Precision contour tracking is one of the most important factors used to determine product quality in a machining tool. An interval type-2 fuzzy proportional–integral (PI) sliding mode control (IT2FPISMC) system is proposed herein to control the mover position of the two-axis motion stage with optical encoder sensors for trajectory feedback. A type-2 fuzzy method that can handle rule uncertainties is developed to approach the unknown nonlinear systems. The PI term is used to approximate the discontinuous control signal and mitigate the chattering phenomenon in the presence of unmodeled system dynamics and external disturbances. The adaptive control laws are derived based on the Lyapunov theorem, such that the closed-loop stability is guaranteed, and the output tracking errors of the system asymptotically converge to zero. A non-uniform rational B-spline interpolator with high accuracy is adopted in the biaxial linear stage. Moreover, typical circular, bowknot, heart, and star reference contours are tested. The results on the average tracking error and the tracking error standard deviation are experimented and compared to illustrate the performance of our proposed method. The tracking performance obtained from the IT2FPISMC method is better than that of the conventional method. Furthermore, the proposed method can achieve robustness for tracking different reference contours in industrial applications.

精确的轮廓跟踪是确定加工工具产品质量的最重要因素之一。本文提出了一种间隔类型为2的模糊比例积分（PI）滑模控制（IT2FPISMC）系统，以通过光学编码器传感器来控制轨迹反馈来控制两轴运动平台的动子位置。提出了一种能够处理规则不确定性的2型模糊方法来处理未知的非线性系统。PI项用于近似不连续的控制信号，并在存在未建模的系统动力学和外部干扰的情况下减轻抖动现象。基于李雅普诺夫定理导出自适应控制律，从而保证了闭环稳定性，并且系统的输出跟踪误差渐近收敛于零。双轴线性位移台采用高精度的非均匀有理B样条插值器。此外，还测试了典型的圆形，蝴蝶结，心脏和星形参考轮廓。实验并比较了平均跟踪误差和跟踪误差标准偏差的结果，以说明所提出方法的性能。从IT2FPISMC方法获得的跟踪性能要优于传统方法。此外，所提出的方法可以实现鲁棒性，以跟踪工业应用中的不同参考轮廓。对平均跟踪误差和跟踪误差标准偏差的结果进行了实验并进行了比较，以说明所提出方法的性能。从IT2FPISMC方法获得的跟踪性能要优于传统方法。此外，所提出的方法可以实现鲁棒性，以跟踪工业应用中的不同参考轮廓。实验并比较了平均跟踪误差和跟踪误差标准偏差的结果，以说明所提出方法的性能。从IT2FPISMC方法获得的跟踪性能要优于传统方法。此外，所提出的方法可以实现鲁棒性，以跟踪工业应用中的不同参考轮廓。