Design of fractional order differentiator using feedback system

A new feedback-based methodology for the implementation of a fractional-order differentiator (FD) is described in this paper. The differentiator can be based on a standard definition of the fractional calculus, such as the Riemann-Liouville or Grunwald-Letnikov definitions. Some methods by which the FD functions can be approximated using a DSP-based implementation (either FIR or IIR) are described, In the new implementation, a classical IIR FD and a fractional-order integrator are combined using a proportional feedback loop. This structure is found to improve the performance of the FD, in terms of both its frequency-domain and time-domain characteristics. Design examples, including appropriate plots, facilitate comparison of the new FD with other FD implementations.