考虑扰动输入/性能输出分布时作动/传感器配置优化

 针对结构振动控制问题，提出了一种考虑扰动输入/性能输出分布信息时作动/传感器的优化配置准则。在降维的模态坐标下建立状态空间形式的结构动力学方程，通过Lyapunov方程求解扰动和作动器的能控性Gramian矩阵，并利用矩阵奇异值分解获得扰动的能控性方向和作动器的能控性方向，通过同时最大化作动器对结构的作动能力以及作动器的能控性方向与扰动的能控性方向的一致性来确定作动器的最优位置。类似思想用于确定传感器的最优位置。以采用压电片为作动器的悬臂梁为例阐述了新准则的应用。

Optimal Locations of Actuators/Sensors when Taking into Account Distribution of Disturbance/Performance

A method of selecting the optimal locations of actuators/sensors in vibration co ntrol application is proposed which takes into account the distribution of distu rbance/performance. The state space dynamics equation of a structure is formed i n reduced modal coordinates. Then, the controllability Gramian matrices of the d isturbance and the actuators are obtained by solving Lyapunov equations. And the singular value decomposition of their controllability Gramian matrices produces the controllability directions of the disturbance and the actuators. The optima l locations of the actuators are obtained by the effort to make the controllabil ity directions of the actuators approach that of the disturbance while maximizin g the controllability of the actuators. And the similar method can be used to ge t the optimal locations of sensors. This new optimization criterion is applied t o determinate the optimal location of a piezoelectric actuator bonded on a canti lever beam.