Time-Optimal Freeform S-Curve Profile Under Positioning Error and Robustness Constraints

The problems on designing a time-optimal motion profile in the motion system with elasticity are briefly reviewed. Related positioning error and robustness constraints are constructed based on the analytic envelope of the residual vibration response, which is formulated by the proposed energy-based approach. The time-optimal model under such constraints is applied in the proposed freeform S-curve profile, which is the superset of symmetric S-curve and asymmetric S-curve profiles, to minimize the positioning time, while keeping the positioning accuracy under a neighborhood range of modeling frequency. The optimized motion profile shows that the proposed freeform S-curve profile allows the time-optimal model to simultaneously optimize the magnitude and phase terms in the residual vibration response in order to obtain an optimal tradeoff between shortening the positioning time and keeping the positioning accuracy. The experimental results show that the proposed optimization model can significantly reduce the positioning time compared with the traditional S-curve under the same physical limits. The universality of the optimization model is verified by experiments with short-distance and long-distance cases. The robustness of the proposed optimization model is also validated by these experiments. Moreover, the analysis on the optimized freeform S-curve profile reveals that perfect waveform cancellation is not always necessary to limit the residual vibration.