基于同步建立时机优化的变同步比圆弧插补方法
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1.北京石油化工学院信息工程学院北京102617; 2.国网山东省电力公司临沂供电公司临沂276000

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TH39TP301.6

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Circular interpolation method with variable synchronization ratio based on the optimization of synchronization establishment timing
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1.College of Information Engineering, Beijing Institute of Petrochemical Technology, Beijing 102617, China; 2.Linyi Power Supply Company, State Grid Shandong Electric Power Company, Linyi 276000, China

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    摘要:

    运动插补方法作为运动控制的关键技术,直接影响着运动对象的轨迹精度及运行效率。针对现有变同步比圆弧插补方法未考虑同步建立过渡过程,导致圆弧插补误差较大且插补精度对速度敏感的问题,提出了一种基于同步建立时机优化的变同步比圆弧插补方法,依据加减速控制策略,计算出每个插补周期内各个同步从轴经过加速或减速过程,达到新的同步状态所需的同步建立过渡过程时间,进而获得各从轴在同步建立过渡过程时间内的角度增量;在此基础上,计算出各从轴同步比改变时同步主轴的准确位置,确定主轴同步比改变时机;通过提前改变主轴同步比,优化同步建立时机,使得从轴运动到圆弧上时,刚好与主轴达到新的同步状态,从而有效减小因同步建立滞后引起的轨迹偏移;通过不断改变同步比,实现高精度圆弧插补。二维运动平台变同步比圆弧插补实验结果表明,与现有变同步比圆弧插补方法相比,所提出方法在速度为10 mm/s、插补步长为1 mm的条件下,完成半径为20和100 mm的整圆插补时,插补轨迹圆心平均偏移距离分别降低了约84.7%和85.6%,均方误差(MSE)平均值分别减小了约58.7%和68.1%,且当插补速度改变时,所得MSE平均值改变幅度较小,进一步提高圆弧插补精度的同时,有效降低了插补精度对速度的敏感性。

    Abstract:

    Motion interpolation methods functioning as a key technology in motion control directly impact the trajectory accuracy and operational efficiency of motional objects. The current circular interpolation method of variable synchronization ratio does not consider the establishment of synchronous transition process, leading to the large interpolation errors in the circular interpolation and low sensitivity of interpolation accuracy to the speed. Thus this study proposes a circular interpolation method with the variable synchronization ratio based on the optimization of synchronization establishment timing. Based on the acceleration and deceleration control strategy, the establishment of synchronous transition process time is calculated in each interpolation cycle, which is required for each synchronous slave axis to reach the new synchronization state after acceleration or deceleration. Then, the angle increment of each synchronous slave axis during the establishment of synchronous transition process time is obtained, thus the precise position of the synchronous master axis corresponding to the changed synchronization ratios of the slave axes is calculated, which facilitates the determination of optimal timing for such changes. By changing the synchronization ratio of the master axis in advance to optimize the synchronization establishment timing, the slave axes reach the new synchronization state with the master axis when it moves to the circular arc, thereby effectively reducing the trajectory deviation caused by synchronization lag. The circular interpolation is achieved by continuously changing the synchronization ratio. The experimental results of variable synchronization ratio circular interpolation on a two-dimensional motion platform show that the proposed method achieves a significant improvement in interpolation accuracy compared to the reported variable synchronization ratio circular interpolation method. When completing the full-circle interpolation with radii of 20 mm and 100 mm, the average offset distances of the interpolation trajectory center at a speed of 10 mm/s and an interpolation step length of 1 mm are reduced by approximately 84.7% and 85.6%, respectively, and the average mean squared error (MSE) values are decreased by about 58.7% and 68.1%, respectively. Moreover, the change of average MSE value is relatively small when the interpolation speed changes. This further enhances the circular interpolation accuracy and effectively reduces the sensitivity of interpolation accuracy to speed.

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魏青轩,王世民,白欣悦,李秋颖,李浩.基于同步建立时机优化的变同步比圆弧插补方法[J].仪器仪表学报,2026,47(1):377-388

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  • 在线发布日期: 2026-03-30
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