Residual Vibration Suppression in Flexible Systems Using a Tuned Four-Segment Acceleration Profile

This study presents a method for tuning input motion to suppress residual vibrations in a flexible link manipulator, with particular relevance to mechatronic positioning systems. The approach is based on a four-segment acceleration profile that combines ramp, cycloid, and ramped-versine trajectories, enabling effective vibration reduction over a wide range of travel times. Unlike the conventional continuous reference profiles considered in this study, the proposed method does not require the total motion duration to be an integer or half-integer multiple of the system’s natural period to suppress residual vibration. The motion consists of acceleration and deceleration phases, each divided into two subsections to ensure smooth transitions. The formulation is developed analytically for both undamped and underdamped systems and is validated through numerical simulations and experiments on a servo-driven mechatronic setup equipped with inertial measurement units. For the cases considered in the quantitative comparison, the proposed method reduced the dominant first-mode residual-vibration amplitude by approximately 97–100% in the simulations and 92–98% in the experiments relative to the corresponding untuned commands. Performance is evaluated using the percent residual vibration (PRV) metric, with comparisons to commonly used motion profiles, including trapezoidal, trigonometric, and cycloidal trajectories. The results indicate that substantial vibration reduction is achieved across different travel times, including cases where the motion duration is shorter than one natural period. Overall, the proposed method offers a practical and flexible alternative to conventional motion tuning techniques and is well suited for high-speed, precision-sensitive applications such as robotic manipulators and automated manufacturing systems.