Observer-based sensor fault estimation in nonlinear systems

Sensor bias faults and sensor gain faults are two important types of faults in sensor. Simultaneous estimation of these sensor faults in nonlinear systems in the presence of input disturbance and measurement noise is challenging and has not been adequately addressed in literature. Hence, this article develops an observer-based sensor fault estimation method for generalized sector-bounded nonlinear systems in the presence of input disturbance and measurement noise. A generalized sector-bounded nonlinearity was chosen because it encompasses a wide range of nonlinearities including Lipschitz, positive real, and dissipative. This article presents necessary and sufficient conditions to achieve a suboptimal cost for a cost function consisting of the sum of the square integrals of the estimation errors to the square integrals of the disturbances in the form of linear matrix inequality. The linear matrix inequality can be solved offline to explicitly calculate observer gain, and the resulting observer simultaneously estimates the system states as well as both bias and gain faults in the sensors. Compared to previous literature, the proposed methodology is designed to work in the presence of both input disturbance and measurement noise. Additionally, this article considers a generalized sector-bounded nonlinearity which encompasses a variety of different physical nonlinearities. Furthermore, the observer does not require the online solution of the Riccati equation and is thus computationally less intensive compared with the methods of extended Kalman filtering. The observer design procedure is demonstrated through two illustrative examples consisting of a fourth-order double spring-mass system and a third-order wind turbine power transmission mechanism.