Active Wave Control of a Flexible Beam Using Fractional Derivative Feedback

摘要

The existence of active wave control has been known in the field of the vibration control of large-size space structures (LSS) since the 1960s. Recently, with the goal of energy and resource conservation, active wave control has come into the spotlight again in the field of the vibration suppression of light and thin members widely used in mechanical structures, including automobiles. Therefore, achieving active wave control is both an old and a new problem. A vibration suppression problem for a thin cantilevered beam is presented as an example for discussion. Results clarified that the active wave controller includes√s and s√s terms. Those terms are realized as a 1/2-order derivative and a 3/2-order derivative using fractional calculus. The active wave controller is realized through fractional calculus, which is shown to be an important step in the analysis of this problem. Specifically, the active wave controller can be implemented using fractional derivative feedback. The controller involving the fractional derivatives is realized with a digital signal processor based on definitions of fractional calculus. The vibration suppression effect of active wave control is demonstrated both numerically and experimentally.