Multi-objective optimization of regenerative damping systems in vibrating structures

A regenerative force actuation (RFA) network consists of multiple electromechanical forcing devices distributed throughout a vibrating structural system, with a forcing capability which is constrained by the requirement that the total network must always dissipate energy. Both viscous damping systems and RFA networks can be modeled as imposing supplemental velocity-proportional damping on structures, but for these two cases the damping matrix is subject to different algebraic constraints. This paper presents an analysis of the degree to which the increased versatility in the damping capabilities of RFA networks may be exploited to improve upon the optimal dynamic performance achievable with linear viscous dampers. The analysis is conducted in the context of a nonconvex, multi-objective H₂ optimal control problem, in which the supplemental damping matrix is treated as a control gain to be optimized. The structural system is excited in stationary stochastic response, and "performance" is defined as the maximum variance over a set of normalized drift and acceleration quantities. Numerical examples are given which compare the optimal performances attainable with viscous and regenerative damping, for a civil engineering application.