N-cycle Control And Stability Of DC-DC Converters Based On Switched Systems Models

Different from the traditional control strategy,one-cycle control method achieves one-cycle voltage control by choosing average voltage over a switching period as feedback signal.Based on DC chopper principles of DC-DC converters,one-cycle manipulation method with high dynamic response characteristics has become an important control strategy for power electronic converters.However,due to the different structures and parameters of diverse power electronic converters,the inherent time-constants of the converter varies greatly,and the one-cycle controller is not suitable for all power converters.In addition,no elaborate mechanism of one-cycle control method and stability analysis were proposed in the view of control theories.Based on the nonlinear systems theories,therefore,the one-cycle control strategy is further recognized,new control strategy and stability analysis method of power electronic converters are presented,which are full of theoretical and practical significance.In this paper,DC-DC converters are considered as periodic switched affine systems.The periodic controllability of the system is analyzed by the theories of switched systems,the periodic controllability index criterion and N-cycle control strategy are also proposed.The N-cycle control strategy covers one-cycle manipulation method.With different structures and time constants,the state variables of the corresponding converters achive completely controllable in 2 cycles,3 cycles,...,and N cycles.Thereby,one-cycle control method is extent to general N-cycle.Furthermore,stability analysis of DC-DC converters are proceeded with switched system theories.The main contributions of the thesis are listed as follows.1.Based on switched systems theories,according to the characteristics of power electronic converters with limited switching period and uncontrollable inputs,periodic switched affine systems models of DC-DC converters are established.Augmented periodic switched autonomous systems models of DC-DC converters are also built through the method of augmentation of state variables in one dimension.These provide the basis for periodic controllability analysis and N-cycle control streategy,as well as stability studies.2.Based on the theories of periodic controllability of switched systems,the controllability of one-cycle and N-cycle control for DC-DC converters are analyzed.The results show that one-cycle controlled Buck converter is one-cycle controllability,and the mechanism of the closed-loop system is clarified theoretically.Meanwhile,one-cycle control method is suitable for Boost converter,Sepic converter,Flyback converter and LLC series resonant DC-DC converter.But Cuk power factor correction converter and Buck-Boost converter is N-cycle controlled instead of one-cycle.3.Based on the periodic controllability index of switched system,the N-cycle control strategy for DC-DC converters is proposed according to the N-cycle controllability.The results show that 2-cycle control method helps Buck-Boost converter achieves dynamical manipulation,which means that there needs 2 cycles of the Buck-Boost converter reaches stable state.In addition,the fastest dynamic stability control of Cuk PFC requires at least 3 periods.4.When the parameters mismatch occur between the control strategy and the power stage,one-cycle controlled DC-DC converter is unstable.A new stability analysis method suitable for DC-DC converters is proposed,and the stable boundary of switching period is obtained.It is shown that when the input voltage is disturbed,the constant on-time one-cycle controlled Buck converter is stable in the stable region,and produces unstable behaviors outside the stable region.5.The nonlinear phenomena of boost converter manipulated by constant on-time one-cycle control law are further studied.The critical boundary of the converter is derived,and the stability of the closed-loop system is analyzed.The results show that the bifurcation of the system will occur when the parameters of the one-cycle control strategy do not match the power stage of the Boost converter.It remarks that a couple of conjugate multipliers of transition matrix cross the unit circle gradually with constan-on time value incearsing,meanwhile the step-up power stage moves from period-1 state into Neimark-sacker bifurcation.Based on the stability analysis,an additional current loop is developed to stabilize the entire system by extending the stable region.