综合模态H2范数下致动器/传感器的优化配置

致动器/传感器的优化配置问题是智能柔性结构振动主动控制中的关键技术问题,基于模态空间H_2范数研究了智能柔性梁系统中压电致动器/传感器的优化配置问题。根据Rayleigh-Ritz理论建立了系统的动力学方程并得到其状态空间表达式。提出了一种衡量系统能控/能观性并考虑模态权重的综合模态H_2范数准则,采用改进遗传算法研究系统中并置致动器/传感器的优化配置问题,得到了系统多个模态、综合模态H_2范数最优的致动器/传感器布局结果。实验结果表明,利用优化结果进行致动器/传感器的布局,系统单个模态和综合模态均具有较好的检测和控制效果,被控模态具有较好的能控/能观性,所提出的优化准则和优化方法是可行的。

Optimization of Piezoelectric Actuators/Sensors Placement Using Synthetic Modal H2 Norm

In active vibration control of a smart flexible structure, the placement of actuators and sensors is a key aspect of the control system design. The optimal placement of piezoelectric actuators and sensors using modal H2 norm criteria is considered. Based on Rayleigh-Ritz and modal theory, the system modal equations and closed-loop state space equations are derived. Then, a synthetic modal H2 norm criterion representing the controllability and observability of the system is proposed. Using an improved genetic algorithm, the optimal configurations of collocated piezoelectric actuators and stress sensors of the system for single and synthetic modals are found. To verify the validity and feasibility of the presented optimal criterion and method, an experimental system is designed and set up. The analytical and experimental results demonstrate that the smart flexible beam system has a high degree of controllability and observability, such that both the single modal of interest and synthetic modals are well observed and controlled. The proposed optimal criterion and method are feasible and effective.