Economic model predictive control based on lattice trajectory piecewise linear model for wastewater treatment plants. (April 2023) - Huang, Yating; Xu, Jun; Liu, Jinfeng; Lou, Yunjiang
Abstract: Economic model predictive control (EMPC) is an effective control strategy for wastewater treatment plants (WWTPs), which are crucial for preventing water pollution and improving the water quality. However, industrial processes typically involve large-scale nonlinear and strongly coupled systems, and it is computationally expensive to solve nonlinear optimization problems based on nonlinear prediction models such as EMPC. In this study, to facilitate the application of EMPC to large-scale nonlinear systems such as WWTPs, the lattice trajectory piecewise linear (PWL) model is used to approximate the nonlinear system with a predefined error bound. The resulting optimization problem can be expressed as a continuous PWL programming problem if the cost function of the EMPC is linear. Therefore, an iterative descent algorithm is proposed to transform the PWL programming problem into a series of linear programming problems. The stability of the nonlinear system operating under EMPC is analyzed. The EMPC scheme based on the lattice trajectory PWL model is applied to a WWTP benchmark problem, in which the state is 78-dimensional and the EMPC cost is linear. The proposed strategy outperforms the EMPC schemes based on the nonlinear prediction model and trajectory PWL prediction model. Overall, the EMPC scheme based on the lattice trajectory PWL prediction model can improve the computational efficiency of optimization problems while ensuring control performance. Highlights: Lattice trajectory piecewise linear approximation of the wastewater process. A novel descent algorithm is proposed for piecewise linear programming problem. Stability of the nonlinear wastewater process is proved. The efficacy of the proposed strategy is shown through simulation.