Simulation of robust control for uncertain structural systems against earthquakes

As tall buildings and long-span bridges become lighter and more flexible, they are more susceptible to effects of vibration. Undesirable responses from earthquakes and strong wind events can vary from total collapse of the structure to uncomfortable accelerations for human beings. This paper provides theory and numerical simulations for different control algorithms of an uncertain structural system against earthquakes. The simulated system is a four-degree-of-freedom building with a normal model and a perturbed model, in view of uncertainties. Control algorithms include LQR and several proposed robust models including a regular gain robust control, a small gain robust control, and a clipped robust control. Features of the robust control include H_∞ disturbance attenuation, H₂ optimality, relative stability, and unstructured uncertainties in system, control input, and disturbance input matrices. Numerical simulations for the uncertain building models excited by the 1940 El Centro, California, earthquake with intensity 1.0 (real) and 0.5 are presented graphically. Simulations show greatly improved performance for the robust control algorithms.