• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2016, Vol. 52 ›› Issue (23): 199-206.doi: 10.3901/JME.2016.23.199

• 数字化设计与制造 • 上一篇    下一篇

始末速度不为零的S型加减速时间规划算法研究*

杨亮亮1,2, 许守金1,2, 史伟民1,2, 葛宏伟1,2   

  1. 1. 浙江理工大学浙江省现代纺织装备技术重点实验室 杭州 310018;
    2. 浙江理工大学教育部现代纺织装备技术工程研究中心 杭州 310018
  • 出版日期:2016-12-05 发布日期:2016-12-05
  • 作者简介:

    杨亮亮(通信作者),男,1978年出生,博士,副教授。主要研究方向为高速高精度运动控制、机器人控制技术和数控技术。

    E-mail:yangliangliang@zstu.edu.cn

  • 基金资助:
    * 国家自然科学基金(51305404)和国家科技支撑计划(2013BAF05B01) 资助项目; 20150811收到初稿,20160514收到修改稿;

Research on S Type Acceleration and Deceleration Time Planning Algorithm with Beginning and End Speed Non-zero

YANG Liangliang1,2, XU Shoujin1,2, SHI Weimin1,2, GE Hongwei1,2   

  1. 1. Zhejiang Provincial Key Lab of Modern Textile Machinery & Technology, Zhejiang Sci-Tech University, Hangzhou 310018;
    2. The Research Center of Modern Textile Machinery Technology of The Ministry of Education,
  • Online:2016-12-05 Published:2016-12-05

摘要:

针对始末速度不为零的非对称S型加减速时间难以规划问题,把加速度曲线分为7个时间段,对关于加速度变化时间的方程组进行分析,化简为一元高次方程,并根据其变化的单调性构造其平方函数,使其转换为单一凸形函数,进而利用牛顿迭代求出其收敛值并根据效率最优原则和加速度、速度约束条件进行修正;对匀加速度时间的规划,直接根据其公式特点,转换为一元二次方程进行规划并根据效率最优原则和加速度、速度约束条件进行修正;对于匀速运动时间直接根据一元一次方程的解法进行规划。该算法解决了现有始末速度不为零的S型加减速时间规划过程复杂、繁琐问题,提供了一种简洁、高效的加减速时间规划算法。通过仿真与试验可知,本算法求解效率提高10.8%,插补效率提高1.32%,插补效果满足精度要求,同时证明了该算法简洁、高效、运行稳定、能够满足高速高精数控要求。

关键词: 单调函数, 非对称S型加减速控制, 牛顿迭代, 时间规划

Abstract:

To solve the problem of planning acceleration and deceleration time of the asymmetric S type speed curve with the beginning and the end speed non zero, acceleration curve is divided into seven time segments and speed and displacement equations are obtained. Construct square function which has argument of derivative of acceleration and the convex feature according to the monotonic change of simplified high order equation transformed from speed and displacement equations. The time segment of derivative of acceleration is obtained by the Newton Iterative and then modified by the principle of efficiency optimization and speed and acceleration limitations. The time segment of acceleration is obtained by solving quadratic equation in one variable and also modified by principle of efficiency optimization and speed and acceleration limitation. And at last the time segment of constant speed is obtained by solving one order equation in one variable. This algorithm solves the problem of the complexity of traditional planning of asymmetric S type acceleration and deceleration time and provides a simple, efficient acceleration and deceleration time planning algorithm. Through simulation and experiment, the efficiency of this algorithm is increased by 10.8%, the interpolation efficiency is increased by 3.39%, and the interpolation accuracy meets the requirements and the algorithm is proved to be simple, efficient and meets the requirements of CNC with high speed and high precision.

Key words: asymmetric S-type acceleration and deceleration control, monotonic function, Newton iteration, time planning