The ability of a model-based real-time optimization (RTO) scheme to converge to the plant optimum relies on the ability of the underlying process model to predict the plant’s necessary conditions of optimality (NCO). These include the values and gradients of the active constraints, as well as the gradient of the cost function. Hence, in the presence of plant−model mismatch or unmeasured disturbances, one could use (estimates of) the plant NCO to track the plant optimum. This paper shows how to formulate a modifed optimization problem that incorporates such information. The so-called modifiers, which express the difference between the measured or estimated plant NCO and those predicted by the model, are added to the constraints and the cost function of the modified optimization problem and are adapted iteratively. Local convergence and model-adequacy issues are analyzed. The modifier-adaptation scheme is tested experimentally via the RTO of a three-tank system.

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An incremental approach for the identification of stoichiometries and kinetics of complex homogeneous reaction systems is presented in this paper. The identification problem is decomposed into a sequence of subproblems. First, the reaction fluxes for the various species are estimated on the basis of balance equations and concentration measurements stemming from isothermal experiments. This task represents an ill-posed inverse problem that requires appropriate regularization. Using target factor analysis, suitable reaction stoichiometries can then be identified. In a further step, the reaction rates are estimated without postulating a kinetic structure. Finally, the kinetic laws, i.e., the dependencies of the reaction rates on concentrations, are constructed by selecting the best model structure from a set of model candidates. This incremental approach is shown to be both efficient and flexible for utilizing the available process knowledge. The methodology is illustrated on the industrially relevant acetoacetylation of pyrrole with diketene. ᭧