Identifying and Mitigating Residual Vibrations in Wave-Based Control of Lumped, Flexible Systems
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Abstract
Wave-based control (WBC) is a technique for motion control of under-actuated flexible sys-tems. It envisages actuator motion as launching a motion wave into the system, while simulta-neously absorbing any wave returning from the system. For rest-to-rest motion the net launch displacement is set at half the target displacement. In absorbing the returning wave and vibra-tions, WBC moves the system the remaining distance to the target, with zero steady-state error. The focus of this paper is on very small residual vibrations around the target position which can endure for a long time after arrival at target. This issue was discovered through a recent devel-opment within WBC context on controlling complex two-dimensional, mass-spring, beam-like arrays. To date their existence has been unidentified. This paper investigates and interprets the nature of these vibrations, explains and identifies them based on wave ideas, and finally offers a new wave-based approach to mitigate or suppress them. It also discusses their implication, not just for WBC but for the general problem of control of flexible systems.