Optimized Fourth-Order Symmetric S-Curve Trajectory for Vibration Control in Dynamic Systems

In a high-speed and high-accuracy point-to-point (P-T-P) motion application, the induction of structural vibration is a common issue. This paper introduces a novel critical motion parameter (CMP) method to appropriately tune the 15-segment fourth-order symmetrical (15-SFOS) S-curve profile for achieving low vibration P-T-P motion in a flexible system. The method provides a tuning rule to optimize the 15-SFOS S-curve profile for suppressing induced residual vibration without explicitly addressing system dynamics, considering a given traveling distance, traveling time (TT), and actuator capacities. The method is formulated with a unitization approach that treats time and displacement as one unit each. This approach is used to present the characteristics of the 15-SFOS S-curve profile as nomograms. These nomograms are employed to determine motion parameter (MP) magnitudes without the need for calculations, according to the solution provided by the CMP method. The proposed trajectory is expressed in both the generalized polynomial equation and the time-Laplace domain method. The feasibility of the proposed method is experimentally demonstrated on the setup of a flexible rotating link. The experimental results are also validated through simulated results.