Time-Optimal Control Algorithm for Path Traversal Problems of CNC Systems

LI Shurong;ZHANG Qiang

Journal of Systems Science and Mathematical Sciences ›› 2010, Vol. 30 ›› Issue (11) : 1581-1591.

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中国科学院数学与系统科学研究院期刊网
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Journal of Systems Science and Mathematical Sciences ›› 2010, Vol. 30 ›› Issue (11) : 1581-1591. DOI: 10.12341/jssms09429
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Time-Optimal Control Algorithm for Path Traversal Problems of CNC Systems

  • LI Shurong, ZHANG Qiang
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Abstract

Aiming at the given path traversal problems of computer numerical control (CNC) system, a kind of acceleration/deceleration control algorithm is proposed to get the minimum time for path traversal of CNC system. The optimized variables (accelerations) of CNC system are linearity with respect to time-optimal objective function and constraint conditions,and the accelerations are bounded along the axis directions. Thus in general, this kind of time-optimal control problems for path traversal has a structure of Bang-bang control, i.e., at any time there exists at least one axis direction along which the acceleration/deceleration is at its bound.
For a class of parametric paths, the relationship between the accelerations along the axis directions and the local characteristic of curve is derived. This relationship can realizes the precise path traversal under the conditions of Bang-bang control.
The simulation results of minimum-time path traversal problems for 14 and 12 circles demonstrate the effectiveness of this algorithm.

Key words

Computer numerical control / Bang-bang control / path traversal / minimum-time.

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LI Shurong , ZHANG Qiang. Time-Optimal Control Algorithm for Path Traversal Problems of CNC Systems. Journal of Systems Science and Mathematical Sciences, 2010, 30(11): 1581-1591 https://doi.org/10.12341/jssms09429
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