基于能量准则的板振动控制的LQR法

针对压电层合结构振动的主动控制问题，为了优化控制效果，本文基于现代控制理论提出了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法。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，分析了压电层合板受到初始位移激励和冲击载荷作用下的控制过程，用Matlab进行系统仿真，得到了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，与一般的LQR控制方法相比，能满足系统多方面的设计要求且控制效果更优，从而验证了该LQR方法运用到结构振动主动控制中的可行性。

LQR Method for Vibration Control of Plates Based on Energy Criterion

To the question of the active vibration control for piezoelectric laminated structure, in order to optimize the effect of the vibration control, based on the modern control method, a LQR method, in which the vibration energy of the structure and the control singal energy were chosen as the object function, was proposed. First, the calculation formulas of weighting factors (matrixes Q and R) in object function were built. Thus, a theoretic basis was provided for selecting the appropriate weighting factors. Secondly, applying the control method in analyzing vibration control of piezoelectric laminated plate, with the external excitation of initial displacement and impulse, by means of system simulation in the Matlab program, the curves of the displacement response at the center of the beam and the control optimal voltage were obtained. Numerical results show that it is effective in controlling the vibration and reducing the control energy . Moreover, compared with traditional LQR method, it can satisfy the multiple design requests of the system and optimize the control effect.