Hybrid Compensation Method for Non-Uniform Creep Difference and Hysteresis Nonlinearity of Piezoelectric-Actuated Machine Tools Under S-Shaped Curve Trajectory

Piezoelectric-actuated machine tools (PAMTs) exhibit nanoscale motion capabilities, with their S-shaped curve trajectory further enabling smooth path execution and reduced terminal pulse. However, the speed changes inherent in multi-order trajectories introduce an additional non-uniform creep difference (NCD), which differs significantly from conventional hysteresis effects. Traditional models are inadequate for addressing this mixed shape nonlinearity. To overcome this limitation, this paper proposes a hybrid compensation method for the S-shaped curve trajectory of piezoelectric-actuated machine tools. The general deformation law is first established through a comprehensive mechanism analysis. The NCD and hysteresis, induced by speed changes and inherent properties, are decoupled and addressed using a pre-known phenomenon model and a clockwise operator model, respectively. Finally, a hybrid feedforward control strategy is developed to integrate these models for effective compensation. Experimental results demonstrate that the hybrid compensation method achieves a maximum relative error of 5.48% and a maximum mean square error of 0.28%, effectively mitigating the dual nonlinear factors arising from the piezoelectric-actuated machine tool’s trajectory in feedforward control.