0
Research Papers

An Equivalent-Plane Cross-Coupling Position Control for Contour-Accuracy Improvement in Three-Axis Free-Form Contour Following Tasks

[+] Author and Article Information
Jian-Wei Ma

Key Laboratory for Precision and
Non-Traditional Machining Technology of
Ministry of Education,
School of Mechanical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: mjw2011@dlut.edu.cn

De-Ning Song

Key Laboratory for Precision and
Non-Traditional Machining Technology of
Ministry of Education,
School of Mechanical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: deningsong@163.com

Zhen-Yuan Jia

Key Laboratory for Precision and
Non-Traditional Machining Technology of
Ministry of Education,
School of Mechanical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: jzyxy@dlut.edu.cn

Wen-Wen Jiang

Key Laboratory for Precision and
Non-Traditional Machining Technology of
Ministry of Education,
School of Mechanical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: 2501394555@qq.com

Fu-Ji Wang

Key Laboratory for Precision and
Non-Traditional Machining Technology of
Ministry of Education,
School of Mechanical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: wfjsll@dlut.edu.cn

Wei Liu

Key Laboratory for Precision and
Non-Traditional Machining Technology of
Ministry of Education,
School of Mechanical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: lw2007@dlut.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received August 8, 2017; final manuscript received November 12, 2018; published online December 19, 2018. Assoc. Editor: Douglas Bristow.

J. Dyn. Sys., Meas., Control 141(4), 041007 (Dec 19, 2018) (15 pages) Paper No: DS-17-1401; doi: 10.1115/1.4042027 History: Received August 08, 2017; Revised November 12, 2018

