Low order vibration control for structures with highly correlated close modes

Abstract

For the problem posed by closely spaced modes, this paper defined the MCC (modal correlation criterion) to measure the degree of correlation between close modes. It was proved that structures with certain features tend to have closely clustered modes and the corresponding mode shapes highly correlated. With this understanding, the closed-form expressions for controllability and observability Grammians were adopted to analyze the impacts of actuator/sensor placement on the controllability/observability of highly correlated close modes. On this basis, the problem of actuator/sensor placement, when the optimization criterion is based on modal controllability/observability, was simplified. Moreover, the dimension of the control/measurement vector in independent modal space control for highly correlated close modes was proved to have the potential to be reduced, therefore fewer actuators and sensors were required in this dimension-reduced control strategy. Finally, the desirable vibration suppression for an example structure showed that the theory and methods of this paper were accurate and effective. close modes, correlation, controllability/observability, sensor/actuator placement, low-order control Citation:Liu X X, Hu J. Low order vibration control for structures with highly correlated close modes.

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