Robust Fault Estimation and Fault‐Tolerant Control for a Class of Fuzzy Singularly Perturbed Systems With State Time Delay Based on Learning Observer

• Published in: International journal of adaptive control and signal processing Vol. 38; no. 12; pp. 3865 - 3882
• Main Authors: Liu, Wei, Sun, Chao, Huang, Shengjuan, Yi, Suhuan
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.12.2024; Wiley Subscription Services, Inc
• Subjects: Actuators; Control systems; dynamic output fault‐tolerant control; Dynamic stability; Fault tolerance; Fuzzy control; Fuzzy systems; Learning; learning observer; Liapunov functions; Output feedback; Parameter estimation; Robust control; robust fault estimation; Singular perturbation; singularly perturbed systems; Time lag; T–S fuzzy models
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.3917

ABSTRACT This article studies the problem of fault estimation (FE) and dynamic output fault‐tolerant control (DOFTC) for a class of Takagi–Sugeno (T–S) fuzzy singularly perturbed systems (SPSs) which subject to time delay, external disturbance and actuator fault. A new fault estimation and fault‐tolerant control scheme was proposed and designed for the influence of the change of perturbation parameter ε$$ \varepsilon $$ on the singularly perturbed system. This scheme adopts the Takagi–Sugeno (T–S) fuzzy model, learning observer and dynamic output feedback fault‐tolerant mechanism, so that the system has multi‐time‐scale dynamic stability. The results show that this method has more accurate estimation effect, faster convergence speed, and very fast steady‐state response of fault‐tolerant control when faults occur. Furthermore, when constructing the Lyapunov function, the improved matrix P(ε)$$ P\left(\varepsilon \right) $$ was selected to ensure that the closed‐loop system is stable for all ε∈(0,ε‾]$$ \varepsilon \in \left(0,\overline{\varepsilon}\right] $$, and at the same time, the conservativeness of the results was reduced. Finally, the feasibility and correctness of the proposed design method were illustrated through two numerical examples. This paper proposes a new fault estimation and fault‐tolerant control scheme for the influence of perturbation parameter changes on singularly perturbed systems. By adopting the learning observer and dynamic output feedback fault‐tolerant mechanism, and solving it through the improved and constructed Lyapunov function, this method can ensure the simultaneous stability of the system under different time‐scale systems. The results show that the proposed method has a more accurate estimation effect, faster convergence speed, and very fast steady‐state response of fault‐tolerant control when faults occur.