Consistent Approximation of Fractional Order Operators

Abstract Fractional order controllers become increasingly popular due to their versatility and superiority in various performances. However, the bottleneck deploying these tools practice is related analog or numerical implementation. Numerical approximations are usually employed which approximation of fractional differintegrator foundation. Generally, following three identical equations always hold, i.e., 1sα1s1−α=1s, sα1sα=1, sαs1−α=s. for approximate models sα, α∈(−1,0)∪(0,1), there exist some conflicts on mentioned equations, might enlarge error even cause fallacies multiple orders occasion. To overcome conflicts, this brief develops a piecewise model provides two procedures designing parameters. The comparison with several existing methods shows that proposed do not only satisfy equalities but also achieve high accuracy. From this, it believed work can serve simulation realization more friendly.