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| Step by step fitting algorithm for multi-order exponential function |
| HU Xu-xiao1, PAN Xiao-hong1, HE Wei2, CHEN Gang3 |
1. Institute of Modern Manufacturing Engineering, Zhejiang University,Hangzhou 310027,China; 2. Hangzhou Machine
Tool Group Co., Ltd., Hangzhou 310022, China; 3. Institute of MechanicsElectrics, Zhejiang Texile and Fashion and
College, Ningbo 315211, China |
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Abstract A step by step fitting algorithm was presented for multi-order exponential function with larger time constant difference. For the exponential function with different time constant has different balance time. The last part is firstly fitted by the algorithm for singleorder exponential function, then confirm the amplitude and time constant of the last item of the multiorder exponential function, then choose the last second section, adopt the same fitting algorithm for singleorder exponential function through translating, and get different time constants and corresponding amplitude separately step by step. The algorithm is simple and practical, with high precision of fitting. It was applied to establish the mathematical model of the nanometer drive parts with large feeding force.
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Published: 01 December 2010
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一类多阶指数函数的逐级递推式拟合算法
针对一类时间常数相差较大的多阶指数函数,提出一种逐级递推式拟合算法.根据不同时间常数的指数函数具有不同平衡时间的特点,首先选取最后一段,采用一阶指数函数的拟合算法进行拟合,从而确定最后一项指数函数的幅值和时间常数；然后选取倒数第二段,通过变换同样采用一阶指数函数的拟合算法进行拟合,逐级递推,分别得到多阶指数函数不同项的时间常数和相应的幅值.此方法简单实用,具有较高的拟合精度,适合于具有大进给力的纳米级热驱动部件的精确建模.
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