振动控制传感器／作动器的数目和位置优化设计

提出一种确定传感器、作动器的数目和优化设计传感器、作动器位置的方法。以独立模态最优控制方法为基础，将模态控制力、作动器作动力和传感器测量的信号处理为随机变量，分别建立了模态控制力能量、作动器作动力能量的自相关矩阵的测量信号的能量自相关矩阵。进一步通过作动力能量的自相关矩阵的和测量信号的能量自相关矩阵包含的能量分别确定了作动器和传感器的数目。在此基础上，建立了基于控制系统作动力消耗能量最小和传感器测量信号能量最大，分别设计了控制系统的作动器和传感器的最优位置。通过数值算例证明了该方法的有效性。

Optimal Design Method for Sensors/Actuators Placement and Numbers in the Vibration Control of Flexible Structure System

An optimal design method for placement and numbers of sensors/actuators in the vibration control of flexible structure system is presented in the paper. Based on the independent modal space control method, the auto correlation matrices of the energy of modal control force, physical control forces of actuators and measured signal are established respectively while the modal control force, physical force and measured signal are treated as random variables. The numbers of sensors/actuators are determined via an efficient method calculating eigenvalues of the auto correlation matrices of the energy of measured signal and physical control force of actuators respectively. The optimization algorithms calculating the optimal sensors/actuator placement are then put forward via the minimization or maximization of an energy criterion, which is chosen as the control index. Numerical examples show the efficiencies of the proposed method.