This paper introduces a class of resonant controllers that can be used to minimize structural vibration using collocated piezoelectric actuator-sensor pairs. The proposed controller increases the damping of the structure so as to minimize a chosen number of resonant responses. The controller can be tuned to a chosen number of modes. This results in controllers of minimal dimension. The controller structure is chosen such that closed-loop stability is guaranteed. Moreover, the controller can be designed such that the spatial 2 norm of the system is minimized. This will guarantee average reduction of vibration throughout the entire structure. Experimental validation on a simply supported beam is presented showing the effectiveness of the proposed controller.Index Terms-Flexible structures, piezoelectric actuator, piezoelectric sensor, smart structures, spatial 2 norm, spatial resonant control, vibrations.
The aim of this paper is to design and experimentally evaluate the performance of a feedback controller to suppress vibration of a flexible beam. The controller is designed to minimize the spatial 2 norm of the closed-loop system to ensure average reduction of vibration throughout the entire structure. Vibrations of the first six bending modes of the beam are to be controlled using a collocated piezoelectric actuator-sensor pair attached to the beam. Feedthrough terms are incorporated into the flexible-structure model to correct the locations of the in-bandwidth zeros. It is shown that the spatial 2 control has an advantage over the pointwise 2 control in minimizing the vibration of the entire structure. The spatial 2 controller minimizes the 2 norm of the entire structure more uniformly, while the pointwise 2 controller only has a local effect. The implemented spatial 2 controller is able to minimize the first six bending modes of the beam effectively. This spatial 2 control can also be applied to more general structural vibration suppression problems.
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