Dynamic Analysis And Control Of Fractional Order DC-DC Converter

As a DC voltage converter,the main function of DC-DC converter is to transform the input voltage into an ideal output voltage.Because it’s a kind of time-varying and nonlinear system,all kinds of nonlinear phenomena are easy to occur,the stability and reliability of the converter will be directly affected by these phenomena.At the same time,because of the operation characteristics of the converter,the nonlinear and discontinuous control strategy is needed.The changes of system parameters and load will affect the controller’s effect,and ultimately affect its response speed and robustness.Early research on dynamic behavior and control of DC-DC converter only for integer order model,the actual current capacitance and inductance are fractional order.The integer order model of inductance and capacitance are used to study their electrical characteristics,the result may be not accurate enough,so the research on dynamic behavior and control of fractional order DC-DC converter become a new research topic.The fractional-order mathematical model and fractional-order state-space averaging model of Buck and Boost converters in continuous conduction mode are established based on the theory of fractional calculus and the fact that actual capacitances and actual inductances are fractional in nature,and the parameter condition of converter operating in continuous conduction mode are given through theoretical analysis.The circuit variables are used as reference variables,the dynamic behavior of the fractional order converter is analyzed by using the bifurcation diagrams and other dynamic characterization.In addition,the fractional order sliding mode controller is designed for the converter based on the fractional order control system stability theory and sliding mode control strategy,which improves the rapidity and robustness of the output response of the system.The following is the main content and innovations of the thesis:(1)The fractional-order mathematical model and fractional-order state-space averaging model of Buck and Boost converters in continuous conduction mode are established based on the theory of fractional calculus and the fact that actual capacitances and actual inductances are fractional in nature,and the parameter condition of converter operating in continuous conduction mode are given through theoretical analysis.The circuit variables are used as reference variables,the dynamic behavior of the fractional order converter is analyzed by using the bifurcation diagrams and other dynamic characterization.The correctness of the theoretical analysis is verified by numerical simulation,the dynamic behavior of the converter is related to the circuit variables.(2)For the fractional order Buck converter and Boost converter,fractional order sliding mode controller is designed based on fractional order sliding mode control,which makes the response speed of the converter further speed up,and increases the anti-interference ability and robustness of the converter.With the addition of a linear term,the state of the converter falls on the sliding surface at the beginning,thus ensuring the global robust control.The correctness of the designed controller is verified by numerical simulation.(3)For the fractional order Buck converter and Boost converter in the case of uncertain parameters and unknown interference upper bounds,a fractional order adaptive sliding mode controller is designed based on the principle of fractional order sliding mode control.Adaptive controller is used to estimate the uncertain parameters and the upper bound of disturbances,so as to eliminate uncertainties and disturbances.The designed controller can effectively reduce the chattering of the controller while ensuring the fast response speed,strong anti-interference ability and good robustness of the converter.The correctness of the designed controller is verified by numerical simulation.