Robust vibration control of piezoelectric actuated smart structures has attracted substantial interest in recent years. Such control laws are desirable for systems where guaranteed stability or performance is required despite the presence of multiple sources of uncertainty. In this work, we review the principal problems that the structural control engineer has to address when designing robust control laws: structural modeling techniques, uncertainty modeling, controller order reduction, and robustness validation. A comprehensive literature review is presented and the different techniques employed are discussed in detail in a tutorial manner for the case of a piezoelectric smart plate, with the aim of providing a comprehensive and unitary methodology for designing and validating robust H∞ controllers for active structures.
This paper presents the development of a multimodal H∞controller for piezoelectric actuated plates designed to simultaneously suppress vibrational components of the first two modes. The controller is developed for a reduced structural model. The closed-loop control scheme is subject to both uncertainties due to control and observation spillover in the unmodeled residual modes and to parametric errors in the structural model. The closed-loop stability and performance robustness is analyzed using μ-analysis, and numerical investigations indicate that the controller tolerates uncertainties of significant size.
This paper presents a numerical investigation of the material elastic properties for short-length mostly in-plane random fiber composites, based on microscale geometrical modeling. The particular case considered is that of materials in which the majority of fibers' orientations are contained or slightly deviate from a dominant plane. Representative volume elements for two types of random fiber composite material geometries with different fiber aspect ratios and volume fractions are generated using a novel technique. The elastic properties of the equivalent homogeneous material are determined using direct three-dimensional finite element analysis. A windowing-type analysis is employed to investigate the influence of the fiber distribution homogeneity on the homogenized elastic properties. The results are compared and validated using two alternative approaches -first, by orientation averaging of the stiffness tensor of the equivalent unidirectional composite determined by direct FEM analysis and, second, by employing the laminated random strand method.
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