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

: pp. 43–57
Received: October 29, 2020
Revised: November 30, 2020
Accepted: December 01, 2020

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

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.

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