DC/DC变换器的切换仿射线性系统模型及控制

DC/DC变换器控制的主要难点之一在于它所特有的混杂特性。从切换线性系统理论及无源系统理论角度提出了DC/DC变换器建模和调节问题的新方法。首先建立基本DC/DC变换器Buck、Boost和Buck-Boost的切换仿射线性系统模型，然后根据凸组合稳定条件及无源性理论，选取电感和电容的储能函数为各切换子系统的共同Lyapunov函数，据此划分各子系统的运行区域，构造切换律保证系统在任意切换下的二次稳定，最后进行了仿真分析和验证。所提出方法不仅适用于开关变换电路的控制，亦适用于其他具有端口受控哈密顿结构的切换系统的控制。

Switched Affine Systems Modeling and Control of DC/DC Converters

The main difficulties in controlling DC-DC power converters arise from their hybrid nature. A novel approach to the modeling and regulation problem of DC/DC converters is presented from the combined perspective of switched system and passivity system theory. Three basic types of converter, namely Buck, Boost and Buck-Boost are modeled as switched affine systems, respectively. Then, based on the sufficient condition for quadratic stability of convex combination of the controllers, combined with using the stored energy in the inductance and the capacitance as a common Lyapunov function, switching rules and activation region of all the subsystems can be defined to assess quadratic stability of the switched system. Simulation results are provided that demonstrate the validity of this approach. The proposed modeling and control methodology can be extended to any kind of switched power converter and the other port-controlled Hamiltonian switched systems.