Bilinear black-box identification and MPC of the activated sludge process

In this paper the activated sludge process, which is a process for biological nitrogen removal in municipal wastewater treatment plants, is modeled as a discrete-time bilinear system by application of a recursive prediction error method system identification technique. A novel bilinear model predictive control algorithm is also derived and applied on a simulation model of the activated sludge process. For discrete-time bilinear systems, a quadratic cost on the predicted outputs and inputs, together with input/state constraints, results in a nonlinear non-convex optimization problem. An investigation is performed where the suggested control algorithm is compared with a linear counterpart. The results reveals that even though the identified bilinear black-box model describes the dynamics of the activated sludge process better than linear black-box models, bilinear model predictive control only gives moderate improvements of the control performance compared to linear model predictive control laws.