Abstract The control performance of linear motor (LM) is deteriorated by payload variations, friction, and external disturbances. In this paper, a robust recursive sliding mode controller combined with an adaptive disturbance observer (RSM-ADO) is proposed for the high-speed and high-precision control of an LM positioner. The benefits of the proposed ADO lie in that it can be designed without the need for the upper bound information of the disturbance and its derivative. Hence, the ADO is ideally capable of rejecting any time-varying disturbances. Furthermore, a recursive integral sliding surface is constructed for the RSM controller such that the reaching phase is eliminated. Benefiting from the proposed recursive structure, the tracking error can converge to zero in finite time. Besides, system chattering is eliminated in the reaching control input due to the integral element. Lyapunov analysis is investigated to prove the finite time convergence of the tracking error under the proposed RSM-ADO control scheme. Experiments demonstrate the superior property of stronger robustness and fewer chattering effects of the proposed method compared to existing disturbance observers and adaptive recursive terminal sliding mode (ARTSM) controller.

中文翻译：

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具有自适应扰动观测器的线性电机定位器递归滑模控制

摘要 直线电机 (LM) 的控制性能会因有效载荷变化、摩擦和外部干扰而恶化。在本文中，提出了一种结合自适应扰动观测器 (RSM-ADO) 的鲁棒递归滑模控制器，用于 LM 定位器的高速和高精度控制。所提出的 ADO 的好处在于它可以在不需要扰动及其导数的上限信息的情况下进行设计。因此，理想情况下，ADO 能够拒绝任何时变干扰。此外，为 RSM 控制器构造了一个递归积分滑动面，从而消除了到达阶段。受益于所提出的递归结构，跟踪误差可以在有限时间内收敛到零。除了，由于积分元件，在到达控制输入中消除了系统颤动。研究 Lyapunov 分析以证明在所提出的 RSM-ADO 控制方案下跟踪误差的有限时间收敛。实验证明，与现有的干扰观测器和自适应递归终端滑模（ARTSM）控制器相比，所提出的方法具有更强的鲁棒性和更少的颤振效应。