Chord error constraint based integrated control strategy for contour error compensation
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RESEARCH ARTICLE
Tie ZHANG, Caicheng WU, Yanbiao ZOU
Chord error constraint based integrated control strategy for contour error compensation
© Higher Education Press 2020
Abstract As the traditional cross-coupling control method cannot meet the requirements for tracking accuracy and contour control accuracy in large curvature positions, an integrated control strategy of cross-coupling contour error compensation based on chord error constraint, which consists of a cross-coupling controller and an improved position error compensator, is proposed. To reduce the contour error, a PI-type cross-coupling controller is designed, with its stability being analyzed by using the contour error transfer function. Moreover, a feed rate regulator based on the chord error constraint is proposed, which performs speed planning with the maximum feed rate allowed by the large curvature position as the constraint condition, so as to meet the requirements of large curvature positions for the chord error. Besides, an improved position error compensation method is further presented by combining the feed rate regulator with the position error compensator, which improves the tracking accuracy via the advance compensation of tracking error. The biaxial experimental results of non-uniform rational Bsplines curves indicate that the proposed integrated control strategy can significantly improve the tracking and contour control accuracy in biaxial contour following tasks. Keywords cross-coupling controller, contour error, tracking error, position error compensator, feed rate regulator
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Introduction
In biaxial motion control tasks, the great difference in the motion characteristics of coordinate axes in the feed system may result in low contour tracking accuracy when simply using the single-axis servo control. Specific contour Received March 30, 2020; accepted July 9, 2020
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Tie ZHANG ( ), Caicheng WU, Yanbiao ZOU School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510641, China E-mail: [email protected]
control techniques, such as cross-coupling control (CCC) [1,2], must be used. The basic idea of CCC is to build a real-time contour error model based on the feedback information and interpolation information of each coordinate axis, seek and establish an optimal contour error control law to compensate the contour error, thus reducing and eliminating the contour error. A common crosscoupling controller mainly consists of two parts, one is the real-time contour error estimation model and the other is the control and compensation strategy [3]. The contour error is defined as the shortest normal distance from the actual cutting position to the target reference path [4,5], as shown in Fig. 1. Contour error estimation methods have been the focus of many scholars. For example, Koren and Lo [2] and Yang and Li [6] locally approximate the free-curve profile with an intimate circle and used McLaughlin’s expansion to achieve a second-order estimation of the contour error. Shih et al. [7] adopted Taylor’s
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