engleski

Unstructured uncertainty modeling for coupled dynamical systems

Dynamical systems are becoming more complex and thereby demands in terms of robustness and efficiency are set high when synthesizing such dynamical systems. Due to size of these systems they need to be modeled in a pragmatic way. Common paradigm is to utilize various approximations of the system and this is where spatial discretization techniques come in handy but with a tradeoff - unknown approximation error is introduced. On the other hand, in order to make a system robust it is necessary to model systems uncertainties. We stress, that for special cases of coupled dynamical systems, aforementioned approximation error can be successively modeled as system uncertainty using uncertainty models from rich library of uncertainty classes obtained through integral quadratic constraints (IQC) framework. Over the last two decades system analysis via IQC- framework has become an essential tool for analyzing stability and performance properties of uncertain dynamical systems. Unstructured uncertainty models are commonly used within robust control framework to cover unmodeled dynamics. In this paper a novel strategy for constructing unstructured uncertainty models for a class of dynamical mechanical systems comprised of a number of interconnected (coupled) dynamical subsystems is presented. Each subsystem is discretized using finite elements together with appropriate mesh refining technique in order to obtain a series of successively finer spatial discretization. Weighted unstructured uncertainty model is constructed for each level of discretization. Each subsystem is assumed to be dissipative. By taking into the account that the individual subsystem is coupled with neighboring subsystems we are able to improve the uncertainty models and reduce conservatism in the resulting uncertain models. 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 ; integral quadratic constraints

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