Active Vibration Control System Design for Flexible Structures

本文提出了两种柔性结构振动主动控制系统设计的新方法：一个是用于确定传感器和致动器的定位，基于标准最优控制中的最小二次成本泛函的最小化，二是考虑刚体控制力等外部输入的振动控制系统优化设计。第一种方法是通过控制使耗散能最大化，其控制效果具有明确的物理意义，并且可以自由地改变加权矩阵。应用该方法的悬臂梁产生几个错位的传感器和致动器的位置，这是局部最优的。一个扩展的情况下，使用的模态滤波器也检查。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的影响。即使考虑外力，也必须事先知道外力的未来值，进一步过多的计算使其在实际应用中无法考虑。该方法基于独立模态空间控制，在考虑采样外力的情况下，对离散系统构造最优数字控制系统，从而减少了计算量。所设计的控制系统由模态滤波器的状态变量反馈和采样外力前馈两部分组成。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态滤波器的估计误差。

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.