弹性板振动的多模态主动控制

采用多对压电片对板振动的多阶模态进行主动控制。为了改善结构振动控制的效果，本文对选用结构振动能量和控制信号能量作为控制目标函数的LQR控制算法作了初步研究。首先，按能量准则推导了控制目标函数中权系数矩阵(Q矩阵和R矩阵)的理论计算公式，为权系数矩阵的选取提供了一定的理论依据。然后，运用该算法，在研究了单对压电片进行振动主动控制的基础上．本文深入分析了压电层合板振动的多阶模态控制的问题，用Matlab进行系统仿真，得到了压电层合板受到初始位移激励下板中心点的位移和控制电压大小随时间变化的曲线。数值模拟的结果表明，该方法能达到更有效控制结构振动和减小控制能量消耗的目的．进一步验证了该方法能达到有效控制结构振动和减小控制能量消耗的目的。

LQR Method for Multimodal Vibration Control of Plates Based on Energy Criterion

Using several patches of piezoelectric sensors/actuators to control multiple vibration modes of the plate, in order to improve the effectiveness of the vibration control for piezoelectric laminated structure, this paper made some analysis of the linear quadratic requlator (LQR) control method, which chooses the vibration energy of the structure and the control signal energy for the object function. Firstly, calculation formulas of weighting factors (matrixes Q and R) in object function are built. Thus, a theoretic basis is provided for selecting the appropriate weighting factors. Secondly, after successfully applied for vibration control with single patch of piezoelectric sensor/actuator, the control method is developed to analyze multimodal vibration control of piezoelectric laminated plates. By means of system simulation in the Matlab program, the curves of the displacement response at the center of the plate and the control optimal voltage are obtained, with the external excitation of initial displacement and impulse. Numerical results showed that it is effective in suppressing the vibration and reducing the control energy.