Nonlinear observer design and observability of an aerobic bioreactor using respirometry

In this work the observability analysis of the model of an aerobic bioreactor, used in the waste water treatment, with measurement of the dissolved oxygen concentration is carried out in order to decide if (theoretically) this variable can be used to globally estimate the state of the reactor. Although global observability can be asserted generically, except for some bad inputs that make some pairs of initial states undistinguishable, it cannot be concluded that an asymptotic observer exists for the system, at least for the good inputs. Furthermore there is no general method to design observers for observable systems. A review of several observer design techniques and their requirements is therefore made. This study shows that the requirements of none of the reviewed design methods are satisfied by the bioreactor and therefore none provides a global observer. Furthermore the velocity of convergence of the observers cannot be tuned up as desired. The results of this paper point out to the gap between the observability properties of a system and the existence of techniques to design an observer for a specific system.