Robust fault detection observer design for nonlinear distributed parameter systems

This paper addresses the problem of robust fault detection observer (FDO) design for a class of nonlinear distributed parameter systems described by partial differential equations (PDEs). Firstly, applying modal decomposition techniques, the PDE system can be transformed to an equivalent infinite-dimensional ordinary differential equations (ODE) system. Based on the spectrum of spatial differential operator, the ODE system can be represented by a finite-dimensional slow subsystem and a coupled infinite-dimensional fast subsystem. Subsequently, a finite-dimensional FDO is designed based on the slow subsystem such that the normal residual system is asymptotically stable for all admissible unknown nonlinear dynamics and fast subsystem dynamics. Then, the corresponding time-varying threshold is proposed to implement fault detection. Finally, numerical simulations are performed to demonstrate the effectiveness of the developed FDO design methodology.