A modified optimal asymmetric S‐curve profile for residual vibration suppression

To realize fast movement with low vibration in the precision manufacturing field, the conventional S‐curve profile assumes the elastic dynamics to be an undamped model to ensure time‐optimality. However, their vibration suppression performance will be undermined significantly when a motion system's damping coefficient is non‐negligible. To this end, a generalized residual vibration model is formulated by modeling the freeform S‐curve and the spring‐mass‐damper system to analyze the drawbacks of the conventional S‐curve profiles. Further, we propose a novel asymmetric S‐curve (AS‐curve) profile that has two structures for different optimization cases with only one extra parameter, which can reduce the complexity of parameter tuning. To obtain an optimal tradeoff between positioning efficiency and accuracy, the weighted output of residual vibration energy and total traveling time is utilized as the optimization objective of the extra parameter. The numerical simulation and experimental results verify that the proposed AS‐curve achieves better vibration suppression and robustness in under‐damped motion systems compared with the conventional S‐curve profile. Moreover, computation‐time tests on a microcontroller platform demonstrate the low computational complexity of the proposed optimization algorithm and its suitability for engineering applications.