Boost变换器全分数阶化系统分析与控制性能研究

Research on Analysis and Control Performance of Full Fractional-order Boost Converter System

实际存在的系统大多具有分数阶特性,利用分数阶微积分理论对原系统进行建模能够更加准确地描述系统行为,并且用分数阶PID控制器代替整数阶PID控制器可以获得更好的系统性能。首先利用Oustaloup算法对s0.8进行5阶拟合,进而构建出5阶拟合的分数阶电感电容模型,相比10阶模型得到简化。在建立了Boost变换器的分数阶数学模型基础上,采用分数阶PID控制器形成了电压电流双闭环的Boost变换器全分数阶化系统。利用MATLAB软件对分数阶电路模型、分数阶数学模型以及全分数阶化系统进行仿真。研究结果表明,分数阶模型可以更准确地描述Boost变换器特性,分数阶PID控制的全分数阶化系统具有良好的稳态和动态性能。

In practice,most systems have fractional-order characteristics.Therefore,the modeling based on fractional-order calculus theory can describe the system behavior more accurately,and fractional-order PID controllers instead of integer-order PID controllers can achieve better system performance.In this paper,the Oustaloup algorithm is used to perform the fifth-order fitting of s0.8 at first.Then,the fifth-order fitting fractional-order inductance and capacitance model is constructed,which is simplified compared with the tenth-order model.Based on the establishment of the fractional-order mathematical model of a Boost converter,a full fractional-order system of the Boost converter with voltage-current double closed-loop is formed by using the fractional-order PID controller.The fractional-order circuit model,fractional-order mathematical model,and full fractional-order system are simulated using software MATLAB,and results show that the fractional-order model can describe the characteristics of the Boost converter more accurately,while the full fractional-order system controlled by the fractional-order PID has satisfying steady-state and dynamic performances.