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Journal of Systems Science and Complexity

, Volume 28, Issue 1, pp 80–95 | Cite as

Time optimal feedrate generation with confined tracking error based on linear programming

  • Jianxin GuoEmail author
  • Qiang Zhang
  • Xiao-Shan Gao
  • Hongbo Li
Article

Abstract

In this paper, the problem of time optimal feedrate generation under confined feedrate, axis accelerations, and axis tracking errors is considered. The main contribution is to reduce the tracking error constraint to constraints about the axis velocities and accelerations, when the tracking error satisfies a second order linear ordinary differential equation. Based on this simplification on the tracking error, the original feedrate generation problem is reduced to a new form which can be efficiently solved with linear programming algorithms. Simulation results are used to validate the methods.

Keywords

CNC machining dynamics linear programming optimal control time optimal feedrate planning tracking error 

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References

  1. [1]
    Shiller Z, On singular time-optimal control along specified paths, IEEE Trans. Robot. Autom., 1994, 10: 561–566.CrossRefGoogle Scholar
  2. [2]
    Timar S D and Farouki R T, Time-optimal traversal of curved paths by Cartesian CNC machines under both constant and speed-dependent axis acceleration bounds, Robotics and Computer-Integrated Manufacturing, 2007, 23(5): 563–579.CrossRefGoogle Scholar
  3. [3]
    Zhang K, Yuan C M, and Gao X S, Efficient algorithm for time-optimal feedrate planning and smoothing with confined chord error and acceleration, Int. J. Adv. Manuf. Technol., 2013, 66(9–12): 1685–1697.CrossRefGoogle Scholar
  4. [4]
    Sun Y W, Zhou J F, and Guo D M, Variable feedrate interpolation of nurbs toolpath with geometric and kinematical constraints for five-axis CNC maching, Journal of Systems Science and Complexity, 2013, 26(5): 757–776.CrossRefzbMATHGoogle Scholar
  5. [5]
    Yuan C M, Zhang K, and Fan W, Time-optimal interpolation for CNC machining along curved tool pathes with confined chord error, Journal of Systems Science and Complexity, 2013, 26(5): 836–870.CrossRefzbMATHMathSciNetGoogle Scholar
  6. [6]
    Sencer B, Altintas Y, and Croft E, Feed optimization for five-axis CNC machine tools with drive constraints, Int. J. of Mach. Tools and Manu., 2008, 48: 733–745.CrossRefGoogle Scholar
  7. [7]
    Lai J Y, Lin K Y, Tseng S J, and Ueng W D, On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk, Int. J. Adv. Manuf. Technol., 2008, 37: 104–121.CrossRefGoogle Scholar
  8. [8]
    Lee A C, Lin M T, Pan Y R, and Lin W Y, The feedrate scheduling of NURBS interpolator for CNC machine tools, Computer-Aided Design, 2011, 43: 612–628.CrossRefGoogle Scholar
  9. [9]
    Gasparetto A, Lanzutti A, Vidoni R, and Zanotto V, Experimental validation and comparative analysis of optimal time-jerk algorithms for trajectory planning, Robotics and Computer-Integrated Manufacturing, 2012, 28: 164–181.CrossRefGoogle Scholar
  10. [10]
    Zhang K, Gao X S, Li H, and Yuan C M, A greedy algorithm for feed-rate planning of CNC machines along curved tool paths with confined jerk for each axis, Robotics and Computer Integrated Manufacturing, 2012, 28: 472–483.CrossRefGoogle Scholar
  11. [11]
    Fan W, Gao X S, Yan W, and Yuan C M, Interpolation of parametric CNC machine tool path under confined jounce, Int. J. Adv. Manuf. Technol., 2012, 62: 719–739.CrossRefGoogle Scholar
  12. [12]
    Koren Y, Cross-coupled biaxial computer control for manufacturing systems, ASME Transactions, Journal of Dynamic Systems, Measurement and Control, 1980, 102(4): 265–272.CrossRefzbMATHGoogle Scholar
  13. [13]
    Visioli A, Optimal tuning of PID controllers for integral and unstable processes, MIEEE Proceedings Control Theory and Applications, 2006, 148(2): 180–184.CrossRefGoogle Scholar
  14. [14]
    Chuang H Y and Liu C H, A model-referenced adaptive control strategy for improving contour accuracy of multiaxis machine tools, IEEE Trans. on Industry Applications, 1992, 28(1): 221–227.CrossRefGoogle Scholar
  15. [15]
    Kulkarni P K and Srinivasan K, Optimal contouring control of multi-axial feed drive servomechanisms, Journal of Engineering for Industry-Transactions of the ASME, 1989, 10: 1115.Google Scholar
  16. [16]
    Zhao C and Huang Y, ADRC based input disturbance rejection for minimum-phase plants with unknown orders and/or uncertain relative degrees, Journal of Systems Science and Complexity, 2012, 25(4): 625–640.CrossRefzbMATHMathSciNetGoogle Scholar
  17. [17]
    Dong J and Stori J A, A generalized time-optimal bidirectional scan algorithm for constrained feed-rate optimization, Journal of Dynamic Systems, Measurement, and Control, 2006, 128(2): 379–390.CrossRefGoogle Scholar
  18. [18]
    Dong J and Stori J A, Optimal feed-rate scheduling for high-speed contouring, Journal of Manufacturing Science and Engineering, 2007, 129(1): 63–76.CrossRefGoogle Scholar
  19. [19]
    Ernesto C A and Farouki R T, Solution of inverse dynamics problems for contour error minimization in CNC machines, Int. J. Adv. Manuf. Technol, 2010, 49: 589–604.CrossRefGoogle Scholar
  20. [20]
    Guo J X, Zhang Q, and Gao X S, Tracking error reduction in CNC machining by reshaping the Kinematic trajectory, Journal of Systems Science and Complexity, 2013, 26(5): 817–835.CrossRefzbMATHGoogle Scholar
  21. [21]
    Lin M T, Tsai M S, and Yau H T, Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm, Int. J. of Mach. Tools and Manu, 2007, 47: 2246–2262.CrossRefGoogle Scholar
  22. [22]
    Tsai M S, Nien H W, and Yau H T, Development of an integrated look-ahead dynamics-based NURBS interpolator for high precision machinery, Computer-Aided Design, 2008, 40: 554–566.CrossRefGoogle Scholar
  23. [23]
    Karmarkar N, A new polynomial time algorithm for linear programming, Combinatorica, 1984, 4(4): 373–395.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Jianxin Guo
    • 1
    Email author
  • Qiang Zhang
    • 2
  • Xiao-Shan Gao
    • 1
  • Hongbo Li
    • 1
  1. 1.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.College of Information and Control EngineeringChina University of Petroleum (East China)QingdaoChina

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