Optimal preview control for seismic-excited active damping mechanical systems with earthquake actions

Abstract

This paper is concerned with the preview control problem for a class of mechanical systems abstracted from a class of seismic-excited active damping structures. First of all, the class of systems is transformed into state equation form, and then it is discretized. By introducing a performance index to reflect the characteristics of the problem, the complete optimal control problem is formulated. The seismic activity is mostly presented in the aspects of the system affected by ground motion acceleration, and the approximate data for these effects can be obtained from history records. Thus, we design an optimal controller with preview action based on these effects. By constructing an augmented system, the problem is converted into a general regulator system, and then the controller is designed. Returning to the original system, the optimal preview controller is obtained. If a lifting technique is used sufficiently in the design, the time delay in input can be formally eliminated. In this paper, the controllability (stabilizability) and observability (detectability) of the augmented system are discussed exactly. A numerical simulation for a 3-degrees-of-freedom building structure model validates the theory of the paper.