Continuous-time and discrete-time implementations of fractional-order controllers

Abstract

In the previous chapters, different types of fractional-order controllers are addressed. The most difficult problem yet to be solved is how to implement them. Although some work has been performed with hardware devices for fractional-order integrator, such as fractances (e.g., RC transmission line circuit and Domino ladder network) [154] and fractors [155], there are restrictions, since these devices are difficult to tune. An alternative feasible way to implement fractional-order operators and controllers is to use finite-dimensional integer-order transfer functions. Theoretically speaking, an integer-order transfer function representation to a fractional-order operator sα is infinite-dimensional. However it should be pointed out that a band-limit implementation of fractional-order controller (FOC) is important in practice, i.e., the finite-dimensional approximation of the FOC should be done in a proper range of frequencies of practical interest [17, 51]. Moreover, the fractional-order can be a complex number as discussed in [51]. In this book, we focus on the case where the fractional order is a real number.