Approximation degree selection for one kind of fractional-order filter

Better approximation results can be obtained by rational approximation of fractional calculus operator, and approximation accuracy of fractional-order filter and system performance are directly related 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 approximation 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 approximation 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 approximation degree will be five.