Economic performance analysis in the design of on-line batch optimization systems

In this paper, the on-line optimization of batch reactors under parametric uncertainty is considered. A method is presented that estimates the likely economic performance of the on-line optimizer. The method of orthogonal collocation is employed to convert the differential algebraic optimization problem (DAOP) of the dynamic optimization into a nonlinear program (NLP) and determine the nominal optimum. Based on the resulting NLP, the optimization steps are approximated by neighbouring extremal problems and the average deviation from the true process optimum is estimated dependent on the measurement error and the parametric uncertainty. The true process optimum is assumed to be represented by the optimum of the process model with the true parameter values. A back off from the active path and endpoint inequality constraints is determined at each optimization step which ensures the feasible operation of the process. Based on the analysis results the optimal structure of the optimizer in terms of measured variables and estimated parameters can be determined. The method of the average deviation from optimum is developed for the fixed terminal time case and for time optimal problems. In both cases, the theory is demonstrated on an example.