Robust TS Fuzzy-based Sliding Mode Observer Design for Actuator Fault Reconstruction: Non-quadratic Lyapunov Function Approach

This paper proposes a sliding mode observer (SMO) for actuator fault reconstruction of nonlinear systems subjected to external disturbance. In the proposed approach, first, the nonlinear system is modelled by a Takagi-Sugeno fuzzy model with immeasurable premise variables. Then, SMO is used to estimate the states and fault. Finally, by using a non-quadratic Lyapunov function (NQLF), the stability of the error system is proved. By considering  performance criteria, the effect of the exogenous disturbance on the state estimations is minimized which provides effective fault estimation. Furthermore, the states and fault estimations asymptotically converge to their actual values for the non-perturbed systems. In the stability analysis and the observer gains design, some change of coordinates are proposed which the transformation matrix of one of them is obtained by solving linear matrix inequalities (LMIs). The proposed approach has some superiority over the existing methods. First, employing the NQLF leads to more relaxed results and better estimation performance. Second, using SMO for fault reconstruction makes the proposed approach insensitive to the uncertainties and unknown inputs and besides detecting the fault, its shape and size are determined. Third, since the premise variables are assumed to be unmeasurable, the presented approach is applicable for a wide class of nonlinear systems. Finally, a continuous stirred tank reactor (CSTR) process is considered and numerical simulation is carried out to illustrate the effectiveness and the accuracy of the proposed approach comparison with the recently published methods.