Compliant micro-nano multi-axis trajectory tracking with nonlinear coupling stiffness using a predefined-time extended state observer

This work proposes a novel control methodology to achieve high-precision multi-axis coordinated trajectory tracking of a compliant micro-nano positioning stage system with nonlinear coupling stiffness. It addresses the problem of a positioning stage control using compliant parallel mechanisms (CPMs) to undertake complex trajectory tracking, in which multi-axis coupled motions and external disturbances significantly affect the tracking accuracy. To address this, the proposed control method is developed by utilizing the predefined-time extended state observer (PTESO) with linear sliding mode control (SMC), in which the PTESO incorporates the nonlinear stiffness model of CPMs with its stability proven through Lyapunov stability analysis. This method ensures reduced uncertainty in system coupling as disturbance observation converges to the desired accuracy within a predefined time, independent of initial conditions. By solely utilizing position signals, the control system achieves faster and more accurate velocity estimation and disturbance compensation in multi-axis coordinated trajectory tracking, thereby enhancing overall the robustness and dynamic performance. Experimental validation on a 4 PPR (Prismatic-Prismatic-Revolute) planar three-degree-of-freedom compliant stage demonstrates a tracking accuracy of 0.1 μm in a 1-Hz circular trajectory experiment. Compared to SMC with traditional ESO, the proposed scheme significantly reduces the root mean square error (RMSE) by 79.17 %. Notably, significant performance improvements are also observed when tracking other complex trajectories, compared to conventional ESO-based control schemes. The proposed control methodology also effectively mitigates time delays and enables high-precision real-time trajectory tracking at the micro-nano level.