Fault Estimation for T-S Fuzzy Fractional-Order Systems With Multiple Faults Based on Adjustable-Order Observer

Abstract

This paper addresses the fault estimation (FE) issue for a kind of nonlinear fractional-order systems affected by unknown inputs, disturbances and multiple faults. Firstly, the T-S fuzzy method is adopted to approximate the nonlinear fractional-order dynamics, which makes our scheme different from the existing FE methods required to satisfy the Lipschitz constraint. Secondly, the system states, process faults and sensor faults are augmented into a new state vector to achieve the simultaneous estimation of the system states and multiple faults. Meanwhile, to meet different needs in practical engineering applications, an adjustable-order observer is designed. Specifically, the order of this observer can be flexibly selected by the designer within a specific range, achieving a trade-off between estimation accuracy and cost, which is unattainable by a fixed-order observer. Additionally, the given observer can also decouple the unknown input from the error dynamic. The final results on the boundedness of error systems are presented in the form of linear matrix inequalities (LMIs). At last, the effectiveness and practicability of the proposed method are verified through two examples. Note to Practitioners—This paper aims to achieve fault estimation (FE) for T-S fuzzy fractional-order systems affected by unknown inputs, disturbances and multiple faults. The practical significance is mainly reflected in two aspects. Firstly, many actual physical processes (such as electrochemical processes and viscoelastic materials) inherently exhibit fractional-order dynamic characteristics and are generally accompanied by nonlinear phenomena. To more accurately describe such systems and be closer to engineering practice, we thus study nonlinear fractional-order dynamics and utilize the T-S fuzzy model to handle nonlinear terms. Secondly, in the face of increasingly complex industrial systems, it is crucial to strike a balance between estimation cost and estimation accuracy. This paper establishes a novel adjustable-order observer design method. Unlike traditional fixed-order observers, this method allows engineers to flexibly select the order of the observer within a specific range according to actual needs. This design not only achieves effective estimation of concurrent faults in actuators and sensors but also breaks the constraints of existing fixed-order methods, providing a more flexible solution for fault diagnosis in complex systems.