Fixed-time disturbance observers-based fault-tolerant control for a class of nonlinear systems with prescribed performance

This paper explores the issue of fault-tolerant control for a class of nonlinear systems that encounter the actuator fault and external disturbances. The uncertainties arising from the actuator fault and external disturbances are treated as lumped uncertainties, and fixed-time observers are designed to observe them. The fault-tolerant controller with full-state constraints is then developed using the fixed-time backstepping method, integrating the Improved Prescribed Performance Function (IPPF) method and the Barrier Lyapunov Function (BLF) method. Additionally, command filters with error compensations are devised to resolve the 'explosion of complexity' problem during the controller derivation process. The parameters of the designed controller are optimised using the Northern Goshawk Optimization (NGO) algorithm to enhance nonlinear systems' dynamic performance. Lastly, the validity and practicality of the proposed approach are verified through the comparative study of simulations and experiments, with the permanent magnet synchronous motor (PMSM) position system employed as a case study.