Near optimal interval observers bundle for uncertain bioreactors

In this paper we design an interval observer for the estimation of unmeasured variables of uncertain bioreactors. The observer is based on a bounded error observer, as proposed in [1], that considers a loose approximation of the growing rate. We first show how to generate guaranteed upper and lower bounds on the state, provided that known intervals for the initial condition and the uncertainties are available. These so called “framers” depend on a tuning gain. They can be run in parallel and the envelope provides the best estimate. An optimality criterion is introduced leading to the definition of an optimal observer. We show that this criterion provides straightforwardly a gain set containing the best framers. The method is applied to the estimation of the total biomass of an industrial wastewater treatment plant, demonstrating its efficiency.