基于牛顿迭代法的S形加减速时间算法研究

中国机械工程 ›› 2015, Vol. 26 ›› Issue (7): 912-916,942.

基于牛顿迭代法的S形加减速时间算法研究

杨亮亮1,2;许守金1,2;史伟民1,2;葛宏伟1,2

1.浙江省现代纺织装备技术重点实验室,杭州,310018
2.浙江理工大学,杭州,310018

出版日期:2015-04-10 发布日期:2015-04-24
基金资助:
国家自然科学基金资助项目（51305404）；国家科技支撑计划资助项目(2013BAF05B01)

Research on Algorithm of S_shape Acceleration and Deceleration Time Based on Newton Iterative Method

Yang Liangliang1,2;Xu Shoujin1,2;Shi Weimin1,2;Ge Hongwei1,2

1.Zhejiang Provincial Key Lab of Modern Textile Machinery & Technology,Hangzhou,310018
2.Zhejiang Sci-Tech University,Hangzhou,310018

Online:2015-04-10 Published:2015-04-24
Supported by:
National Natural Science Foundation of China（No. 51305404）;The National Key Technology R&D Program（No. 2013BAF05B01）

摘要/Abstract

摘要：

S形加减速控制涉及求解多元高次方程或者不等式，且要求求解出来的最终解是非负数，为此根据时间最优原则和速度、加速度的限制条件，把S形加减速控制中所涉及的五元非线性方程组分解为2个二元非线性方程组和1个一元线性方程。采用牛顿迭代法和迭代修正的方式逐步求解出符合要求的加减速时间，进而求出速度曲线，进行插补运算。仿真与实验结果证明,该算法简明高效、运行稳定，能够满足高速高精数控要求。

关键词: S形加减速控制, 五元非线性方程, 牛顿迭代法, 时间最优原则

Abstract:

Due to S_shape acceleration and deceleration control involved solving multiple high-order equation or inequality, and the final solution was non negative, so that it was difficult to calculate.Therefore nonlinear equations of five independent variables of S_shape acceleration and deceleration control were decomposed into two nonlinear equations of two independent variables and a linear equation according to time optimal principle and the constraints of speed, acceleration. The final solutions were obtained by Newton iterative method and the iterative correction method then the velocity curve and interpolation algorithm were found. The simulation and experiments were presented to prove that the algorithm is simplicity, stable operation and the ability to meet the requirements of high speed and high precision of computer numerical control.

Key words: S_shape acceleration and deceleration control;nonlinear equations of , five , independent variables;Newton iterative method;time optimal , principle

中图分类号:

TP391

杨亮亮, 许守金, 史伟民, 葛宏伟, . 基于牛顿迭代法的S形加减速时间算法研究[J]. 中国机械工程, 2015, 26(7): 912-916,942.

Yang Liangliang, Xu Shoujin, Shi Weimin, Ge Hongwei, . Research on Algorithm of S_shape Acceleration and Deceleration Time Based on Newton Iterative Method[J]. China Mechanical Engineering, 2015, 26(7): 912-916,942.

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https://www.cmemo.org.cn/CN/Y2015/V26/I7/912

参考文献

[1]黄艳,李家霁,于东,等.CNC系统S型曲线加减速算法的设计与实现[J].制造技术与机床, 2005(3):55-58.
Huang Yan,Li Jiaqi,Yu Dong,et al.Design and Implementation of S_shape Acceleration and Deceleration Algorithm on CNC System[J].Manufacturing Technology and Machine Tool,2005(3):55-58.
[2]罗钧,汪俊,刘学明,等.基于S型加减速的自适应前瞻NURBS曲线插补算法[J].计算机集成制造系统,2013,19（1）:55-59.
Luo Jun,Wang Jun,Liu Xueming,et al.Adaptive NURBS Interpolation Algorithm with Look-ahead Function Based on S-shape Acceleration Deceleration[J].Computer Integrated Manufacturing Systems，2013，19（1）：55-59.
[3]Ren Kun,Fu Jianzhong,Chen Zichen.Motion Velocity Smooth Link in High Speed Machining[J].Chinese Journal of Mechanical Engineering,2007,20(2):17-20.
[4]乔志峰. 适用于复杂形面加工的多轴运动控制系统设计理论与方法研究[D].天津:天津大学,2012.
[5]潘海鸿,杨微,陈琳,等.全程S曲线加减速控制的自适应分段NURBS曲线插补算法[J].中国机械工程,2010,21(2):190-195.
Pan Haihong,Yang Wei,Chen Lin,et al.Adaptive Piecewise NURBS Curve Interpolator Algorithm for Entireness Process S-curve ACC/DEC Control[J].China Mechanical Engineering,2010,21(2)：190-195.
[6]南京工程学院.运动控制系统S曲线加减速的实现方法：中国，201310683011.X[P].2014-04-09.
[7]穆海华,周云飞,严思杰,等.超精密点对点运动三阶轨迹规划精度控制[J].机械工程学报, 2008,44(1):126-127.
Mu Haihua,Zou Yunfei,Yan Sijie,et al.Precision Control of Third-order Profile Planning for High Accuracy Point-to-point Motion System[J].Journal of Mechanical Engineering,2008,44(1):126-127.
[8]郭新贵,李从心.一种新型柔性加减速算法[J].上海交通大学学报,2003,37(2):205-207.
Guo Xingui,Li Congxin.A New Flexible Acceleration and Deceleration Algorithm[J].Journal of Shanghai Jiaotong University, 2003, 37(2):205-207.
[9]徐瑞民.二元非线性方程组求根的牛顿迭代[J].山东轻工业学院学报,2009,23(4):90-91.
Xu Ruimin.Newton’s Method for the Nonlinear Function of Two Independent Variables[J]. Journal of Shan Dong Institute of Light Industry,2009,23(4):90-91.
[10]孙玉娥，林浒，李建伟.面向高速加工的样条曲线实时插补算法[J].机械工程学报,2011,47(3):186-191.
Sun Yue,Lin Hu,Li Jianwei.Spline Real-time Interpolation Algorithm for High-speed Machining[J].Journal of Mechanical Engineering, 2011,47（3）：186-191.
[11]罗福源,游有鹏,尹涓.NURBS曲线S型加减速双向寻优插补算法研究[J].机械工程学报,2012，48（5）:147-155.
Luo Fuyuan,You Youpeng，Yin Juan.Research on the Algorithm of NURBS Curve Bidirectional Optimization Interpolation with S-type Acceleration and Deceleration Control[J].Journal of Mechanical Engineering,2012,48(5):147-155.

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