State estimation of two-time scale multiple models with unmeasurable premise variables. Application to biological reactors

International audience; This paper deals with the problem of the state estimation of a nonlinear system. The system under study is characterized by a two-time scale model. The state estimation is performed by designing a proportional integral observer (PIO) with unknown inputs. In order to design such an observer, the nonlinear system is transformed into an equivalent multiple model form and the fast dynamics are considered as unknown inputs. An application to an ASM1 model of Wastewater Treatment Plants (WWTP) is considered and the obtained numerical results show the performances of the proposed approach.