By Alain Oustaloup
According to a dependent method of range, significantly encouraged via a number of kinds of variety of traditional origins, range and Non-integer Derivation utilized to method Dynamics presents a learn framework to the advent of the non-integer by-product as a modeling instrument. Modeling instruments that spotlight unsuspected dynamical performances (notably damping performances) in an "integer" method of mechanics and automation also are integrated. Written to let a two-tier interpreting, this can be a necessary source for scientists, researchers, and business engineers drawn to this topic a. �Read more...
summary: in line with a dependent method of variety, significantly encouraged via quite a few kinds of range of average origins, range and Non-integer Derivation utilized to method Dynamics presents a examine framework to the creation of the non-integer by-product as a modeling software. Modeling instruments that spotlight unsuspected dynamical performances (notably damping performances) in an "integer" method of mechanics and automation also are integrated. Written to allow a two-tier analyzing, this is often an important source for scientists, researchers, and business engineers attracted to this topic a
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Extra info for Diversity and Non-integer Differentiation for System Dynamics
Moreover, through the recursive factors α and η, which express the difference from one pore to another, the damping ratio turns out to be exclusively linked to the difference introduced in the porous face. To conclude, it is then diversity that determines the damping. This damping is structural because it depends only on the structure intrinsic ratios α and η. 2. 19). 19. 53] expresses a non-integer integration (of unit gain frequency ω u = 1 / τ ) where the order n appears no longer as a differentiation non-integer order, but as an integration non-integer order.
3] the recursive factors α and η being greater than 1. 1. 2. On the asymptotic diagrams at stake What about the factor of rank i , 1+ jω / ωi' 1+ jω / ωi ? 2(a)): – 1 for ω << ωi' and ωi , namely a gain of 20 log1 = 0 in dB and a nil phase; – j ω for ωi' << ω << ωi , namely a gain of 20 log ω in dB and a phase of π 2; ωi' ωi' – ωi = α for ω >> ωi' and ωi , namely a gain of 20 log α in dB and a nil phase.
36 Diversity and Non-integer Differentiation for System Dynamics The “non-integer” approach indeed enables us to overcome the mass-damping dilemma in mechanics and, consequently, the stability-precision dilemma in automatic control. Furthermore, the metallic and hydropneumatic versions of the CRONE suspension are the subject of a unified presentation through various forms of diversity leading to non-integer differentiation. To illustrate our strategy through a study system, we have studied the relaxation of water on a porous dyke.