基于结构奇异值理论的压电柔性结构振动鲁棒控制

Robust Vibration Control of Flexible Piezoelectric Structure Based on Structured Singular Value Theory

基于结构奇异值μ理论,针对含压电作动器和传感器的柔性结构,提出了不确定性振动控制系统的一般分析框架和鲁棒控制器设计方法。考虑了结构的模态参数不确定性和高阶未建模动态,通过引入适当的虚拟输入、输出和相应的加权函数分离出系统的不确定部分,建立适合于鲁棒μ控制器设计的增广系统,用D_K迭代算法求解控制器,以使闭环系统同时满足鲁棒稳定性和鲁棒性能要求。以含一个压电作动器和传感器的悬臂梁为例设计了鲁棒控制器,仿真结果表明对结构振动具有很好的抑制效果。

Based on the structured singular value theory a generalized synthesis framework for the uncertain vibration control system and the robust controller design method are presented in order to damp the vibration of flexible structure using piezoelectric actuators and sensors. Modal parameter perturbations and unmodeled high frequency dynamics of the structure are analyzed. The augmented system that fits the μ, synthesis framework is built by introducing fictitious in-out signals and weighted transfer functions to separate the uncertainties. The controller is solved by D_K iteration technique, and the resulting closed system has both robust stability and robust performance. A robust controller is designed for a cantilever beam with a piezoelectric actuator and a piezoelectric sensor, and the simulation results show that the method proposed is effective and the vibration of the cantilever beam is damped rapidly.