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Low order vibration control for structures with highly correlated close modes

Science China(Technological Sciences) 2011年第7期54卷 1855-1864页

作者： LIU XiaoXiang HU Jun Beijing Institute of Control Engineering Beijing 100190 China State Key Laboratory of Science and Technology on Space Intelligent Control Beijing 100190 China

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.

关键词： close modes correlation controllability/observability sensor/actuator placement low-order control

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On the placement of actuators and sensors for flexible structures with closely spaced modes

引用

Science China(Technological Sciences) 2010年第7期53卷 1973-1982页

作者： LIU XiaoXiang1,2 & HU Jun1,2 1 Beijing Institute of Control Engineering, Beijing 100190, China 2 State Key Laboratory of Science and Technology on Space Intelligent Control, Beijing 100190, China Beijing Institute of Control Engineering Beijing China State Key Laboratory of Science and Technology on Space Intelligent Control Beijing China

This paper analyzed the fundamental limitations of previous work and developed a new method to optimally locate actuators and sensors for structures with close modes. Optimization criteria were defined based on the distinguishing modal controllability and observability measures of close modes. An appropriate genetic algorism was adopted as the optimization algorism. Solving the high order Lyapunov functions was avoided by means of the closed-form expressions for controllability and observability Grammians. Since structure with widely separated natural frequencies is approximately balanced, computational efficiency was improved by grouping close modes together and dealing with the resulting subsystems independently. Finally, the effectiveness and optimality of the novel placement scheme were verified on a model structure with close modes.

关键词： close modes controllability/observability sensor/actuator optimization criterion optimization algorithm

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