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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Stable and Unstable Behaviors for Brushless Motor with Harmonic Disturbance via Discrete Implicit Maps

Discontinuity, Nonlinearity, and Complexity 7(4) (2018) 463--477 | DOI:10.5890/DNC.2018.12.010

Jianzhe Huang

Department of Power and Energy Engineering, Harbin Engineering University, Harbin, 150001, China

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Dynamic model for brushless motor in the rotating frame is studied in this paper, where a periodic disturbance is introduced in the quadrature-axis voltage. The methodology of discrete implicit maps is adopted to investigate the dynamical response of such brushless motor system. Multiple closed semi-analytic bifurcation routes for period-1 motions are found by varying frequency of disturbance of the quadrature-axis voltage. The stability conditions for periodic motions will be given through eigenvalue analysis. From the semi-analytical prediction of period-1 motions, the corresponding frequency-amplitude characteristics are obtained. Finally, the stable and unstable period-1 motions will be presented numerically. With such discrete implicit maps method, the unstable motion of such brushless motor with strong nonlinearity can be obtained. Compared to the method of generalized harmonic balance, the dimension of Jacobian matrix can be dramatically decreased and the numerical error can be avoided without using QR algorithm.


This study is supported by the National Natural Science Foundation of China (Grant no. 51375104), Heilongjiang Province Funds for Distinguished Young Scientists (Grant no. JC 201405), China Postdoctoral Science Foundation (Grant no. 2015M581433), and Postdoctoral Science Foundation of Heilongjiang Province (Grant no. LBH-Z15038).


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