Active Wave Control of String Near Fixed Boundary

Abstract

We studied a wave control of a string near a fixed end. The equation of motion of a string is approximated as a lumped-parameter spring-and-mass system using the finite difference method. Finite difference equations (FDEs) for interior node points have the same set of coefficients, whereas the FDEs for boundary node points have a different set of coefficients. By using the control, the latter equation is modified to be as the same equation as the former one. The propagating wave is absorbed through a control actuator as if no boundary existed, and virtually, an infinite system is thus realized. Control is at the string position of the finite difference mesh spacing inside the fixed boundary that is free from supporting loads. We confirmed the effectiveness of the controller by numerical simulation for the traveling string and also did that by numerical simulation and by an experiment for the nontraveling string.