Coupling framers to get enhanced interval observers. Application to growth rate estimation in a photobioreactor

This paper proposes strategies to couple a set of framers (called bundle of framers), that all give a state bounding provided that a bounding of the initial condition is known. We first show that the best state estimate can be used at any time to enhance the estimate of each framer. Then we show how to build a framer which provides the best estimate at any time. We introduce a bounded estimate within the framer bundle in order to ensure the boundness of the estimate and finally get an interval observer. This enhanced interval observer design is applied to the estimate of state variables in a photobioreactor, and especially to the specific growth rate evaluation. The microalgal model is Droop model, from which the dynamics of the growth and substrate uptake rates are derived. Various framers can be derived from this model, guarantying bounds on the prediction error. These framers are then coupled together and lead to an improved estimate.