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  4. Calculation of stable and unstable periodic orbits in a chopper-fed DC drive

Calculation of stable and unstable periodic orbits in a chopper-fed DC drive

MMC.
2021;
Volume 8, Number 1
: pp. 43–57
https://doi.org/10.23939/mmc2021.01.043
Received: October 29, 2020
Revised: November 30, 2020
Accepted: December 01, 2020

Mathematical Modeling and Computing, Vol. 8, No. 1, pp. 43–57 (2021)

Authors:
  1. O. O. Kuznyetsov
1
Hetman Petro Sahaidachnyi National Army Academy

It is well known that electric drives demonstrate various nonlinear phenomena.  In particular, a chopper-fed analog DC drive system is characterized by the route to chaotic behavior though period-doubling cascade.  Besides, the considered system demonstrates coexistence of several stable periodic modes within the stability boundaries of the main period-1 orbit.  We discover the evolution of several periodic orbits utilizing the semi-analytical method based on the Filippov theory for the stability analysis of periodic orbits.  We analyze, in particular, stable and unstable period-1, 2, 3 and 4 orbits, as well as independent on stability they are significant for the organization of phase space.  We demonstrate, in particular, that the unstable periodic orbits undergo border collision bifurcations; those occur according to several scenarios related to the interaction of different orbits of the same period, including persistence border collision, when a periodic orbit is changed by a different orbit of the same period, and birth or disappearance of a couple of orbits of the same period characterized by different topology.

DC drive
stability
periodic orbits
bifurcations
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