Predefined-Time Disturbance Observer-Based Nonsingular Sliding Mode Control with Prescribed Performance for Robotic Manipulators

To achieve manipulator trajectory tracking under uncertainties and external disturbances, this study develops a prescribed performance nonsingular sliding mode control strategy. A new sufficient condition for predefined-time stability is established and proved. A predefined-time nonlinear disturbance observer is designed to estimate the lumped disturbance, and a prescribed performance function is introduced to confine the tracking error within predefined bounds. A predefined-time nonsingular sliding mode surface is constructed, while a saturation function and a hyperbolic tangent function are adopted to address singularity and chattering, respectively. Numerical simulations are conducted on a two-degree-of-freedom manipulator subject to 20% parametric uncertainties and time-varying external disturbances. The effectiveness of disturbance compensation is evaluated by comparing the control performance with and without observer compensation, and the proposed method is further compared with fixed-time and finite-time sliding mode controllers. Quantitative results show that, with observer compensation, the integral absolute error (IAE), integral squared error (ISE), and root mean square error (RMSE) are reduced by 71.63%, 12.95%, and 6.60% for Joint 1, and by 79.24%, 35.57%, and 19.55% for Joint 2, respectively. Moreover, compared with the fixed-time method, the proposed controller reduces the IAE by 54.3% for Joint 1 and 63.1% for Joint 2, while the corresponding reductions relative to the finite-time method are 89.0% and 93.3%, respectively. These results verify the effectiveness of the proposed scheme in disturbance rejection and tracking accuracy.