基于切换线性系统平衡实现的Boost变换器模型降阶

Reduced-order model of Boost converter based on balanced realization theory of switched linear system

针对电力电子系统经线性化处理后可看成具有多个线性子系统的切换线性系统的模型降阶问题,提出了一种切换线性系统的模型降阶方法。对切换线性系统若直接采用传统线性系统模型降阶法降阶,将无法保证降阶后系统的稳定性和保留原系统的主要特征。首先依据切换线性系统平衡实现理论得到的模型降阶方法,对切换线性子系统的可控和可观格莱姆矩阵分别取平均,得到一个新的平衡变换矩阵;然后以平衡变换矩阵对子系统分别进行平衡变换得到新的平衡系统;再根据平衡系统的Hankel奇异值大小,保留平衡系统中的关键状态变量进行平衡截断,得到降阶后的系统。最后以含寄生参数的Boost实际电路为例,基于所提降阶算法建立其降阶模型,通过仿真分析验证了所提降阶算法的有效性与准确性。

A model reduction method of switched linear system was proposed to solve the model reduction problem of switched linear system which can be regarded as a switched linear system with multiple linear subsystems after linearization.If the traditional linear system model reduction method is directly used to reduce the order of switched linear system,the stability of the reduced order system and the main charac-teristics of the original system could not be guaranteed.According to the model reduction method obtained from the balancing realization theory of switched linear system,a new average balancing transformation matrix was obtained by averaging the controllable and observable gramians of the switched linear subsys-tems.Then,the balancing transformation matrix was used to balance the subsystems to obtain a new bal-anced system.According to the Hankel singular value of the balanced system,the key state variables in the balanced system were retained for balanced truncation,and the reduced order system was obtained.Finally,a boost circuit with parasitic parameters was taken as an example,and the reduced order model was established based on the proposed reduced order algorithm.Through simulation analysis,effective-ness and accuracy of the proposed order reduction algorithm are verified.