Active Vibration Control System Design for Flexible Structures

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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.