To reduce the contouring errors in computer-numerical-control (CNC) contour-following tasks, the cross-coupling controller (CCC) is widely researched and used. However, most existing CCCs are well-designed for two-axis contouring and can hardly be generalized to compensate three-axis curved contour following errors. This paper proposes an equivalent-plane CCC scheme so that most of the two-axis CCCs or flexibly designed algorithms can be utilized for equal control of the three-axis contouring errors. An initial-value regeneration-based Newton method is first proposed to compute the foot point from the actual motion position to the desired contour with a high accuracy, so as to establish the equivalent plane where the estimated three-dimensional contouring-error vector is included. After that, the signed contouring error is computed in the equivalent plane, thus a typical two-axis proportional-integral-differential (PID)-based CCC is utilized for its control. Finally, the two-axis control commands generated by the typical CCC are coupled to three-axis control commands according to the geometry of the established equivalent plane. Experimental tests are conducted to verify the effectiveness of the presented method. The testing results illustrate that the proposed equivalent-plane CCC performs much better than conventional method in both error estimation and error control.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Khalick, M. A. E. , and Uchiyama, N. , 2011, “ Discrete-time Model Predictive Contouring Control for Biaxial Feed Drive Systems and Experimental Verification,” Mechatronics, 21(6), pp. 918–926. [CrossRef]
Huo, F. , and Poo, A. N. , 2013, “ Precision Contouring Control of Machine Tools,” Int. J. Adv. Manuf. Technol., 64(1–4), pp. 319–333. [CrossRef]
Ramesh, R. , Mannan, M. A. , and Poo, A. N. , 2005, “ Tracking and Contour Error Control in CNC Servo Systems,” Int. J. Mach. Tools Manuf., 45(3), pp. 301–326. [CrossRef]
Lie, T. , and Robert, G. L. , 2013, “ Multiaxis Contour Control—The State of the Art,” IEEE Trans. Control. Syst. Technol., 21(6), pp. 1997–2010. [CrossRef]
Lie, T. , and Robert, G. L. , 2012, “ Predictive Contour Control With Adaptive Feed Rate,” IEEE Trans. Mechatronics, 17(4), pp. 669–679. [CrossRef]
Dong, J. , Wang, T. , Li, B. , and Ding, Y. , 2014, “ Smooth Feedrate Planning for Continuous Short Line Tool Path With Contour Error Constraint,” Int. J. Mach. Tools Manuf., 76, pp. 1–12. [CrossRef]
Tomizuka, M. , 1987, “ Zero Phase Error Tracking Algorithm for Digital Control,” ASME J. Dyn. Syst. Meas. Control, 109(1), pp. 65–68. [CrossRef]
Torfs, D. , Deschutter, J. , and Swevers, J. , 1992, “ Extended Bandwidth Error Phase Error Tracking Control of Nonminimal Phase Systems,” ASME J. Dyn. Syst. Meas. Control, 114(3), pp. 347–351. [CrossRef]
Altintas, Y. , Erkorkmaz, K. , and Zhu, W. , 2000, “ Sliding Mode Controller Design for High Speed Feed Drives,” Ann. CIRP, 49(1), pp. 265–270. [CrossRef]
Koren, Y. , 1980, “ Cross-Coupled Biaxial Computer Control for Manufacturing Systems,” ASME J. Dyn. Syst. Meas. Control, 102(4), pp. 265–272. [CrossRef]
Srinivasan, K. , and Kulkarni, P. , 1990, “ Cross-Coupled Control of Biaxial Feed Drive Servomechanisms,” ASME J. Dyn. Syst. Meas. Control, 112(2), pp. 225–232. [CrossRef]
Koren, Y. , and Lo, C. , 1991, “ Variable-Gain Cross-Coupling Controller for Contouring,” CIRP Ann. Manuf. Technol., 40(1), pp. 371–374. [CrossRef]
Yeh, S.-S. , and Hsu, P.-L. , 1999, “ Theory and Applications of the Robust Cross-Coupled Control Design,” ASME J. Dyn. Syst. Meas. Control, 121(3), pp. 524–530. [CrossRef]
Chin, J. , Cheng, Y. , and Lin, J. , 2004, “ Improving Contour Accuracy by Fuzzy-Logic Enhanced Cross-Coupled Precompensation Method,” Robot. Comput. Integr. Manuf., 20(1), pp. 65–76. [CrossRef]
Jee, S. , 1998, “ Fuzzy Logic Cross-coupling Controller for Precision Contour Machining,” KSME Int. J., 12(5), pp. 800–810. [CrossRef]
Barton, K. L. , and Alleyne, A. G. , 2008, “ A Cross-Coupled Iterative Learning Control Design for Precision Motion Control,” IEEE Trans. Control. Syst. Technol., 16(6), pp. 1218–1231. [CrossRef]
Chen, W. , Wang, D. , Geng, Q. , and Xia, C. , 2016, “ Robust Adaptive Cross-Coupling Position Control of Biaxial Motion System,” Sci. China Tech. Sci., 59(4), pp. 680–688. [CrossRef]
Yeh, S.-S. , and Hsu, P.-L. , 1999, “ Analysis and Design of the Integrated Controller for Precise Motion Systems,” IEEE Trans. Control Syst. Technol., 7(6), pp. 706–717. [CrossRef]
Cheng, M.-Y. , Su, K.-H. , and Wang, S.-F. , 2009, “ Contour Error Reduction for Free-Form Contour Following Tasks of Biaxial Motion Control Systems,” Int. J. Mach. Tools Manuf., 25(2), pp. 323–333.
Cheng, M. , and Lee, C. , 2007, “ Motion Controller Design for Contour-Following Tasks Based on Real-Time Contour Error Estimation,” IEEE Trans. Ind. Electron., 54(3), pp. 1686–1695. [CrossRef]
Huo, F. , and Poo, A. , 2012, “ Improving Contouring Accuracy by Using Generalized Cross-Coupled Control,” Int. J. Mach. Tools Manuf., 63, pp. 49–57. [CrossRef]
Yang, J. , and Li, Z. , 2011, “ A Novel Contour Error Estimation for Position Loop-Based Cross-Coupled Control,” IEEE/ASME Trans. Mechatronics, 16(4), pp. 643–655. [CrossRef]
Chen, H. , Cheng, M. , Wu, C. , and Su, K. , 2016, “ Real Time Parameter Based Contour Error Estimation Algorithms for Free Form Contour Following,” Int. J. Mach. Tools Manuf., 102, pp. 1–8. [CrossRef]
Yeh, S.-S. , and Hsu, P.-L. , 2002, “ Estimation of the Contouring Error Vector for the Cross-Coupled Control Design,” IEEE/ASME Trans. Mechatronics, 7(1), pp. 44–51. [CrossRef]
Zhao, H. , Zhu, L. , and Ding, H. , 2015, “ Cross-Coupled Controller Design for Triaxial Motion Systems Based on Second-Order Contour Error Estimation,” Sci. China Technol. Sci., 58(7), pp. 1209–1217. [CrossRef]
Zhu, L. , Zhao, H. , and Ding, H. , 2013, “ Real-Time Contouring Error Estimation for Multi-Axis Motion Systems Using the Second-Order Approximation,” Int. J. Mach. Tools Manuf., 68, pp. 75–80. [CrossRef]
Khalick, M. A. E. , and Uchiyama, N. , 2011, “ Contouring Controller Design Based on Iterative Contour Error Estimation for Three-Dimensional Machining,” Robot. Comput. Integr. Manuf., 27, pp. 802–807. [CrossRef]
Jia, Z.-Y. , Song, D.-N. , Ma, J.-W. , Hu, G.-Q. , and Su, W.-W. , 2017, “ A NURBS Interpolator With Constant Speed at Feedrate-Sensitive Regions Under Drive and Contour-Error Constraints,” Int. J. Mach. Tools Manuf., 116, pp. 1–17. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Scheme of the traditional three-axis cross-coupling controller

