Research On Modeling And Control Of Fractional-order DC-DC Converters

In recent years,fractional calculus theory has been widely applied in circuit analysis.According to the research,the actual external characteristics of inductance and capacitance in the circuit show fractional order.Approximating inductance and capacitance in DC-DC conversion as integral order will cause modeling error,thus affecting the analysis and control of the converter.In order to study DC-DC converter more accurately,fractional calculus theory is needed to study DC-DC converter.Based on the model of fractional-order Buck converter established by state-space averaging method,a fractional-order PID controller is designed in this paper,and then the model of fractional Buck-boost converter is established by using equivalent small parameter method.The main contents are as follows:1.The fractional-order modeling of Buck circuit is introduced by using the state-space average method.The Oustaloup wave filter is used to build its numerical simulation model,meanwhile,the circuit model is also built for simulation.Matlab/Simulink is used to conduct simulation verification,so as to verify the correctness of the model.2.The advantages of fractional-order PID controller and three commonly used design methods of fractional-order PID controller are introduced.The fractional-order PID controller design method based on numerical optimization is used to compensate and control the obtained fractional-order Buck circuit,so as to obtain better design effect.And the transfer function is simulated and analyzed to improve the steady-state performance of the system.Then,based on the design of integer-order PI controller,a PI~?controller is designed to compensate the system,and the control effects of integer-order PI controller and PI~?controller are compared.3.The study introduced what superiorities a fractional-order PID controller holds and three frequently-applied design methods for them.To obtain a better design effect,a numerical optimization-based designing method was exercised to apply compensatory control over the obtained fractional-order Buck circuit.Then,its transfer function was simulated and analyzed,with a view to perfect the stability of the system.Finally,based on the design of the integer-order PI controller,a PI~?controller was designed to compensate the system.The control effects of the integer-order PI controller and the PI~?controller were compared.4.By equivalent small parameter method,the study modeled and analyzed the fractional Buck-boost converter in mode of continuous inductor current.In combination with the principle of harmonic balance,an approximate analytical steady-state solution of state variables was obtained.Based on the methods proposed here,the study obtained the conditions of converter operation and continuous inductor current modes.Besides,harmonic analyses were involved.They helped analyze out the influence of order changes on the capacitor voltage and the size of each inductor current harmonic.At last,the study,based on the approximation of Oustaloup filter,numerically simulated the Buck-boost converter and devised a fractional-order capacitor and inductor,so as to verify the effectiveness of the method by simulate the circuit model.