Continuous-time and Discrete-time Implementations of Fractional-order Controllers

Part of the Advances in Industrial Control book series (AIC)


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 s α 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.


Reduce Order Model Continue Fraction Expansion Bode Plot Frequency Response Data Discrete Transfer Function 
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© Springer-Verlag London Limited 2010

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