Adaptive full-order time-varying sliding mode control for second-order nonlinear systems

This paper presents an innovative adaptive robust controller designed for uncertain second-order nonlinear systems. The proposed method incorporates a novel sliding surface that seamlessly blends the benefits of both time-varying and fast terminal sliding surfaces. This integration aims to eliminate the reaching phase, enhance robustness, reduce steady-state error, eradicate chattering, and avoid singularity in the control signal. Additionally, an adaptive law is formulated to estimate the bounds of uncertainties. The closed-loop stability and convergence are demonstrated using the Lyapunov stability method. Simulation results indicate the superior performance of the presented controller.