Tall, slender structures and long bridges inherit numerous uncertainties due to model errors, stress calculations, material properties, and load environments and may undergo large forces from natural hazards such as earthquakes and strong wind events. This paper develops a robust active control approach with para metric uncertainty in the system and control input and unstructured uncertainty in the disturbance input ma trices based on an uncertain structural system. A special single-valued decomposition (SVD) is applied to structured uncertain structures. The robust control law provides robust relative stability, an H∞-norm distur bance attenuation, and H2 optimality. The H∞ norm of the transfer function from the external disturbance forces (e.g., earthquake, wind, etc.) to the observed system states is restricted by a prescribed attenuation in dex δ. Preservation of robust H2 optimality of uncertain structural systems is discussed. This paper considers both structured uncertainties and norm-bounded unstructured uncertainties. Numerical simulations that use the robust controller show significant reduction in vibrations.

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Natural hazards such as earthquakes and strong wind events place large forces on tall, slender structures and on long-span bridges that inherit numerous uncertainties due to model errors, stress calculations, material properties, and load environments. Thus, a robust feedback control for structural systems is needed. This paper develops a robust active control approach for uncertain structural systems with acceleration sensors and white noise. The approach is based on a robust state feedback control, with the robust a-degree relative stability, robust H 1 d-degree disturbance rejection and robust H 2 optimality, and a modified Kalman filter, with a 0 -degree relative' stability. The uncertainties considered include structural ones in the system and control input matrices and multiplicative nonstructural ones in the disturbance input matrices. Special singular value decomposition (SVD) is applied to structured uncertain structures. Numerical simulations excited by the 1940 El Centro, California, earthquake data have been carried out for the proposed different robust controllers and LQG for comparison. The resulting approach to robust control may be applied to analysis and design of practical structural systems.

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Recent research has demonstrated that static magnetic fields (SMF) can generate an analgesic effect in different conditions. The present study explored effects of SMF on pain levels and expressions of P2X3 receptors in trigeminal ganglion (TG) in mice after experimental tooth movement (tooth movement induced by springs between teeth). Experiments were performed in male mice (body mass: 25-30 g) and divided into SMF + force group, force group, and no force group. Exposure time was over 22 h per day. Mouse Grimace Scale was used for evaluating orofacial pain levels during experimental tooth movement at 4 h and 1, 3, 7, and 14 days. Meanwhile, expression levels of P2X3 receptors in the TG were evaluated by immunohistochemistry and western blotting at same time points. We finally found that during experimental tooth movement, pain levels of mice peaked at 3 days, and then decreased. While pain levels of mice were reduced in the SMF environment at 4 h, 1 and 3 days, there was a significant difference at 1 and 3 days. Meanwhile, under the action of SMF, expression levels of P2X3 receptors in TG were significantly lower at 4 h, 3 and 7 days. These results suggest that SMF can reduce pain levels in mice, and down-regulate P2X3 receptors in TG. Bioelectromagnetics. 38:22-30, 2017. © 2016 Wiley Periodicals, Inc.

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