一类分数阶滤波器逼近阶次的选择

针对分数阶微积分算子的有理逼近可以取得很好的逼近效果,而逼近阶次的选择对分数阶滤波器的逼近精确度和系统性能有直接的影响的问题,通过合理选择逼近阶次可以使二者之间达到一个最佳综合。在分析Oustaloup算法的基础上,详细研究分数阶滤波器分数阶次与有理逼近阶次之间的关系。通过计算逼近模型与理论模型的幅、相频率特性及其误差来观察逼近阶次n与逼近精确度的关系,并确定最佳逼近阶次。仿真结果与误差分析表明,对于一类分数阶滤波器,当有理逼近阶次大于5时,随着逼近阶次的提高,逼近精确度的改善已经变得很有限。折中考虑逼近精确度与系统性能,可选择5作为最佳逼近阶次。

Approximation degree selection for one kind of fractional-order filter

Better approximation results can he obtained by rational approximation of fractional calculus operator, and approximation accuracy of fractional-order filter and system performance are directly relat-ed to the approximation degree, the optimal synthesis each other can be reached by proper selection of approximation degree. Based on the analysis of the Oustaloup's algorithm, relationships between the approximation accuracy of fractional-order filters and the rational approximation degree were discussed in detail. By calculating the amplitude and phase-frequency characteristic and error of approximate model and theoretical model to observe the relationship between approximation degree n with approxima-tion accuracy. And therefore the optimal approximation degree can be determined. The simulation and error analysis show that, when the rational approximant degree is more than five, the influence of ap-proximation degree to approximation accuracy will be negligible for the fractional order filter given in this paper. Trade-off approximation accuracy and system performance, the optimal rational approxima-tion degree will be five.