Adaptive Optimal Control of Membrane Processes to Minimize Fouling

Abstract

This paper presents an adaptive optimal control algorithm to minimize membrane fouling and energy to deal with model uncertainty and disturbances in the characteristics of the water to be filtered. The Membrane BioReactor under interest is operated at constant flux and the objective is to minimize energy requirements such that the quantity of water filtered over a given period of time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{t}_{f}$</tex> equals <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{p}^{\ast}$</tex>. The algorithm is based on the iterative application of the optimal strategy initially proposed in [1] to account on input water characteristics changes. With such a modified control approach, it is shown in simulations that the ratios between filtration and backwash time periods adapt over the time to take account on unknown water input variations.