Adaptive Second-Order Fixed-Time Nonsingular Terminal Sliding Mode Control Based on Barrier Function for Nonlinear Systems

For the arbitrary-order systems with disturbances and uncertainties, this article proposes a novel adaptive second-order fixed-time nonsingular terminal sliding mode control based on barrier function (BF). First, a second-order integral terminal sliding surface is designed to avoid singular problems, achieve fixed time stability, and reduce steady-state errors. Second, a high-order controller based on BF is constructed to further compensate for unknown uncertainties and disturbances, which ensures the adaptive adjustment of the controller gain with the change of disturbances. Then, by the Lyapunov stability theorem, it proves the fixed-time convergence of the system, which is only dependent on the controller parameters, and eliminates the slow-varying assumptions commonly present in the traditional adaptive control law. Finally, the proposed method is simulated and compared with some typical methods to prove the advantages of the proposed method. And it is further extended to a multicylinder hydraulic press model to verify its applicability in engineering practice.