Frequency Domain Optimal Control Strategies for Aseismic Protection

Abstract

This paper discusses frequency domain optimal control strategies for active control of civil engineering structures under seismic loading. The basic problem formulation is presented, and a description of two specific techniques, the $H_2$ and $H_{\infty }$ control methods, are given. Numerical examples showing $H_2$ control of a seismically excited eight‐story building are given to illustrate the application and delineate the advantages of the frequency domain approaches. The main thrusts of the examples are to show that frequency‐domain design methods can be effectively used to: (1) Optimally control a structure using output feedback of acceleration measurements; and (2) selectively shape the output structural response in a desirable manner. In contrast to previously reported time‐domain‐based controllers, the numerical studies show that these control techniques are capable of reducing the building's response in both the first and second mode response using an active mass damper. The frequency domain optimal control design methods are shown to be flexible and to offer a good match between control concepts and engineering practice.