Design of Supplemental Dampers for Control of Structures

A suggested method for design of supplemental dampers in multistory structures is presented. Optimal control theory using a linear quadratic regulator (LQR) is adapted to design linear passive viscous or viscoelastic devices dependent on their deformation and velocity (best represented by Kelvin model). The design is aimed at minimizing a performance cost function that produces a most suitable minimal configuration of devices while maximizing their effect. The method is fully effective using full-state static feedback. Since the active feedback action require a linear combination of all states and it cannot be supplied by passive devices, the paper introduces a methodology to eliminate the off-diagonal interactions between states using various engineering ways. This paper shows the development for velocity feedback only, for the sake of simplicity. However, the full-state formulation can be manipulated similarly to obtain a combined position-velocity feedback design. This paper shows a numerical implementation of the design methodology for a structural model prepared for further experimental considerations.