Genetic Hybrid Predictive Controller for Optimized Dissolved-Oxygen Tracking at Lower Control Level

A hierarchical two-level controller for dissolved-oxygen reference trajectory tracking in activated sludge processes has been recently developed and successfully validated on a real wastewater treatment plant. The upper level control unit generates trajectories of the desired airflows to be delivered by the aeration system to the aerobic zones of the biological reactor. A nonlinear model predictive control algorithm is applied to design this controller. The aeration system itself is a complicated hybrid nonlinear dynamical system. The lower level controller (LLC) forces the aeration system to follow these set-point trajectories, minimizing a cost of energy due to pumping of the air and accounting for system operational limitations such as the limits on the allowed frequency of switching of the blowers and on their capacity. The predictive control is also applied to design the LLC based on a piecewise-linearized hybrid dynamics of the aeration system. Casting the mixed-integer nonlinear optimization problem under heterogeneous constraints due to the limits on the blower switching frequency into the approximated mixed-integer form is done at a cost of introducing large number of auxiliary variables into the lower level predictive controller optimization task. This paper derives another nonlinear hybrid predictive control algorithm for the LLC. It is directly based on the nonlinear hybrid dynamics and logical formulation of the switching constraint. A genetic algorithm is derived with dedicated operators allowing for efficient handling of the switching constraint and nonlinear hybrid system dynamics. The efficiency of the control algorithm is validated by simulation based on real data records.

I. Introduction

An activated sludge wastewater treatment plant can be classified as a complex system due to its nonlinear dynamics, large uncertainty, multiple time scales in the internal process dynamics, and multivariable structure. In addition, rather limited measurements are available during plant operation.