Active vibration isolation of a flexible structure mounted on a vibrating elastic base

The problem of isolating the vibration at any location on a flexible structure mounted on a vibrating flexible base is considered using a Kalman-based active feedforward–feedback controller (KAFB) with non-collocated sensors and actuators. The control strategy developed in this study focuses on lowering the force transmitted to the structure through its vibrating elastic foundation in the presence of process and measurements noise. A state-space model of the structure is constructed from the natural frequencies and mode shapes generated via finite element modal analysis of the structure. The important aspect of the proposed control strategy is that, while itʹs design is based on a full order model of the physical structure (plant), its implementation is reduced to the realization of a second order estimator regardless of the order of the plant model, and with negligible effect on its accuracy and performance. Therefore, the proposed control strategy requires low computational effort, which makes it well suited for real time control applications. Another unique aspect of this control strategy is its agility and speed in compensating for any phase or magnitude mismatch between transmitted force and control force. Moreover, the stability of the control system is implicitly attained by the controllability condition posed by the Kalman filter on the model. Thus, proper choice of Kalman gains will drive the states of the structure, at the sensor location, ideally to zero. In addition to that, digital implementation of the proposed controller can be easily done considering the fact that the discrete Kalman filter is exact. Numerical simulation of the controller performance is carried out and the results are presented.