engleski

Unstructured uncertainty modeling for coupled vibration systems

Unstructured uncertainty models are commonly used within robust control framework to cover unmodeled dynamics, particularly at high frequency. The resulting uncertain linear time invariant (LTI) models (i.e. models comprised of a LTI nominal model and an uncertainty model) are then used in robust controller synthesis procedure, and have significant influence on the controller performance. This paper proposes a novel procedure for constructing unstructured uncertainty models for a class of mechanical vibration systems comprised of a number of interconnected (coupled) vibration subsystems. For each subsystem, a finite element mesh refinement technique is used to construct a series of successively finer spatial discretizations. After constructing a low-order nominal model of the subsystem via appropriate model order reduction technique, a weighted unstructured uncertainty model is constructed for each level of discretization. The resulting uncertainty models primarily cover discretization errors and resulting higher order dynamics. Furthermore, by taking into the account that the individual subsystem is coupled with neighbouring subsystems, which we assumed to be dissipative, we are able to improve the uncertainty models. To be more specific, we discard frequency content which is effectively damped by the neighbouring subsystems and have no significant influence on the response of the entire vibration system. When performing the uncertainty improvement, we also investigate the use of a reduced order model which approximates a set of neighbouring subsystems. As the result of the proposed procedure, we are able to significantly reduce conservatism in the resulting uncertain LTI models of the individual subsystems, thus improving the performance of subsequent robust control strategies. We illustrate the results on a numerical example comprised of a series of simply-supported beams coupled with a set of springs and viscous dampers.

weighted unstructured uncertainty, coupled mechanical systems

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