| This thesis studies the region stability of switching circuit systems with multiple equilibrium points.That is,the region stability issues are studied for the DC-DC converters consisting with switching circuit systems working in two different modes of CCM and DCM.From the viewpoint of theoretical analysis,based on the form of switched linear systems with multiple equilibrium points,by using the mathematical modeling technology and the general solution solving method,we analyze some classes of switching circuits of BUCK circuits,BOOST circuits,and BUCK-BOOST circuits working in both the CCM mode and the DCM mode,and then obtain several criteria of the region stability of the above switching circuits.The main study contents and results are as follows.(1)The mathematical model formulations.By using the basic circuit principles of Kirchhoff’s voltage law(KVL),Kirchhoff’s current law(KCL),and the Ohm’s law,we analyze the topological structures of the BUCK circuits,the BOOST circuits,and the BUCK-BOOST circuits working in both the CCM mode and the DCM mode,and formulate their mathematical models in the form of switched linear time-invariant systems with multiple equilibrium points.(2)Region stability analysis.Firstly,by using the theorems of region stability of switched systems with multiple equilibrium points,we show that the switching circuit system of the BUCK circuit in the CCM mode is asymptotically regional stable based on the fact that resistance,inductance,and capacitance are all positive constants in such kind of switching circuits.Secondly,by using the general solutions of the Cauchy problem of ordinary differential equations and the successive iteration method,we solve the general solutions of the BOOST circuits and the BUCK-BOOST circuits in the CCM mode,respectively.Based on the definition of the region stability of the switched linear systems with multiple equilibrium points,by using the mathematical analyzing tools and methods of the norms of matrix and vector as well as the methods of determining the convergent condition of the matrix series,we analyze the general solutions obtained for the switching circuit systems of the BOOST circuits and the BUCK-BOOST circuits in the CCM mode,and obtain several results of region stability of the two kinds of switching circuits,respectively.In the DCM mode,the method of general solution is also adopted to analyze the regional stability of the three kinds of circuits,and several sufficient conditions for regional asymptotic stability are obtained.(3)Numerical simulations and experimental tests.Firstly,based on the theoretical results obtained in this master’s thesis,several numerical examples are carried out for three types of switching circuit systems of BUCK circuit,BOOST circuit and BUCKBOOST circuit in the two modes of CCM and DCM via MATLAB software.Then,by means of MULTISIM software,three classes of practically switching circuits are built;And the corresponding experiments are accomplished.Finally,both the numerical simulations and the experimental results verify the feasibility,validity and operability of the regional stability results obtained in thesis for the multi-equilibria switching circuit systems of the DC-DC converters. |
