Non-fragile sliding mode observer based fault estimation for interval type-2 fuzzy singular fractional order systems
Xuefeng Zhang, Jin‐Xi Zhang, Wenkai Huang, Peng Shi
Abstract
In this paper, an interval type-2 fuzzy model is presented to describe the nonlinear singular fractional order systems (SFOSs) with 0<α<2. The problem of actuator and sensor fault estimation is addressed by designing a non-fragile sliding mode observer (SMO). Firstly, a new criterion is provided to analyse the admissibility of SFOSs, which does not need to divide the fractional order interval (0,2) into interval (0,1) and interval [1,2) to study them separately. Then, by expanding the dimension of the SFOS, the non-fragile SMO and the sliding surface are constructed and the accurate estimations of faults and the SFOS state simultaneously are achieved. A new reaching law is designed, which can divide the process of the system moving to the sliding surface into three stages. Further the control law is constructed to guarantee the observation error reaches the sliding surface in finite time. Finally, three examples show the effectiveness of the proposed scheme.