【摘要】 为了进一步提高变换器建模的精度，准确地描述其真实的动力学行为，并为变换器的优化控制提供更为准确的理论依据，基于电感和电容本质是非整数阶的事实，根据分数阶微积分理论，建立电流连续模式下Cuk变换器的分数阶模型，并采用分数阶PI~λD~μ控制器进行控制。其次为了降低分数阶PI~λD~μ控制器的参数整定难度，提出一种基于BP神经网络的Cuk变换器分数阶PI~λD~μ控制策略。最后在Matlab/Simulink仿真平台上进行仿真验证，分析了分数阶PI~λD~μ控制的分数阶Cuk变换器的稳态、鲁棒性及动态性能，并与整数阶PID控制器作对比。实验结果表明：建立的变换器分数阶模型可以更准确地描述实际系统的真实特性；和整数阶PID控制对比，分数阶PI~λD~μ控制系统鲁棒性更强，控制灵活性更好，进一步提升了系统的动态特性。更多还原

【Abstract】 The purpose of this paper is to further improve the modeling accuracy of the converter,describe its real dynamic behavior more accurately,and provide a more accurate theoretical basis for the optimal control of the converter. On the basis of the fact that the inductance and capacitance are essentially non-integer order,the fractional-order model of Cuk converter in current continuous mode is established according to the theory of fractional calculus,and the fractional-order PI~λD~μ controller is used to control it. In order to reduce the parameter tuning difficulty of fractional-order PI~λD~μ controller,a fractional-order PI~λD~μ control strategy for Cuk converter is proposed. This control strategy is based on BP neural network. At last,the steady state,robustness and dynamic performance of fractional-order Cuk converter controlled by fractional-order PI~λD~μ are analyzed by verification simulation on platform Matlab/Simulink,and it is contrasted with integer-order PID controller. The experimental results show that the fractional-order model of the converter can describe the real characteristics of the actual system more accurately. In comparison with integer-order PID control,fractional-order PI~λD~μ control system has stronger robustness and better control flexibility,which further improves the dynamic characteristics of the system.更多还原