Adaptive Global Super-Twisting Sliding Mode Control for Trajectory Tracking of Two-Link Flexible Manipulators

This paper proposes a new adaptive supertwisting global sliding mode control method for the nonlinear two-link flexible manipulator's exponentially changing trajectory tracking control. This technique consists of an adaptive super-twisting to prevent chattering and the robustness issue, and a global sliding mode control structure to eliminate the reaching phase of the tip trajectory tracking of the flexible manipulator with unknown disturbances and variation in the payloads. The tip trajectory tracking control and the stability analysis of the system is guaranteed using Lyapunov method for the convergence to zero in finite time while mitigating the traditional drawback of the high frequency chattering. By tuning the gains of the new adaptive method, the controller can handle the flexible manipulator's parametric variations and avoid the aggressive control inputs. Moreover, the upper boundaries of the perturbation of the system information are not necessary when utilising the adaptation laws. Lesser tracking error in terms of integral absolute error, quick tip deflection suppression in terms of 2-norm, no chattering, no reaching phase, lesser input torque energy in terms of 2-norm and total variance are the effective matrices used to validate the effectiveness of the suggested method. The effectiveness of the proposed controller is assessed by means of simulation validation and compared with other controllers of the state of art in the literature. It is shown that our proposed control technique ensures robustness with low tracking error, reduced tip deflection, lower control inputs, no chattering, and smoother control, while achieving 94.92% energy efficiency, 57.64% improved tracking accuracy, and stability under increased payloads.