Peak-gain-bounded design of constrained controllable damping in vibrating structures

This paper concerns the design of mechanical vibration suppression systems with controllable mechanical damping. For such systems, the paper illustrates techniques for both linear and nonlinear damping design, which place an upper bound on the peak gain from the structural disturbances to response performance outputs. The technique is an extension of many Lyapunov-based damping techniques in the open literature on semiactive systems. Presently, such techniques admit performance measures which depend only on the system state. This paper discusses theoretical extensions to those methods to accommodate performance measures which are explicitly dependent on the external disturbance and control forces. The theory is illustrated via simulation of a base-excited structure equipped with viscous, semiactive, or regenerative damping systems, with the objective of minimizing the peak gain from the base acceleration amplitude to the vector of inter-story drifts and structural accelerations.