Active vibration control in a specific zone of smart structures

Abstract : This research aims at solving a particular vibration control problem of smart structures. We aim at reducing the vibration in a specific zone of the smart structure under the disturbance that covers a wide frequency band. Moreover, at this specific zone, neither actuation nor sensing is possible.Here we face several main challenges. First, we need to control the vibration of a specific zone of the structure while we only have access to measurements at other zones. Second, the wide bandwidth of the disturbance implies that numerous modes should be controlled at the same time which requires the use of multiple actuators and sensors. This leads to a MIMO controller which is difficult to obtain using classical controller design methods. Third, the so-called spillover problem must be avoided which is to guarantee the closed-loop stability when the model-based controller is applied on the actual setup. To tackle these challenges, we investigate two control strategies: the centralized control and the distributed control.For centralized control, we propose a methodology that allows us to obtain a simple MIMO controller that accomplishes these challenges. First, several modeling and identification techniques are applied to obtain an accurate low-order model of the smart structure. Then, an H_∞ control based synthesis method with a particularly proposed H_∞ criterion is applied. This H_∞ criterion integrates multiple control objectives, including the main challenges. In particular, the spillover problem is transformed into a robust stability problem and will be guaranteed using this criterion. The obtained H_∞ controller is a standard solution of the H_∞ problem. The final controller is obtained by further simplifying this H_∞ controller without losing the closed-loop stability and degrading the performance. This methodology is validated on a beam structure with piezoelectric transducers and the central zone is where the vibration should be reduced. The effectiveness of the obtained controller is validated by simulations and experiments.For distributed control, we consider the same beam structure and the same control objectives. There exist methods aiming at designing distributed controllers of spatially interconnected system. This research proposes a FEM based method, combined with several model reduction techniques, that allows to spatially discretize the beam structure and deduce the state-space models of interconnected subsystems. The design of distributed controllers will not be tackled in this research.
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Peng Wang. Active vibration control in a specific zone of smart structures. Other. Université de Lyon, 2019. English. ⟨NNT : 2019LYSEC007⟩. ⟨tel-02108253⟩

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