Nonlinear feedback strategies in active structural control

A number of active control systems have been developed, fabricated and installed in full-scale structures and they have been subjected to actual wind forces and seismic ground motions. Based on the observed response of several of these systems, a number of improvements to the hardware and software design of these systems are desirable. One of which is concerned with the control algorithms used. For example, linear quadratic regulator (LQR) has been used extensively but full-scale structural applications have shown that it is sometimes difficult to employ LQR to produce a significant peak response reduction when the peak response occurs during the first few cycles of the time history. Thus, one of the tasks at hand is to improve upon LQR and other generally linear control laws in order to produce better peak response reduction under control resource constraints.; The emphasis of this dissertation is placed on the development of effective nonlinear control laws based on nonlinearization strategies. Two types of nonlinear control laws are considered. The first is derived based on the minimization of a higher-order performance criterion which is an approximation of the minimax criterion. It is shown that the classical LQR is a special case in the proposed general higher-order control algorithms. As more and more higher order terms are included in the algorithm, the solution approaches that based on the minimax problem. The second type is derived based on the optimal bang-bang control principle which overcomes the large control force requirement as in nonlinear algorithms of the first type. Their effectiveness in peak response control and implementability are studied through extensive numerical simulation and experimental verification in the laboratory. In order to design active control systems as simply as possible at the preliminary stage, a group of design spectra for actively controlled structures are developed based on convex models. The application of these spectra to a full-scale building shows a good agreement with other more complicated design procedures.