论文部分内容阅读
In this paper,Noether symmetries and solutions of the Buck-Boost converter are investigated,and the time responses of the converter are analyzed with these solutions.Firstly,the Euler-Lagrange equations of the Buck-Boost converter are built up.Secondly,based on the invariance of Hamilton action of the system,under the infinitesimal transformation on the generalized electric charges and the time,the generalized Noether quasi-symmetry transformation,the generalized Noether identity and the generalized Killing equations are obtained for the Buck-Boost converter.Thirdly,the generalized Noether theorem and corresponding conserved quantities are presented.Furthermore,the exact solutions of the converter are obtained,and then the transient and steady responses of inductor currents and capacitor voltages are calculated by exact solutions.We also do some simulations,which are coincident with the existing experimental results,about inductor current and output voltage of the converter.