时滞系统模型简化问题的一种两阶段解法

Model simplification of time delay systems using a two stage method

给出了一种适用于时滞系统的频域模型简化算法,该算法分为2个阶段.在第1阶段,根据时滞不影响系统的幅频响应这一事实,利用Levy法进行幅频响应曲线拟合,进而通过多项式分解得到简化模型分母系数的初值.在第2阶段,使用单纯形法搜索简化模型的时滞和分母中未知参数;对于固定的时滞和分母系数,分子系数利用线性最小二乘方法得到.最后,利用一个来自于文献中的算例检验算法的性能.结果表明,该算法能够以较小的计算量得到高精度的简化模型.

A two stage approach is proposed for frequency domain optimal model simplification of time delay systems. In the first stage,according to the fact that time delay does not affect the system's magnitude response,magnitude response curve fitting is carried out with Levy's method. Polynomial decomposition is then used to obtain the initial values of the denominator coefficients of the approximate model. In the second stage,the simplex method is used to search for the optimal denominator coefficients and time delay. Numerator coefficients are obtained by the linear least squares method for fixed denominator coefficients and time delay. An example from literature was used to test the performance of the proposed method. The results show that the proposed method can find an accurate approximate model at low computational cost.