Vibration Control of High Raised Structures, a Dissipative Approach

This contribution presents two examples for the protection of earthquake excited high raised buildings by linear and nonlinear control. The first one consists of a passive base isolation and an additional active damper located at the basement level. The design of the control law is based on differential geometric methods, dissipativity and almost disturbance decoupling. Nonlinear and hysteretic effects of the restoring forces and the torques of the flexible columns are taken into account, as well as an n-DOF model for each story. It is shown that the proposed controller renders the system stable independently of the number of stories and for a wicde class of constitutive laws. Since the control law uses measurable quantities only it can easily be implemented. The second example deals with a twenty story buidling based on the structure models provided by the university of NOTRE DAME. After a reduction of the high order model, a nonlinear H2-controller, and an LQG-LQR-controller are designed. Finally, simulations show the excellent damping of the proposed control systems.