Trajectory tracking control of micro positioning platform based on dynamic sliding mode
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摘要:
音圈电机驱动的微定位平台作为高精密度运动平台，被广泛应用于精密加工、微机电等领域. 针对音圈电机驱动的微定位平台的高精度平稳跟踪控制问题，结合归一法和理论建模的参数建立具有参数不确定性的二阶微分方程数学模型，以柔性机构实际位移作为输入，平台控制率作输出；鉴于模型参数不确定的特点，通过建立误差的二阶滑模面，提出基于动态滑模的微定位平台跟踪控制，通过李雅普诺夫稳定性理论获得系统稳定的结论. 通过平台试验对比分析提出的控制算法，结果表明提出的动态滑模控制算法在保证较小抖振的前提下，都能完成轨迹跟踪，跟踪精度比传统滑模提高13.4%和4%，且跟踪更平稳，具有良好的工程前景.
Abstract:As a high-precision motion platform, the micro positioning platform driven by the voice coil motor is widely used in precision machining, micro-electromechanical and other fields. Aiming at the high-precision and stable tracking control problem of the micro positioning platform driven by the voice coil motor, combining normalization method with theoretical modeling parameters, a mathematical model of second-order differential equation with parameter uncertainties was established, and the actual displacement of the flexible mechanism was taken as input and the platform control rate was taken as output. In view of the uncertain characteristics of the model parameters, the second-order sliding mode surface of the error was established to propose tracking control of micro positioning platform based on dynamic sliding mode, and the conclusion of system stability through Lyapunov's stability theory was obtained. The proposed control algorithm was analyzed by platform test comparison, the results show that the proposed dynamic sliding mode control algorithm can complete the trajectory tracking with less chatter. The tracking accuracy of the algorithm has improved by 13.4% and 4% compared to traditional sliding mode control, which has a smoother tracking and a good engineering prospects.
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Key words:
- micro positioning platform /
- dynamic sliding mode /
- motor driven /
- trajectory tracking
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图 5 不同控制器作用下轨迹跟踪变化曲线
Figure 5. Trajectory tracking variation under different controllers
表 1 不同信号跟踪误差
Table 1. Different signal tracking error
信号种类 动态滑模 传统滑模 最大稳态
误差/mm均方根稳
态误差/mm最大稳态
误差/mm均方根稳
态误差/mm正弦 0.1900 0.0475 0.5467 0.1067 阶跃 0.0245 0.0295 0.1243 0.0308 三角波 0.2013 0.0538 2.0462 0.9752 
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