, discretized CDR models with specific boundary conditions. For such models, it turns out that the response and regressor functions can be formulated explicitly as functions of the number of compartments, sensor and actuator location. Once available, they can further be used for a priori identifiability checks, parameter and input sensitivity analysis. Results are illustrated by two diffusion examples with different boundary conditions.
Finally, the last contributions are a static and a dynamic boundary observer for CDR systems. Detectability and observability results aid in the design of a static gain boundary observer of an infinite-dimensional system where only boundary measurements are available. The dynamic observer is synthesized by formulating an H∞-filtering problem in a linear fractional transformation framework in order to cope with disturbances on the input and output of the system. Both observer synthesis approaches are illustrated by a CDR model of Case B.