| The objective of this work is to develop an optimization strategy that is capable of solving large (>1000 differential-algebraic equations) optimization problems, while making use of existing nonlinear programming (NLP) problem formulations, differential-algebraic equation (DAE) solvers, and NLP strategies that are already in widespread use in industry. In contrast to current dynamic optimization approaches, this approach applies an adjoint strategy for the calculation of objective function and constraint gradients.; Furthermore, we consider two constraint aggregation approaches, the Kreisselmeier-Steinhauser (KS) function and the smoothed penalty function, for state variable constraints. The advantage of this aggregation is to reduce the burden in the calculation of the adjoint system. The resulting implementation has a significant advantage over current strategies that rely on the solution of sensitivity equations, especially for large dynamic optimization problems. Performance of this approach is demonstrated on several dynamic optimization problems in process engineering.; Also, we develop the model for a large industrial problem based on the cryogenic air separation unit (ASU) separation problem. The equations are reformulated for use with the dynamic optimization strategy developed here. Results for an ASU ramping optimization problem are shown for a set of unconstrained and constrained (individual and KS function) examples. These results demonstrate the potential of the proposed methodology for dynamic process optimization. |
