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

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

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 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.

Keywords

Reduce Order Model Continue Fraction Expansion Bode Plot Frequency Response Data Discrete Transfer Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 2010

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