Nonlinear Dynamics Of DC-DC Buck Converter Using Sliding Mode Method

With the continuous introduction of the policies to reduce energy consumption,lacking good quality of the converted electricity will be a problem demanding prompt solution for the power industry.It is also the focus center in the control science.It is reported in the Electrical and Electronic reports that the consumption of electric energy takes up fifty-five percent of the whole energy consumption.And seventy percent of the electric energy is used after conversion.In this paper,the DC-DC Buck converter is selectedas the controlled object,aiming to study the nonlinear dynamic behaviors in the Buck converter arise from sliding mode control.Besides,some problems such as stability,high-frequency chattering,bifurcation,unmodeled dynamics are analyzed in detail both in time domain and frequency domain.At last,the nonlinear behaviors of Buck converter are reduced quantitatively by multiple-phase sliding mode control.Buck converter is a typical kind of variable structure system containing switching characters.A huge amount of literature has proved that the relay control character of sliding mode control(SMC)is greatly fit for the Buck converter.In this paper,the basic theory of the sliding mode control will be elaborated first.Based on the uniform differential equation model of the Buck converter,which considers the switch both on and off,the design processes of linear sliding mode control,terminal sliding mode control and non-singular terminal sliding mode controlwhich are commonly used are given particularly.The stable condition of Buck converter is deduced in the time domain.The parameters of the controllers are set and the switching frequency of the switch is calculated.Buck converter is a kind of typical time-varying nonlinear system.The nonlinearity of energy storing elements capacitor and inductor and hysteresis modulation's boundary all have effects on the transient response of the system and quality of output voltage.In this paper,the stability is selected as the control target and the sampled-data model of Buck converter is built.The Filippov method is used to analyze and study the nonlinear behaviors of Buck converter.The supply voltage is selected as the bifurcation parameter and the capacity voltage in a sawtooth wave period is taken as the variable to judge and analyze t he bifurcation of the circuit.According to the eigenvalues,select circuit parameters and analyze the influences to the system performance of different nonlinear circuit parameters.Thus the oscillation phenomenon in the circuit can be restrained and the stability is guaranteed.Unmodeled dynamics in the Buck converter is also an important factor which will affect the nonlinear dynamic behaviors in the Buck converter controlled by sliding mode control.It will cause chattering problems and lead to high frequency harmonics.Thus,the consumption will increase and the system will oscillate or even lose stability.In this paper,the Buck converter's model containing the dynamics of sensors and actuators is built and its small time constant's effect to the Buck converter is deduced.Based on the describing function method,the high frequency harmonics in the output voltage is analyzed in quantity in the frequency domain and the amplitude and frequency of the chattering is deduced.The nonlinearity of hysteresis modulation is proved to be a big factor to influence the nonlinear dynamic behaviors in the Buck converter.And in practice,it is realized by power switch tube and complex voltage harmonics is caused.In this paper,the multi-phase sliding mode control method is introduced and applied to the Buck converter.By adjusting the phase difference between different phases,the harmonics can be counteracted and the quality of the Buck converter is improved.All the researches above are all expanded around sliding mode control.The methods in this paper are proved to be effective and feasible through simulations.