Fault diagnosis for nonlinear systems represented by heterogeneous multiple models

This paper proposes two observer-based FDI strategies for nonlinear systems represented by a particular class of multiple model using heterogeneous submodels. The structure of this interesting multiple model is firstly presented in order to design two kinds of state observers. The first observer, known as proportional observer (PO), is an extension of the classic Luenberger observer, in this way, it can be used to obtain an estimation of the system state. The second proposed observer, known as proportional-integral observer (PIO), makes it possible the simultaneous state and unknown input (e.g. a fault) estimation of the system under investigation. The convergence towards zero of the estimation errors provided by these observers is investigated with the help of the Lyapunov method. The P observer as well as the PI observer are employed in a FDI strategy in order to accomplish the detection, the localisation and eventually the estimation of sensor faults acting on the system. These two strategies are finally validated in simulation by considering a simplified model of a bioreactor.