An enhanced nonlinear damping approach accounting for system constraints in active mass dampers

Active mass dampers are a viable solution for mitigating wind-induced vibrations in high-rise buildings and improve occupants׳ comfort. Such devices suffer particularly when they reach force saturation of the actuators and maximum extension of their stroke, which may occur in case of severe loading conditions (e.g. wind gust and earthquake). Exceeding actuators׳ physical limits can impair the control performance of the system or even lead to devices damage, with consequent need for repair or substitution of part of the control system. Controllers for active mass dampers should account for their technological limits. Prior work of the authors was devoted to stroke issues and led to the definition of a nonlinear damping approach, very easy to implement in practice. It consisted of a modified skyhook algorithm complemented with a nonlinear braking force to reverse the direction of the mass before reaching the stroke limit. This paper presents an enhanced version of this approach, also accounting for force saturation of the actuator and keeping the simplicity of implementation. This is achieved by modulating the control force by a nonlinear smooth function depending on the ratio between actuator׳s force and saturation limit. Results of a numerical investigation show that the proposed approach provides similar results to the method of the State Dependent Riccati Equation, a well-established technique for designing optimal controllers for constrained systems, yet very difficult to apply in practice.