Payload variations, friction, and external disturbances deteriorate the control performance of linear motor (LM) positioners. To provide high-speed and high-precision performance for the LM, an adaptive recursive terminal sliding-mode (ARTSM) controller is proposed in this article. For the controller, a fast nonsingular terminal sliding function and a recursive integral terminal sliding function are developed in a recursive structure such that the sliding surfaces are arrived successively and ultimately the tracking error can converge to zero in a finite time. Furthermore, by setting an appropriate initial value for the integral element of the ARTSM controller, the control system is enforced to start on the sliding surface at the initial time such that the reaching time is reduced. Stability analysis is presented to prove the finite-time convergence and zero tracking error of the closed-loop system under the proposed ARTSM controller. Experimental results also demonstrate the effectiveness of the controller in terms of significantly reduced tracking errors and faster disturbance rejection in comparison with a recently reported fast nonsingular terminal sliding-mode (FNTSM) controller for the LM positioner.

中文翻译：

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使用自适应递归终端滑动模式的线性电机定位器的有限时间控制

有效载荷变化、摩擦和外部干扰会降低线性电机 (LM) 定位器的控制性能。为了为 LM 提供高速和高精度的性能，本文提出了一种自适应递归终端滑模 (ARTSM) 控制器。对于控制器，在递归结构中开发了快速非奇异终端滑动函数和递归积分终端滑动函数，使得滑动面连续到达，最终跟踪误差可以在有限时间内收敛到零。此外，通过为ARTSM控制器的积分元素设置适当的初始值，控制系统被强制在初始时间在滑动表面上启动，从而减少到达时间。稳定性分析被提出以证明在所提出的ARTSM控制器下闭环系统的有限时间收敛和零跟踪误差。与最近报道的用于 LM 定位器的快速非奇异终端滑模 (FNTSM) 控制器相比，实验结果还证明了控制器在显着减少跟踪误差和更快干扰抑制方面的有效性。