Adaptive backstepping control using a novel dual-differentiator for multi-degree-of-freedom manipulator uncertain systems with unknown multi-disturbances

In this article, the adaptive sliding mode backstepping controller (ASMBC) using a novel dual-differentiator is proposed for multi-degree-of-freedom (MDOF) manipulator systems with uncertain states and multi-disturbances. The dual-differentiator comprises a tracking differentiator (TD) and a disturbance observer (DOB) based on the proposed TD. A novel tracking differentiator based on the inverse hyperbolic sine function and terminal attractor function (IHSTD) is introduced to reconstruct unknown states like velocity responses of the manipulator systems. Furthermore, the other differentiator, DOB based on aforementioned IHSTD (IHSTD-DOB), is involved in estimating the uncertain and stochastic multi-disturbances affecting the manipulator systems. Then, an ASMBC scheme, combining proposed dual-differentiator, is developed for achieving accurate tracking control of manipulator. Additionally, to handle the “explosion of term” issue in backstepping control, the designed IHSTD is also utilized to estimate the derivative of the virtual control law. The stability of the controller is rigorously analyzed using the Lyapunov method. Finally, numerical simulation results are presented to validate the effectiveness of the proposed scheme. Comparison experiments with the traditional DOB, the scheme except IHSTD, and the classical sliding mode control method are carried out by Simulink. The results illustrate that the present control method not only has an excellent tracking performance but also accurately estimates the unpredictable multi-disturbance and reconstructs the unknown states of the manipulator systems.