Fault Estimation for Nonlinear Dynamic System Based on the Second-Order Sliding Mode Observer

This paper is concerned with the problem of fault estimation for a class of Lipschitz nonlinear systems. In order to settle the chattering problem caused by traditional sliding mode observer for fault estimation, a second-order sliding mode observer is proposed on the basis of the super-twisting algorithm. Firstly, linear coordinate transformations are introduced to decouple the fault signal from the system. Secondly, the Lyapunov function approach is applied to derive the criteria guaranteeing the stability of the observer error dynamic system. The obtained results eliminate the cumbersome proving process for the stability of the super-twisting algorithm by the geometric method. Thirdly, an estimation of the fault is generated by the proposed second-order sliding mode observer. Furthermore, only the output information of the system and observer is necessary for fault estimation. Finally, a robotic arm system is employed to show the effectiveness of the proposed fault estimation method.