Robust control for structural systems with parametric and unstructured uncertainties

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