Estimation of uncertain models of activated sludge processes with interval observers

This paper deals with the designs of observers (software sensors) for uncertain models of wastewater treatment. We assume that the model (4 state variables) is such that the growth rate is unknown and other parameters (e.g. the organic concentration in the influent) are uncertain, i.e. we only know their upper and lower bounds. Given the measurements of the dissolved oxygen concentration, we build interval observers, giving dynamic bounds containing the variables to estimate. The width of these bounds are related to the width of the uncertainty bounds of the parameters. In some cases, we show that we can estimate exactly the unknown variables despite the uncertainties on the model.