Fixed-time convergence of second-order nonlinear systems based on nonsingular fractional sliding mode

Cheng Lei, Y. Lan, Yunpeng Sun, Zelai Xu, Xiaolei Shi
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Abstract

In this paper, a fixed-time convergence scheme for fractional sliding modes is proposed for nonlinear second-order systems. Firstly, a fixed-time fractional-order sliding mode surface is designed by combining the fixed-time theory with fractional-order sliding mode control, which has a faster convergence rate and less chattering. Secondly, the proposed sliding mode controller is applied to a class of second-order nonlinear systems subject to uncertainties and external perturbations to ensure that the system is globally robust fixed-time stable. Then, a continuous fractional order approach law is designed and the proposed sliding mode controller is shown to converge in fixed time by Lyapunov function and the convergence time is related to the choice of controller parameters. Finally, the fixed-time fractional-order sliding mode control strategy is applied to a second-order nonlinear magnetic levitation system system, and the simulation results verify the effectiveness of the proposed method.
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基于非奇异分数滑动模式的二阶非线性系统的固定时间收敛性
本文针对非线性二阶系统提出了分数滑模的固定时间收敛方案。首先,通过将固定时间理论与分数阶滑动模态控制相结合,设计了一种固定时间分数阶滑动模态面,它具有更快的收敛速度和更小的颤振。其次,将所提出的滑模控制器应用于一类受不确定性和外部扰动影响的二阶非线性系统,以确保系统具有全局鲁棒的定时稳定性。然后,设计了连续分数阶方法定律,并通过 Lyapunov 函数证明了所提出的滑模控制器在固定时间内收敛,且收敛时间与控制器参数的选择有关。最后,将固定时间分数阶滑动模态控制策略应用于二阶非线性磁悬浮系统,仿真结果验证了所提方法的有效性。
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