Design and dynamic characteristic analysis of NTSM with variable gains for full-parameter perturbation systems: A case of DC-DC converters

The non-singular terminal sliding mode (NTSM) is widely applied in various nonlinear systems due to its rapid response and non-singularity properties. However, its dynamic characteristics during convergence are often neglected in current studies, which severely restricts the in-depth development of the NTSM. This paper takes the typical nonlinear system, DC-DC buck converters, as an example. A novel adaptive NTSM (ANTSM) with embedded variable gain design is proposed to achieve high-precision output and strong stability of the system under full parameter perturbations. Furthermore, the phase trajectory convergence dynamics and the stability of the existence domain boundary conditions of ANTSM are fully revealed. Initially, a state-space model for the buck converter is developed by incorporating bounded perturbations of both internal and external parameters. Subsequently, the ANTSM is designed by integrating an integral error regulation mechanism and an adaptive zero-crossing gain. The system Lyapunov-based stability and the finite-time convergence characteristics in different sliding mode stages in the time-domain are explicated, along with its open-loop frequency-domain behaviors. Besides, the impact of variations in control parameters on the system's dynamic and static performance is analyzed, with stability conditions for the ANTSM parameters clarified by phase trajectory analysis. Finally, simulation and experimental results indicate that compared to the traditional NTSM, the average disturbed recovery time and steady-state accuracy of the system output voltage with full-parameter perturbations are improved by 33.2% and 34.4% respectively, and the transient overshoot and average ripple error of the output current are reduced by 56.8% and 4.2% respectively, demonstrating better control accuracy and robustness.