基于遗传算法的不确定压电柔性结构H_2/H_∞混合振动控制  

APPLICATION OF GENETIC ALGORITHM ON MIXED H_2/H_∞ VIBRATION CONTROL FOR UNCERTAIN PIEZOELECTRIC FLEXIBLE STRUCTURES

作　　者：徐亚兰[1] 陈建军[1] 

机构地区：[1]西安电子科技大学机电工程学院,西安710071

出　　处：《工程力学》2013年第4期1-6,共6页Engineering Mechanics

基　　金：中央高校基本科研业务费专项资金项目(JY10000904012);国防预研基金项目(51421060505DZ0155)

摘　　要：无穷范数和2-范数是优化控制理论的两个重要系统性能指标。前者考虑可能发生振动的最坏情况,过于保守;后者考虑系统的综合性能,未考虑共振情况;将两种指标结合起来将会同时兼顾鲁棒稳定性和系统时域性能。该文考虑不确定压电柔性结构模态参数的不确定性及模型误差,建立了结构模态空间的线性分式模型,给出了一种基于遗传算法的结构混合动态输出反馈振动控制器设计方法。首先通过线性矩阵不等式得到了多个无穷范数性能指标下的控制器,然后通过遗传算法对所得到的控制器进行了系统2-范数性能优化,设计了兼顾鲁棒性和系统时域性能要求的混合动态输出反馈控制器。H-infinity norm and 2-norm are two important indexes in optimal control theory.The former considers the worst situation involving vibration and tends to be conservative,while the latter takes the overall performance of the system into consideration without concerning the worst vibration situation.Both robust performance and time-domain performance may be obtained by combining two indexes.Taking into account uncertainties due to modal parameters variation and un-modeled residual modes,the linear fractional representation is developed for piezoelectric flexible structures and a general approach is proposed to design mixed dynamic output feedback controllers by genetic algorithm（GA）.H-infinity control laws are obtained by using linear matrix inequality before the 2-norm performance of system is optimized by GA.The simulation results show that the closed loop system possesses both robust performance and time-domain performance.

关 键 词：压电柔性结构 不确定性 振动控制 遗传算法 输出反馈 

分 类 号：TH113[机械工程—机械设计及理论] TP13[自动化与计算机技术—控制理论与控制工程]