【目的】针对激光跟踪仪永磁直流力矩电机(PMDCTM)伺服系统中，传统比例积分微分(PID)控制因参数变化、外部干扰及非线性摩擦等因素导致的轨迹跟踪精度不足及高频抖振显著等问题，提出了一种基于自适应切换增益的PMDCTM位置环非奇异终端滑模控制(NTSMC)方法。【方法】首先，基于激光跟踪仪方位轴电机的机电模型建立了基于角度误差的状态空间表达式；其次，选用分数阶次的饱和函数滑模面，并结合自适应控制思想设计了自适应增益的切换律，在避免奇异性的基础上，有效抑制了系统中的不确定性因素；最后，通过Lyapunov稳定性理论证明了控制系统的有限时间收敛特性，并且探索了本文设计的滑模面参数与系统收敛速度的关系。【结果】利用Matlab/Simulink软件以及增强型可编程多轴控制器平台进行仿真与试验对比，结果表明，在表征系统快速性的阶跃响应中，基于自适应非奇异终端滑模控制(ANTSMC)的PMDCTM位置环阶跃响应收敛时间较NTSMC缩短41.2%，较PID控制缩短66.3%；在跟踪仪方位轴电机换向的应用场景中，基于ANTSMC的PMDCTM位置环瞬时跟踪误差峰值较NTSMC缩短37.2%，较PID控制缩短76.9%，且大幅减少了到达稳态后的抖振，系统抵抗外部扰动的能力显著增强。【结论】本文所提ANTSMC方法能够有效提高PMDCTM位置环的控制精度，增强激光跟踪仪伺服系统的动态响应能力，减弱抖振现象，表现出优异的鲁棒性。

[Objective] This study aims to address the issues of insufficient trajectory tracking accuracy and significant high-frequency chattering in permanent magnet direct current torque motor (PMDCTM) servo systems of laser trackers, which are caused by parameter variations, external disturbances, and nonlinear friction in conventional proportional-integral-derivative (PID) control. An nonsingular terminal sliding mode control (NTSMC) method with adaptive switching gain is proposed for PMDCTM position loop. [Methods] Firstly, a state-space representation based on angular error was developed using the electromechanical model of the azimuth axis motor in the laser tracker. Next, a fractional-order saturated function was selected as the sliding mode surface, and an adaptive switching gain law was designed by integrating adaptive control theory. This design effectively mitigated system uncertainties while avoiding singularities. Finally, the finite-time convergence of the control system was verified using Lyapunov stability theory, and the relationship between the designed sliding mode surface parameters and system convergence speed was analyzed. [Results] Comparative simulations and experiments were conducted using Matlab/Simulink software and enhanced programmable multi-axis controller platform. The results showed that, in the step response characterizing system rapidity, the PMDCTM position loop based on adaptive NTSMC (ANTSMC) reduced the convergence time by 41.2% compared to NTSMC and by 66.3% compared to PID control. In the application scenario of commutation of the tracker's azimuth axis motor, the ANTSMC-based PMDCTM position loop demonstrated a 37.2% reduction in peak transient tracking error compared to NTSMC and 76.9% reduction compared to PID control. Furthermore, the steady-state chattering was significantly reduced, thereby enhancing the system's ability to resist external disturbances. [Conclusion] The proposed ANTSMC method effectively improves the control accuracy of PMDCTM position loop, enhances the dynamic response performance of laser tracker servo systems, mitigates chattering phenomena, and demonstrates excellent robustness.

四川省国防科技工业领域XX项目(J0024-2325-QT)