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Self-excited oscillations systems with switchings: Theory, calculating, investigating
Periodic Control Systems, Volume # 3 | Part# 1
Authors
Yurii Dusavitskii
Digital Object Identifier (DOI)
10.3182/20070829-3-RU-4912.00013
Page Numbers:
83-86
Index Terms
self-excited oscillations,cycles,switching
Abstract
It is accepted for the systems: autonomy, quick and slow motions, the feedback switchings with hysteresis, the variable structure on the intervals. The mathematical description is m differential equations of the nth order, which change one to another periodically. Some values of the intervals during (tk) are put under the cycles equations, which are changed into algebraic instead of transcendental. Then the surfaces for cycles (SC) are calculated and constructed. The switching conditions are put under SC. The intersections of the curves make the parameters of oscillations. It is proved the existence and the unique of SC. They have special points and lines and may by Multisheeted. It is possible to find the required switching conditions. There are two numerical examples.
References
[1] Dusavitskii, Yu. Ya. (2003). A switched stabilizer:
An investigation usinig the method of surfaces
for cycles. Electricity 12, 50-57. (in Russian).
[2] Gupta, P. and A. Patra (2005). Hybrid mode-switched
control of DC-DC boost converter
circuits. IEEE Trans. Circuits Syst. II
52, 734-738.