Flyback变换器的分数阶建模与控制研究

Research on fractional-order modeling and control of Flyback converter

为了建立更准确的变换器模型并提高变换器的稳定性和抗干扰性,文中基于分数阶微积分理论和状态空间平均法,建立了电感电流连续模式(CCM)下Flyback变换器的分数阶数学模型和分数阶状态平均模型。首先,推导出直流稳态工作点、电感电流、电容电压的纹波和峰值表达式,并分析了Flyback变换器运行于CCM模式下的参数条件;其次,在建立的Flyback变换器分数阶数学模型基础上,结合滑模控制强鲁棒性的特性,提出分数阶终端滑模的控制策略,并设计给出了分数阶终端器的滑模面和控制率;最后,利用Simulink对Flyback变换器分数阶模型和分数阶滑模控制器进行仿真。结果表明,Flyback变换器的分数阶模型能更真实地反映变换器的动力学行为,设计的分数阶终端滑模控制器能有效跟随目标输出电压、电流并降低系统纹波,从而提高系统的稳定性和鲁棒性。

In order to establish more accurate converter model and improve the stability and anti-interference performance of the converter,the fractional-order mathematical model and the fractional-order state-average model of the Flyback converter in the inductive current continuous mode(CCM)are established based on the fractional-order calculus theory and the state space averaging method. The expressions of ripple and peak value of DC steady-state operating point,inductive current and capacitor voltage are derived,and the parameter conditions of Flyback converter operating in CCM are analyzed. On the basis of the established Flyback converter fractional-order mathematical model,a control strategy for fractional-order terminal sliding mode is proposed by combing the strong robustness of sliding mode control,and the sliding-mode surface and control rate of the fractional-order terminator are designed. The Flyback converter fractional-order model of Flyback converter and fractional-order sliding mode controller are simulated by means of Simulink. The results show that the fractional-order model of the Flyback converter can more truly reflect the dynamic behavior of the converter,and the designed fractional-order terminal sliding mode controller can effectively follow the target output voltage and current,reduce the system ripple,and improve the stability and robustness of the system.