Error-Compensated Extended State Observer for Robust Disturbance Rejection of Nano-Stage With Time Delay Control

Precision motion control systems are frequently challenged by exogenous disturbances and plant uncertainties, which compromise tracking accuracy and operational stability. To address these issues, the extended state observer (ESO) has been developed to estimate both system states and disturbances in real time. However, conventional ESOs rely on an integral-based mechanism, necessitating a high observer bandwidth to handle rapidly varying disturbances. This, in turn, increases noise sensitivity and reduces stability margins. In this article, we introduce a novel error compensation mechanism that dynamically minimizes the estimation errors inherent in traditional ESOs, thus eliminating the need for a high observer bandwidth. Furthermore, we propose a time delay controller, leveraging historical input–output data to mitigate residual disturbances and plant variations. Experimental results validate the efficacy of our approach: settling time is reduced from 49.81 (conventional ADRC) to 2.74 ms (the proposed method), while disturbance convergence time decreases from 49.94 to 2.41 ms. These results underscore its superiority in high-precision applications that require robustness against disturbances and uncertainties.