Vibration Suppression in the Underactuated Dynamics of ATMD Systems Under Earthquake Excitation.

Purpose: The active tuned mass damper (ATMD) system is underactuated where the number of actuators is less than the number of system's DOF. It is well known that the regulation of an underactuated system is challenging. Few reports can be found in the literature relating to the design of ATMD systems from the view point of their underactuated dynamics. In this paper, we firstly clarify the underactuated behavior of an ATMD system whose ill-conditioned controllability matrix largely limits the flexibility of controller design. Controllers are proposed to circumvent the underactuated dynamics to ensure vibration attenuation during the earthquake and rapid state convergence in the ATMD when the earthquake vanishes. Methods: This paper proposes a redefined output function to destroy the underactuated dynamics so that a stabilizing controller can be designed to regulate the new output. A low pass filter is suggested in the control loop to give boundedness of primal and auxiliary systems simultaneously supported by BIBO stability. Results: The simulation results show that the proposed ATMD design can give much better performance in both time and frequency responses compared with the traditional TMD design under the 1940 El Centro earthquake and 1985 Mexico City earthquake. Conclusion: The proposed output redefinition design removes the underactuated dynamics in the ATMD system effectively, and the low-pass filter inclusion preserves system passivity so that convergence of the states can be obtained. These have been justified by mathematical proofs and simulation verifications. [ABSTRACT FROM AUTHOR]