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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。
Infinite norm and 2-norm are two important system performance indicators of optimal control theory. The former considers the worst case of possible vibration and is too conservative. The latter considers the overall performance of the system and does not consider the resonance situation. Combining the two indicators will take into account the robust stability and the time-domain performance of the system. In this paper, the uncertainties and model errors of uncertain modal parameters of piezoelectric flexible structures are considered. A linear fractional model of structural modal space is established. A hybrid dynamic output feedback vibration controller based on genetic algorithm method. Firstly, a series of controllers with infinite norm performance were obtained by linear matrix inequalities. Then the system performance of the controller was optimized by genetic algorithm, and the robustness and time-domain performance Required Hybrid Dynamic Output Feedback Controller.