Control of nonlinear structural dynamic systems - Chaotic vibrations

In recent years, chaotic behavior has been observed in a large number of physical systems. The appearance of these unpredictable, broadband frequency responses in structural dynamic systems presents a possible threat to the integrity of aerospace structures because of their erratic time histories. Thus, the objective of this paper is to investigate the control of chaotic motions through the simple example of a buckled beam. As an initial attempt, a nonlinear control methodology termed feedback linearization was utilized. In this method, the nonlinearities causing chaos are eliminated from the closed-loop system through nonlinear feedback. Although effective in eliminating chaotic motions, this scheme does have some disadvantages such as the demand for accurate models and, in general, full state measurements. As an alternative, the feasibility of using smart structural concepts to control chaotic vibrations was examined. This technique utilized the introduction of so-called electronic damping to move the system out of a chaotic parameter region. The method was shown to be feasible and holds promise for future applications. Thus, this work demonstrates that a controller capable of controlling a chaotic system can be developed. From this study, directions for further research in the area of controlling chaotic systems were obtained.