Control strategy for single-layer warp tension in a carbon fiber 3D loom based on fixed-time theory and sliding mode theory

The stable control of warp tension in a carbon fiber three-dimensional (3D) loom plays a decisive role in the performance of 3D woven fabrics. Aiming at nonlinear, time-varying, and strongly coupled characteristics of the warp tension system, the stable control of warp tension is carried out based on fixed-time theory and sliding mode theory. First, the mathematical model of the tension system is established by taking into account the influence of the beating-up mechanism and shedding mechanism as the unmodeled part. Then, according to the characteristics that only warp tension in the system can be measured, the unmodeled part and external disturbance are regarded as a lumped disturbance. After analysis, a fixed-time extended state observer (FESO) is proposed to observe the lumped disturbance and unmeasured system state. Second, relying on the observed results, a novel logarithmic fixed-time fast convergent sliding surface (LF-FCSS) is constructed. Subsequently, based on this sliding surface, a non-singular sliding mode controller (NS-SMC) is designed, which allows the tension tracking error to converge rapidly while weakening the buffeting phenomenon and eliminating the singularity of the controller. Stability proof of the closed-loop system is given theoretically, which ensures that warp tension can be controlled stably. Finally, simulation models are built in Simulink to verify the fast convergence performance of the proposed sliding surface and the effectiveness of the non-singular controller. The superiority of the proposed control strategy is proved by comparing it with the existing methods of sliding mode control in the literature.