A novel TDE error compensation method based on manipulator time-delay control

The classic model-free controller, the time delay controller (TDC), operates under complex conditions with large external disturbance changes and suffers from time delay estimation (TDE) errors, which can lead to reduced controller performance. To compensate for the TDE error, a novel compensator is proposed in the TDC framework by considering the TDE error as a separate disturbance term. This compensator innovatively combines a gradient error compensator and a disturbance observer to correct fast-time-varying TDE errors using the gradient error compensator and slow-time-varying TDE errors using the disturbance observer. Furthermore, a high-order time delay observer (HOTDEO) is designed based on the first-order disturbance observer. Compared to the first-order and second-order observers, the HOTDEO has a lower steady-state error. The designed high-order time delay compensator is used as a supplementary term for traditional TDC and applies to various TDC frameworks. Additionally, the stability theory for both the observer and controller is analyzed in detail, and their convergence conditions are verified. Finally, simulation and experimental results demonstrate that the proposed high-order time delay compensator significantly improves the tracking accuracy and robustness of the control algorithm, particularly in terms of TDE error compensation. This research provides valuable contributions to the further development of TDC in the field.