Hierarchical nonlinear model predictive control with multi-time-scale for wastewater treatment process

Different time scales are inevitable for the controlled variables of wastewater treatment process (WWTP), which may degrade the operation performance or even destroy the stability of the closed-loop system. In this paper, a hierarchical nonlinear model predictive control (HNMPC) strategy is developed to deal with the different time scales of controlled variables to improve the operation performance of WWTP. The main merits of HNMPC are three-fold. First, a hierarchical control structure is developed to obtain reasonable control laws. Then, the controlled variables with different time scales can be tracked by different level controllers. Second, a gradient method is developed to solve the hierarchical optimization problem of HNMPC to reduce the computational cost. Then, the fast response of HNMPC can be achieved to improve the operation performance. Third, the stability of HNMPC is proved in theory. Then, the corresponding stability conditions are given to guide the practical application. Finally, the testing results on the benchmark simulation model verify that the proposed HNMPC can achieve suitable operation performance in terms of control accuracy. • In this work, a hierarchical nonlinear model predictive control (HNMPC) strategy is developed to deal with the different time scales of control variables to improve the operation performance of wastewater treatment process. • Firstly, a hierarchical control structure is developed to obtain reasonable control laws. Then, the control variables with different time scales can be tracked by different level controllers. • Secondly, a gradient method is developed to solve the hierarchical optimization problem of HNMPC to reduce the computational cost. Then, the fast response of HNMPC can be achieved to improve the operation performance. • Thirdly, the stability of HNMPC is proved in theory. Then, the corresponding stability conditions are given to guide the practical application.