Nonlinear Integral Sliding Mode Control with Adaptive Extreme Learning Machine and Robust Control Term for Anti-External Disturbance Robotic Manipulator

To overcome the limitations of the traditional sliding mode control (SMC) method, including steady-state errors, low tracking accuracy, external disturbances, and difficulties in estimating uncertain parameters, a nonlinear integral SMC method with an adaptive extreme learning machine (ELM) and a robust control term is developed. First, the ELM is used to approximate the uncertain parameters in the manipulator dynamics model to improve the tracking accuracy of the manipulator. In this process of using an ELM to approximate uncertain parameters, a method of adaptively updating the output weight is applied to improve the stability and closed-loop tracking accuracy of the system and ensure the real-time performance of manipulator control. A new nonlinear integral sliding mode function is designed to reduce the steady-state error of the system, avoid the issue of system instability caused by large initial errors of the system, and enable the system to track the desired trajectory quickly. Moreover, a robust control term is added to the SMC law to compensate for the error of ELM approximation, which increases the robustness of the manipulator and reduces the fluctuation amplitude of the control input in the presence of external disturbances. Finally, a simulation analysis is performed and stable convergence of the proposed method using Lyapunov stability functions is demonstrated.