A New Control Strategy Based on the Concept of Non Integer Derivation: Application in Robot Control

Oustaloup, Alain; Melchior, Pierre; Yagoubi, A. El

doi:10.1016/b978-0-08-037023-1.50113-8

Cited by 2 publications

(1 citation statement)

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“…Since the early 1990's, some scientists and engineers have been working with those different forms, having in mind the perspective of practical applications [33], [34], [35], [36]. It is important to refer the pioneering works of Oustaloup's group in control and identification [37], [38], [39], [40], [41], [42]. The fractional electrical circuits started being investigated [43], [44], [45], [46], [47], [48].…”

Section: B a Short Historymentioning

confidence: 99%

The 21st Century Systems: An Updated Vision of Continuous-Time Fractional Models

Ortigueira

Machado

2022

IEEE Circuits Syst. Mag.

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This paper presents the continuous-time fractional linear systems and their main properties. Two particular classes of models are introduced: the fractional autoregresive-moving average type and the tempered linear system. For both classes, the computations of the impulse response, transfer function, and frequency response are discussed. It is shown that such systems can have integer and fractional components. From the integer component we deduce the stability. The fractional order component is always stable. The initial-condition problem is analysed and it is verified that it depends on the structure of the system. For a correct definition and backward compatibility with classic systems, suitable fractional derivatives are also introduced. The Gr ünwald-Letnikov and Liouville derivatives, as well as the corresponding tempered versions, are formulated.

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