压电结构作动/传感器配置优化

A new method for determining optimal location of piezoelectric actuator/sensor

提出了一种压电结构中作动/传感器优化配置的新方法.首先用有限元方法建立结构的动力学方程,并用模态方法进行降阶,然后通过Lyapunov方程分别求解扰动输入和作动器输入的能控性Grammian矩阵,通过使作动器输入的能控性矩阵向量在扰动能控性矩阵上投影长度的平方和最大值得到压电作动器的最优位置,同样的思想用于确定传感器的最优位置.

A new method for determining the optimal location of piezoelectric actuator and sensor are proposed. The piezoelectric structural dynamic equation is formed by finite element method and then transformed into lower dimension-alequation using modal subspace transformation, and the state space equation is established. The controllability matrices of the actuator input and the disturbance input are solved through Lyapunov equations, and the actuator controllability matrix is projected onto the disturbance controllability matrix to make a projection matrix. The optimal location of the actuator is obtained by maximizing the sum of squares of the length of the weighted column vectors in the projection matrix. Analogous method could be used to get the optimal location of the sensor.