Chebyshev-Padé型极点降阶及传输线方程应用

Chebyshev-Padé Type Pole Order Reduction and Application of Transmission Line Equation

为提高工程应用中用于输入输出系统的渐近波形估计方法的模拟精度,提出了Chebyshev-Padé型极点降阶算法。利用Chebyshev函数系和幂级数系的关系,将传递函数展开为Chebyshev级数,获得广义矩。通过匹配广义矩得到降阶后系统传递函数的极点,根据极点是单重和多重的不同情形,分别使用Chebyshev-Padé型单重极点算法和Chebyshev-Padé型多重极点算法对其降阶。进一步由广义矩方程组求解出极点对应的留数,可得降阶系统传递函数的表达式。针对传输线模型给出了Chebyshev-Padé型极点降阶算法的具体步骤。最后,数值算例表明以上算法能够在很少的降阶阶数下提高模型的近似精度。

In order to improve the simulation accuracy of the asymptotic waveform estimation method for inputoutput systems in engineering applications,a Chebyshev-Pade type pole order reduction algorithm is proposed.By using the relationship between the Chebyshev function series and the power series,the transfer function was expanded into Chebyshev series to obtain the generalized moments.According to the different cases where the poles are single and multiple,the order was reduced by the Chebyshev-Pade type single pole order reduction and multiple pole order reduction algorithm,respectively.Further,the residues were solved by the generalized moments equations,and the expression of the transfer function of the reduced order system was obtained.Moreover,the specific steps of this algorithm were given for the transmission line model.Finally,numerical examples show that the algorithm can improve the approximation accuracy with a low reduced order.