Abstract: The contour controllers were usually designed as a P controller, and the gain value was the key parameter to determine the control effectiveness. In order to design the gain values of contour controllers quantitatively, a gain design method of contour controllers was proposed based on stability margin herein. Firstly, the discrete transfer functions of each axis of the machine tool were identified by applying the least squares method. Secondly, the stability domain of the gain was calculated based on the Jury criterion and transfer functions. Finally, the objective function was constructed, and the gain values satisfying the stability margin requirements were obtained in the stability domain. A contour controller was designed on a three-axis machine tool, and a trajectory tracking experiment was carried out to verify the effectiveness of the proposed method. The experimental results show that the contour controller designed based on stability margin may reduce the maximum trajectory error of the spiral trajectory by 39.06% and the maximum trajectory error of the fan-shaped trajectory by 34.33%, under the conditions of ensuring the motion stability of the machine tools.

Key words: trajectory error, contour controller, stability margin, multi-axis machine tool

摘要： 机床轮廓控制器通常被设计为P控制器，其控制增益是决定控制效果的关键参数。为定量设计轮廓控制器增益值，提出了基于稳定裕度的控制器增益设计方法。首先基于最小二乘法辨识机床各轴的离散传递函数模型,然后根据传递函数模型及Jury准则确定增益的稳定域，最后根据稳定裕度构造目标函数，并在稳定域内求解满足稳定裕度要求的轮廓控制器增益值。在三轴机床上设计轮廓控制器，实施轨迹联动实验，以验证方法的有效性。实验结果表明，基于稳定裕度设计的轮廓控制器可在保证机床运动平稳性的条件下使螺旋形轨迹的轨迹误差最大值减小39.06%，扇形轨迹的轨迹误差最大值减小少34.33%。

关键词: 轨迹误差, 轮廓控制器, 稳定裕度, 多轴机床