A hierarchical approach to optimal control of a hybrid chromatographic batch process*

AbstractIn this paper we consider a hierarchical approach to solve an optimal control problem for a hybrid chromatographic batch process. The plant consists of several chromatographic columns which can be connected in an arbitrary way. The plant configuration can therefore be considered as a discrete-valued control input. The dynamics of each chromatographic column is described by two coupled nonlinear partial differential equations. Hence, we have a hybrid optimisation problem with highly nonlinear dynamics.To handle complexity, we propose a hierarchical two-level optimisation scheme: first, we solve a number of continuous optimisation problems that correspond to fixed configurations. In a subsequent step, on the basis of these solutions, we solve a discrete optimisation problem to generate the optimal configuration or configuration signal.Because of the imposed structure, we can of course not expect the overall solution to be optimal. However, we demonstrate that, by using the plant configuration as an an additional control input, performance may be considerably improved when compared to the constant configuration scenario.