Self-excited oscillations systems with switchings: Theory, calculating, investigating
Periodic Control Systems, Volume # 3 | Part# 1
Digital Object Identifier (DOI)
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.
 Dusavitskii, Yu. Ya. (2003). A switched stabilizer: An investigation usinig the method of surfaces for cycles. Electricity 12, 50-57. (in Russian).  Gupta, P. and A. Patra (2005). Hybrid mode-switched control of DC-DC boost converter circuits. IEEE Trans. Circuits Syst. II 52, 734-738.