电感电流伪连续模式下分数阶Boost变换器的非线性控制

基于电容和电感都是分数阶的事实,采用分数阶微积分理论,建立了电感电流伪连续模式下Boost变换器的分数阶状态空间平均模型.针对其分数阶模型具有仿射非线性系统的特点,根据分数阶的类Lyapunov稳定性理论,设计了适用于分数阶电感电流伪连续模式下Boost变换器的一种分数阶非线性控制器.依据分抗链及改进的Oustaloup分数阶近似算法,得到了分数阶电感和电容的等效电路模型,用Matlab/Simulink软件对所设计的控制器进行了仿真验证.结果表明:所设计的分数阶非线性控制器对分数阶电感电流伪连续模式下的Boost变换器的动态和稳态性能有显著的提高,并且在输入电压和负载大幅度波动的情况下,仍然能够确保系统具有良好的稳定性和动态性能.

Non-linear control for the fractional boost converter in pseudo continuous conduction mode

Based on the fact that the inductor and the capacitor are of fractional order in nature, the mathematical model of the fractional order boost converter in pseudo continuous conduction mode is established by using the fractional order calculus theory. Due to the affine non-linear nature in this mathematical model and a similar Lyapunov stability theorem of the fractional order system, a fractional order non-linear controller is designed. On the basis of chain fractance and the improved Oustaloup algorithm, the circuit model of fractional order inductor and capacitor are built. The fractional order controller is verified by the Matlab/Simulink software. Simulation results show that the controller enhances the dynamic and steady-state performance, so as to realize the stability and achieve good dynamic performance of the fractional order system during large fluctuation of power supply and load disturbance.
Keywords：fractional orderboost converterpseudo continuous conduction mode (tri-state mode)non-linear control