<title>Model reduction and frequency-weighted optimal vibration control of smart panels</title>

Abstract

The optimal control algorithm is one ofthefeasiblefeedback algorithmsfor vibration suppression offlexible 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 ofresonance modes as a nominal model with finite modesfor controller design. This paper presents a design ofan optimal controller that is low order and can prevent the spillover problem when the unmodeled resonance modes perturb thefeedback control loop. For low order controller design, this paper proposes modal 1-lankel singular values (MHSV,) for efficient nominal model reduction. Low order controller can be derivedfrom the reduced nominal model. For design ofmore stable controller, this paper appliesfrequency dependant weightfunctions to the costfiinction. The weighifunctions prevent the spillover by making optimal controller not to excite the resonance modes that are not included in nominal model. The optimal controller is derivedfrom the nominal model. This weight function approach optimizes the control performance and control stability by smoothening the discrepancy between the weights 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 controlperformance and stability against high resonance mode spillover.