An algorithm for steady-state system optimization and parameter estimation

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Abstract
In this paper an algorithm is described which uses a steady-state mode! to determine the optimum operating point of a process. The model, which is not required to be an accurate representation of the real process, contains parameters to be estimated and the algorithm involves an iterative procedure between the two problems of system optimization and parameter estimation. Lagrangian analysis is employed to account for the interaction between the two problems, resulting in a procedure which may be regarded as a modified two-step approach in which the optimization objective index includes an extra term. The extra term contains a comparison between model and real process output derivatives and ensures that the optimal steady-state operating condition is achieved in spite of model inaccuracies. The algorithm is shown to perform satisfactorily in a digital simulation study concerned with determining food flow rate and temperature controller set points to maximize the net rate of return from an exothermic chemical reactor using a simplified non-linear model for system optimization and parameter estimation. The simulation is employed to investigate the convergence properties of the algorithm and to study the effects of measurement errors.