Robust Control for Structural Systems with Parametric and Unstructured Uncertainties

Abstract

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 H ₂ 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 H ₂ 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.