19 June 2000 Model reduction and frequency-weighted optimal vibration control of smart panels
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Abstract
The optimal control algorithm is one of the feasible feedback algorithms for vibration suppression of flexible structures. One of the commonly encountered problems of the optimal control implementation is the spillover problem. The spillover generally occurs when modeling a continuous structure that has infinite number of resonance modes as a nominal model with finite modes for controller design. This paper presents a design of an optimal controller that is low order and can prevent the spillover problem when the unmodeled resonance modes perturb the feedback control loop. For low order controller design, this paper proposes modal Hankel singular values (MHSV) for efficient nominal model reduction. Low order controller can be derived from the reduced nominal model. For design of more stable controller, this paper applies frequency dependent weight functions to the cost function. The weight functions prevent the spillover by making optimal controller not to excite the resonance modes that are not included in nominal model. The optimal controller is derived from the nominal model. This weight function approach optimizes the control performance and control stability by smoothening the discrepancy between the weights of on the modeled modes to be controlled and unmodeled modes to be stabilized. A finite element model is exploited to develop the controller and to test its control performance and stability against high resonance mode spillover.
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Woosuk Chang, Woosuk Chang, Vasundara V. Varadan, Vasundara V. Varadan, } "Model reduction and frequency-weighted optimal vibration control of smart panels", Proc. SPIE 3984, Smart Structures and Materials 2000: Mathematics and Control in Smart Structures, (19 June 2000); doi: 10.1117/12.388753; https://doi.org/10.1117/12.388753
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