Event-driven time-optimal control for a class of discontinuous bioreactors

Discontinuous bioreactors may be further optimized for processing inhibitory substrates using a convenient fed-batch mode. To do so the filling rate must be controlled in such a way as to push the reaction rate to its maximum value, by increasing the substrate concentration just up to the point where inhibition begins. However, an exact optimal controller requires measuring several variables (e.g., substrate concentrations in the feed and in the tank) and also good model knowledge (e.g., yield and kinetic parameters), requirements rarely satisfied in real applications. An environmentally important case, that exemplifies all these handicaps, is toxicant wastewater treatment. There the lack of online practical pollutant sensors may allow unforeseen high shock loads to be fed to the bioreactor, causing biomass inhibition that slows down the treatment process and, in extreme cases, even renders the biological process useless. In this work an event-driven time-optimal control (ED-TOC) is proposed to circumvent these limitations. We show how to detect a "there is inhibition" event by using some computable function of the available measurements. This event drives the ED-TOC to stop the filling. Later, by detecting the symmetric event, "there is no inhibition," the ED-TOC may restart the filling. A fill-react cycling then maintains the process safely hovering near its maximum reaction rate, allowing a robust and practically time-optimal operation of the bioreactor. An experimental study case of a wastewater treatment process application is presented. There the dissolved oxygen concentration was used to detect the events needed to drive the controller.