Abstract
This paper deals with an optimal placement problem of sensors and actuators for active vibration control of flexible structures. For undamped flexible structures with collocated sensors and actuators, each solution of two generalized algebraic Riccati equations are obtained explicitly. Using these two solutions, it is shown that the stabilizing H∞ suboptimal controller based on the normalized left coprime factorization approach can be synthesized directly for all candidates of the placement. The sensor/actuator placement problem which optimizes other closed-loop performance can be formulated easily by applying this H∞ controller. As a design example, a placement problem which minimizes H2 norm of the closed loop transfer matrix using this H∞ controller is considered for a cantilevered beam. The experimental results show the effectiveness of the sensor/actuator placement method stated in this paper.
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