Integrating dynamic economic optimization and nonlinear closed-loop GPC: Application to a WWTP

Abstract

In this paper, a technique that integrates methods of dynamic economic optimization and real-time control by including economic model predictive control and closed-loop predictive control has been developed, using a two-layer structure. The upper layer, which consists of an economic nonlinear MPC (NMPC), makes use of the updated state information to optimize some economic cost indices and calculates in real time the economically optimal trajectories for the process states. The lower layer uses a closed-loop nonlinear GPC (NCLGPC) to calculate the control actions that allow for the outputs of the process to follow the trajectories received from the upper layer. This paper also includes the theoretical demonstration proving that the deviation between the state of the closed-loop system and the economically time varying trajectory provided by the upper layer is bounded, thus guaranteeing stability. The proposed approach is based on the use of nonlinear models to describe all the relevant process dynamics and cover a wide operating range, providing accurate predictions and guaranteeing the performance of the control systems. In particular, the methodology is implemented in the N-Removal process of a WWTP and the results demonstrate that the method is effective and can be used profitably in practical cases such as the chemical, refinery and petrochemical process industries.