H8 Control-Based Optimization Design for Active and Passive Dynamic Vibration Absorber

Purpose This paper is concerned with the H-infinity optimization design of passive and active dynamic vibration absorbers (DVAs) attached to an undamped or damped primary system.Methods The proposed optimization method is an efficient non-smooth H-infinity-synthesis algorithm that is utilized to solve structured H-infinity-synthesis in control engineering. This method can conveniently achieve the optimal design for the amplitude magnification factors of both the absolute and the relative displacements of a DVA using the proposed dual H-infinity design, and implement co-design of H-infinity-optimal proportional-integral-differential controllers and passive parameters of an active DVA.Results Two active DVAs and two variant passive DVAs reported in the literature are taken as examples for design improvement. The optimization results indicate that the proposed method has significant advantages over the conventional fixed points-theory-based methods and many numerical global optimization methods.Conclusions The proposed H-infinity optimization design yields much better vibration suppression result for proportional-integral differential control based active DVAs and variant passive DVAs with complicated structures. It is directly based on their equations of motion in state-space forms, and explicit formulations of various amplitude magnification factors, such as those on the absolute and the relative displacements and active force, need not be derived in the MATLAB environment. A possible situation of occurrence of large amplitude of the relative displacement in DVAs rarely considered in the literature can be handled by using the proposed dual H-infinity design.