As for any industrial process, models in biological wastewater treatment have an important role in the process design and the determination of optimal operating conditions. The Sequencing Batch Reactor (SBR) is a process of increasing importance in aerobic bioreactors for the industrial wastewater treatment, in which temporal sequences of phases take place in a single reactor. Indeed, this sequencing process can be considered as a hybrid system. Each phase represents a continuous dynamics, and the changes of phase can be considered as discrete events or switches of continuous systems. Hence the SBR is a single formalism combining continuous and discrete systems simultaneously, well known as hybrid system. This paper proposes a methodology for the time optimal control of the SBR process from the hybrid point of view, by using reach set computation.
Fibrianto, H., & Dochain, D. (2002). Time Optimal Control of the Swiched Continuous Hybrid Model of an Aerobic Biological Waste Water Treatment Process. International Journal of Hybrid Systems, 2(3), 207-220. https://hdl.handle.net/2078.5/60172 (Original work published 2002)