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Over-and under-convergent step responses in fractional-order transfer functions

Tavakoli Kakhki, M ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1177/0142331209356157
  3. Publisher: 2010
  4. Abstract:
  5. In this paper we highlight a remarkable difference between the step responses of a classical second-order transfer function and its fractional-order counterpart. It can be easily shown that the step response of a stable classical second-order transfer function crosses its final value infinitely over time. In contrast, it is illustrated here that the step responses of a fractional-order counterpart of the classical second-order model possess only a finite number of such crossovers. In other words, for such a system one can find a specific time instant after which the step response is over or under-convergent to its final value. This property interprets some phenomena observed in the real-world and should be considered during the design of the control system
  6. Keywords:
  7. Finite number ; Fractional-order systems ; Over-convergent ; Real-world ; Second orders ; Second-order models ; Specific time ; Step response property ; Under-convergent ; Speed control ; Step response ; Transfer functions
  8. Source: Transactions of the Institute of Measurement and Control ; Volume 32, Issue 4 , June , 2010 , Pages 376-394 ; 01423312 (ISSN)
  9. URL: http://journals.sagepub.com/doi/abs/10.1177/0142331209356157