Fuzzy arithmetical robustness analysis of a structural control system against uncertainty-induced spillover

A special methodology based on fuzzy arithmetic is applied to analyze and to quantify the effects of control and observer spillover, induced by uncertainties in an active structural control system. In this concept, piezoelectric patches are attached to the structure for the purpose of reducing undesirable vibrations by active actuation under closed-loop control. Uncertainties may arise in the model parameters due to a lack of exact knowledge of the material properties, the patch or sensor locations, or generally due to unmodeled or uncertain dynamics. These uncertain parameters are represented by fuzzy numbers, and fuzzy arithmetic based on the transformation method is used to evaluate the system and controller equations with fuzzy-valued parameters. To avoid implementation difficulties and hardware limitations, full large-scale finite-element models are reduced by applying a modal truncation approach as well as a modal selection approach based on Hankel singular values, computed for the actuator-to-sensor I/O-functions. After controller design, the non-observed modal states may exhibit unstable behavior, since the control parameters are based on the reduced model with a very limited number of observed and controlled modes only. The approach of fuzzy analysis is finally used to quantify and rate the influence of the parametric uncertainties on the spillover effects.