Grahic Jump Location
Fig. 2

Architecture of the typical two-axis cross-coupling position controller

Grahic Jump Location
Fig. 3

Geometry of the ideal equivalent plane

Grahic Jump Location
Fig. 4

Principle diagram of the initial-value-regeneration based Newton method

Grahic Jump Location
Fig. 5

Geometric relationship between the three-axis space and the two-axis equivalent plane

Grahic Jump Location
Fig. 6

Architecture of the proposed equivalent-plane CCC

Grahic Jump Location
Fig. 7

The three-dimensional butterfly curve used for the simulation tests

Grahic Jump Location
Fig. 8

The control commands and contouring error of the uncoupled system for the butterfly curve: (a) control commands and (b) contouring error

Grahic Jump Location
Fig. 9

The control commands and contouring error of the uncoupled system with diploid gains for the butterfly curve: (a) control commands and (b) contouring error

Grahic Jump Location
Fig. 10

The control commands and contouring error of the coupled system by conventional CCC for the butterfly curve: (a) control commands and (b) contouring error

Grahic Jump Location
Fig. 11

The control commands and contouring error of the coupled system by the proposed equivalent-plane CCC using P controller for the butterfly curve: (a) control commands and (b) contouring error

Grahic Jump Location
Fig. 12

The estimation deviation of the contouring error for the butterfly curve: (a) linear approximation method and (b) proposed equivalent-plane method

Grahic Jump Location
Fig. 13

The control commands and contouring error of the coupled system by conventional CCC with increased P gain for the butterfly curve: (a) control commands and (b) contouring error

Grahic Jump Location
Fig. 14

The control commands and contouring error of the coupled system by the proposed equivalent-plane CCC using P controller with increased gain for the butterfly curve: (a) control commands and (b) contouring error

Grahic Jump Location
Fig. 15

The control commands and contouring error of the coupled system by the proposed equivalent-plane CCC using PID controller for the butterfly curve: (a) control commands and (b) contouring error

Grahic Jump Location
Fig. 16

The experimental platform used for the tests: (a) platform architecture and (b) real connected system

Grahic Jump Location
Fig. 17

The trajectories used for the tests: (a) bone contour and (b) flying-bird contour

Grahic Jump Location
Fig. 18

Estimated contouring errors and the estimation deviations: (a) estimated error for bone contour, (b) estimation deviation of tangential approximation method for bone contour, (c) estimation deviation of the proposed method for bone contour, (d) estimated error for flying-bird contour, (e) estimation deviation of tangential approximation method for flying-bird contour, and (f) estimation deviation of the proposed method for flying-bird contour

Grahic Jump Location
Fig. 19

Deviations between the real and calculated contouring-error components in three directions: (a) deviations for bone contour and (b) deviations for flying-bird contour

Grahic Jump Location
Fig. 20

Control commands of different methods: (a) uncoupled system commands for bone trajectory, (b) CCC commands for bone trajectory, (c) equivalent-plane CCC commands for bone trajectory, (d) uncoupled system commands for flying-bird trajectory, (e) CCC commands for flying-bird trajectory, and (f) equivalent-plane CCC commands for flying-bird trajectory

Grahic Jump Location
Fig. 21

Comparison results of the absolute contouring errors of different methods: (a) results of bone contour and (b) results of flying-bird contour

Grahic Jump Location
Fig. 22

Estimation deviations of different methods for the contouring error of the equivalent-plane CCC system: (a) estimation deviation of tangential approximation method for bone contour, (b) estimation deviation of equivalent-plane method for bone contour, (c) estimation deviation of tangential approximation method for flying-bird contour, and (d) estimation deviation of equivalent-plane method for flying-bird contour

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In