Quantificação da incerteza em sistemas de controle ativo de vibrações aplicado ao problema dinâmico de uma viga de material compósito

Abstract

This work proposes the study and analysis of uncertainty quantification in the matrices of the mathematical model of the composite beam applied to the control design used for vibration attenuation. The mathematical model is identified using the Auto system Realization Algorithm/State Observer Identification. The composite beam is supplied with epoxy resin, fiberglass, and 1045 steel mesh, and a LinearQuadratic Regulator is used for the driver design. The first step of the work involves identifying the deterministic mathematical model, followed by designing the controllers, responsible for reading and measuring the control efforts and acting to reduce the system's vibration amplitude. The second step is to quantify the uncertainty and assess the robustness of the system, which is associated with statistical variations in the parameters of the identified matrices, considering this form of nonparametric uncertainty. The propagation and quantification of uncertainty are investigated using Monte Carlo simulation and the variance reduction technique, Latin Hypercube Sampling. Finally, the numerical simulations and experimental bench tests are compared using responses in the time and frequency domains. It is concluded that the uncertainty acting on matrix [A] has a much greater impact than on matrix [B] and causes instability depending on the magnitude of the pseudorandom number. When applied to [A] and [B] simultaneously, it destabilizes the control. By considering uncertainties, the controller design becomes more robust by indicating the maximum and minimum values that the displacement can reach if any system parameter diverges from the predicted model, fulfilling its role as a vibration attenuator