Fractional-order inverse filters revisited: Equivalence with fractional-order controllers

Abstract

The equivalence of fractional-order inverse filters with fractional-order controllers is demonstrated in this work. This is achieved by appropriately rewriting the filters transfer functions in order to clarify the correspondence between the gain and time-constant of the filters and the scaling factor and differentiation/integration constant of the controllers. Possible implementations of fractional-order inverse filters using second generation voltage conveyors are presented and an application example, related to the control of a motion system, is demonstrated for evaluating the behavior of the introduced structures.