2017
DOI: 10.1007/978-3-319-52950-9
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Fractional-order Modeling and Control of Dynamic Systems

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Cited by 131 publications
(77 citation statements)
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“…The fractional‐order nature of the integration operator, s −δ , makes it digitally nonimplementable. Hence, the fractional integral operator is approximated using a fifth‐order Oustaloup's recursive filter in order to practically implement it using an embedded computers . The lower and upper bounds of the translational frequencies of the filter are empirically selected as ω L = 10 −3 rad/s and ω H = 10 3 rad/s, respectively .…”
Section: Fractional‐order Proportional‐integral Controllermentioning
confidence: 99%
“…The fractional‐order nature of the integration operator, s −δ , makes it digitally nonimplementable. Hence, the fractional integral operator is approximated using a fifth‐order Oustaloup's recursive filter in order to practically implement it using an embedded computers . The lower and upper bounds of the translational frequencies of the filter are empirically selected as ω L = 10 −3 rad/s and ω H = 10 3 rad/s, respectively .…”
Section: Fractional‐order Proportional‐integral Controllermentioning
confidence: 99%
“…For continuous implementation, pole-zero pairs should be in the negative real axis of -plane and for discrete implementation, pole-zero pairs should lie within the unit circle of -plane. More number of pole-zero pairs exhibit better and close approximation, but increases the memory requirements and complexity; however, the advent of modern powerful software can easily deal with additional complexity [106].…”
Section: Implementation Challenges and Softwarementioning
confidence: 99%
“…The fractional operator is denoted by G γ ; where, γ is the positive and real numbered exponent of the operator. The three common definitions of fractional operation are provided by Riemann‐Liouville, Gruunwald‐Letnikov, and Caputo in Equations (25) to (27), respectively Gγf()t=1Γ()nγdnitalicdtnatf()τ()tτγn+1italicdτ, …”
Section: Control System Designmentioning
confidence: 99%