Optimal control and estimation of activated sludge plants

Abstract

Wastewater treatment is facing unprecedented challenges due to stricter effluent requirements, costs minimisation, sustainable reuse of water, nutrients, and other resources, as well as increasing expectations in the public to attain high service standards. Due to their wide diffusion, activated sludge processes play a key role in the biological treatment of wastewater and their efficient operation has a large technological and societal impact. The discipline of control theory offers the mathematical framework for steering wastewater treatment systems toward a desired state. Model predictive control (MPC) and moving horizon estimation (MHE) have been the chosen technologies for many industrial applications, including treatment plants. In this work, the dynamical properties and optimal operation of activated sludge plants are investigated. For the first task, the dynamical system consisting of 145 state variables, 13 controls, 14 disturbances, and 15 outputs, is mapped onto complex networks in which full-state controllability and observability properties are studied, from both a structural and a classical point of view. For the second task, optimal control and estimation strategies are designed for operating an activated sludge plant for both wastewater treatment and reuse operations. In wastewater reuse, a zero-offset predictive controller is designed to operate the plant when it is required to produce water of tailored quality to be used for agricultural crop fertigation. The optimal control and estimation problems are solved through the direct transcription method consisting of converting the problems into nonlinear programs, then solving them numerically. According to our results, activated sludge plants are only controllable in a structural sense, being uncontrollable in the conventional sense and unobservable both in the structural and conventional sense. Being stable under the conventional operation, these processes are still stabilizable and detectable, despite their control and observation being qualified as high-demanding tasks. We present and discuss the simulation results for a predictive controller that is capable to improve the performance of the plant for wastewater treatment under different influent regimes. Then, we show and discuss the results for a zero-offset controller that is capable to track a reference trajectory under constant influent conditions, albeit being only partially capable to track these set-points under dynamic influent. Finally, results are presented for the output model predictive controllers based on partial, noisy, measurements of the plant’s internal state.