Time-delayed control design for active control of structures: principles and applications

In this paper we develop the principles of time-delayed control design for the active control of structures in which the presence of large time delays in the control loop may make it difficult for their effects to be easily eliminated and/or compensated. A control design strategy is proposed that is different from what has been generally accepted hereto; it calls for taking advantage of these large, inherent time delays in the control design. The presence of large time delays in the control loop requires that we understand the infinite dimensionality of the system and so we introduce the concept of non-system poles. This is first done within the framework of an SDOF system with time-delayed velocity feedback control. Several new results are presented dealing with stability and performance issues. These results include and extend those available to date. Having developed control design principles with an SDOF system as the underlying basis, these principles are then developed for multi-actuator, multiple time-delay control of MDOF systems. A numerical example of a building structure modeled as an MDOF system that is subjected to strong earthquake ground shaking is presented. The control design based on the underlying principles shows good stability characteristics and effective performance behavior. We demonstrate its application to a structure subjected to strong earthquake ground shaking, thereby showing its usefulness in hazard mitigation.