Nonlinear Model Predictive Control for Index—one DAE Systems

Abstract

In this paper the nonlinear model predictive control (NMPC) prob­lem for systems described by index-one differential algebraic equations (DAEs) is considered. It is shown, that with no or only minor modifications most of the NMPC schemes for ordinary differential equations can be used in the index-one DAE case and that they also guarantee stability. For the quasi-infinite horizon NMPC concept and the dual-mode control, however, the procedures to compute appropriate terminal penalty terms and terminal regions must be modified for the index-one DAE case and are presented here. The resulting quasi-infinite horizon NMPC scheme for index-one DAEs is demonstrated us­ing a nontrivial process control example, namely the control of a high-purity binary distillation column with 40 trays. To make real-time application fea­sible, a nonlinear reduced order DAE model for the column based on nonlin­ear wave propagation phenomena is introduced. Simulations show promising closed-loop behavior while the on-line computational load permits real-time implementation.