基于牛顿迭代法的S形加减速时间算法研究

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。

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

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.