Robust fuzzy fault estimation based on decoupled transform and unknown input sliding mode observer

In this study, a novel fuzzy unknown input observer for robust fault estimation scheme is developed when both faults and unknown input are considered. The proposed scheme includes component fault with nonlinear distribution matrix in state equation, unknown input signal in state and output equations. After that, Takagi-Sugeno (T-S) model is used to create multiple models. While T-S model is used for only the nonlinear distribution matrix of the fault signal, a larger category of nonlinear system will be included. Two set of observers are considered, the first one is extended fuzzy unknown input observer (EFUIO) and the other one is fuzzy sliding mode observer (FSMO). The approach decoupled the faulty subsystem from the rest of the system through a series of linear transformations. Then, the objective is to design EFUIO to guarantee the asymptotic stability of the error dynamic using the Lyapunov method. Unknown input is removed; meanwhile, FSMO is designed for faulty subsystem to guarantee estimation of fault. Sufficient conditions are established in order to guarantee the convergence of the state estimation error and the results are formulated in the form of linear matrix inequalities (LMIs). Finally, a simulation study on an electromagnetic suspension system (EMS) is presented to demonstrate the performance of the results compared with a pure SMO.