The purpose of this study is to develop an integral sliding mode intelligent fractional-order backstepping controller based on a fixed-time extended state observer (ISMIFOBC-ESO) to control warp tension. First, the time-varying mathematical model of the let-off system was studied and converted into the state equation. Due to the parameter uncertainty and healed motion of the let-off system, the total external disturbance of the system is unknown. We designed a fixed-time extended state observer to deal with this situation, the estimated total interference is updated into the control algorithm in real time to reduce the tracking error. The nonlinear integral sliding surface is designed and integrated into the backstepping control to ensure the finite time convergence and stability of the algorithm. The fractional-order theory with more degrees of freedom is introduced further to enhance the control accuracy and robustness of the algorithm, the stability is proved by the Lyapunov theorem and the control law is designed. The simulation experiment verifies the effectiveness of the designed scheme compared with the other two controllers in the case of sinusoidal-like signals and step signals.
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