Decoupling control law for structural control implementation

Abstract

Multi-story buildings, subjected to wind or earthquake excitation, can be modeled as multi-degree of freedom (MDOF) systems defined by a set of coupled second order ordinary differential equations. In this paper, the dynamic coupling characteristics of multi-story building are examined, and it is found that the coupled property in a system can be described as a positive feedback from the control theory point of view. This positive feedback property of a MDOF system may intensify structural vibration. For the structural control implementation, open-loop and closed-loop decoupling control laws are proposed. All coupled “channels” of the system are “broken off” when the vibration control design is based on the proposed control laws. A complex MDOF structural system, therefore, is equivalent to a set of single degree of freedom (SDOF) systems, and the control design can be carried out independently for any specific degree of freedom. Thus, the proposed control laws provide an efficient tool by which the vibration of a selected floor can be suppressed without any effect on its neighboring floors because the control is one to one. Meanwhile, the computational procedure of the control design can be significantly simplified because all analyses and design are conducted based on SDOF systems.