Randomized algorithms have been proposed as a new paradigm in robust control and as an alternative approach to the worst-case design. They can be adopted to assess the robustness of the controlled structure with uncertain parameters, statistically satisfying systems' constraints. Introducing probability in robustness gained increasing interest in the literature in recent years; thus, the probabilistic approach is now a rather established methodology for robustness analysis and represents a rigorous evolution of Monte Carlobased techniques for analysis and design. In the probabilistic framework the design is considered successful even if it does not guarantee 'a-priori' the fulfillment of the performance for all the possible uncertainties. A probabilistic description of the uncertainty is considered, assuming that the uncertain parameters are random variables with specific probability distribution functions. Although the results of this approach are probabilistic in nature, the level of confidence can be rigorously established at design level by selecting a suitable large number of uncertainty samples for the probabilistic optimization. The algorithm is applied to a case study consisting of a multiple-story frame structure equipped with a control system on top and subjected to seismic excitation. Two different kinds of control devices are considered: a Tuned Mass Damper and an Active Mass Damper. The uncertain parameters are the system's dynamic characteristics, assumed bounded and lognormally distributed. The classical Kanai-Tajimi power spectral density is used to model the seismic load. The performance function is the H∞ norm of the system's transfer function weighted by the input power spectrum. In the study the structural performance is studied by varying the ϵ (accuracy) and δ (confidence) parameters that define the probabilistic performance. The robustness of the passively and actively controlled systems are compared. The procedure shows to be effective and computationally efficient for performance evaluation of uncertain controlled structures.

Randomized algorithm for performance evaluation of controlled structures with uncertainties

M. L. Fravolini;A. Ficola;I. Venanzi
2017

Abstract

Randomized algorithms have been proposed as a new paradigm in robust control and as an alternative approach to the worst-case design. They can be adopted to assess the robustness of the controlled structure with uncertain parameters, statistically satisfying systems' constraints. Introducing probability in robustness gained increasing interest in the literature in recent years; thus, the probabilistic approach is now a rather established methodology for robustness analysis and represents a rigorous evolution of Monte Carlobased techniques for analysis and design. In the probabilistic framework the design is considered successful even if it does not guarantee 'a-priori' the fulfillment of the performance for all the possible uncertainties. A probabilistic description of the uncertainty is considered, assuming that the uncertain parameters are random variables with specific probability distribution functions. Although the results of this approach are probabilistic in nature, the level of confidence can be rigorously established at design level by selecting a suitable large number of uncertainty samples for the probabilistic optimization. The algorithm is applied to a case study consisting of a multiple-story frame structure equipped with a control system on top and subjected to seismic excitation. Two different kinds of control devices are considered: a Tuned Mass Damper and an Active Mass Damper. The uncertain parameters are the system's dynamic characteristics, assumed bounded and lognormally distributed. The classical Kanai-Tajimi power spectral density is used to model the seismic load. The performance function is the H∞ norm of the system's transfer function weighted by the input power spectrum. In the study the structural performance is studied by varying the ϵ (accuracy) and δ (confidence) parameters that define the probabilistic performance. The robustness of the passively and actively controlled systems are compared. The procedure shows to be effective and computationally efficient for performance evaluation of uncertain controlled structures.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1432259
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