Active Vibration Control System Design for Flexible Structures

提出了两种柔性结构振动主动控制系统设计的新方法：一种是基于标准最优控制中最小二次代价泛函最小化的传感器和执行器位置的确定方法；另一种是考虑控制力等外部输入的柔性结构振动控制系统的优化设计方法。与传统的控制耗散能量最大化等方法相比，第一种方法对控制效果具有明确的物理意义，并具有改变加权矩阵的自由度。将该方法应用于悬臂梁，得到了几个错位的传感器和执行器位置，这些位置是局部最优的。还研究了对使用模式滤波器的情况的扩展。在这种情况下，执行器的位置比传感器的位置更敏感，传统的优化设计方法没有考虑外力。即使考虑外力，外力的未来值也必须事先知道，而且计算量太大，在实际应用中是不可能考虑的。该方法基于独立的模态空间控制，构造了考虑采样外力的对象系统离散表示的最优数字控制系统，从而减少了计算负担。所设计的控制系统由状态变量的模式滤波反馈和采样外力的前馈两部分组成。采样周期可以调节反馈和前馈效应之间的平衡。系统的稳定性取决于模式滤波器的估计误差。

We develop two new methods in the active vibration control system design of flexible structures: one is for the determination of sensor and actuator positioning, based on the minimization of the minimum quadratic cost functional in the standard optimal control, and the other is the optimal design of the vibration control system considering the external input such as control forces for the rigid body.Compared with the conventional method such as maximization of dissipation energy by control, the first method has clear physical meaning for control effects and the freedom of varying the weighting matrix. The application of this method to a cantilever beam yields several dislocated sensor and actuator locations, which are locally optimal. An extension to the case where the modal filters are used is also examined. In this case, the location of the actuator is found to be more sensitive than that of sensor.The conventional optimal design method never considers external forces. Even if external forces are considered, the future values of external forces must be known in advance, and further too much calculation makes it impossible to consider them in practical applications. Based on the independent modal- space control, the proposed method construct the optimal digital control system for the discrete representation of the subject system considering sampled external forces, resulting in reduction of calculation burden. The designed control system is composed of both feedback of state variables by modal filters and feedforward of sampled external forces. The sampling period can adjust the balance between feedback and feedforward effects. The system stability depends on estimation errors of modal filters.