Nonlinear control of earthquake excited high raised buildings by approximate disturbance decoupling

This paper deals with a class of hybrid control systems for earthquake excited high raised buildings which consist of a passive base isolation and an additional active damper. The mechanical model of the building is a shear wall structure with nonlinear, hysteretic restoring forces. The differential geometric approach based on exterior differential systems is used to solve the disturbance decoupling problem for the mechanical model. Since the ideal controller is difficult to implement, a new control law is proposed. It solves the decoupling problem only approximately but its implementation is simple because only signals easy to measure are used. The stability is proved by means of the theory of Liapunov in combination with dissipative systems, and it turns out that the closed loop is robust with respect to all the variations of practical interest, too. Finally, computer simulations demonstrate the feasibility and efficiency of the discussed approach.