Robust Higher-Order Nonsingular Terminal Sliding Mode Control of Unknown Nonlinear Dynamic Systems

In contrast to the majority of model-based terminal sliding mode control (TSMC) approaches that rely on the plant physical model and/or data-driven adaptive pointwise model, this study treats the unknown dynamic plant as a total uncertainty in a black box with enabled control inputs and attainable outputs (either measured or estimated), which accordingly proposes a model-free (MF) nonsingular terminal sliding mode control (MFTSMC) for higher-order dynamic systems to reduce the tedious modelling work and the design complexity associated with the model-based control approaches. The total model-free controllers, derived from the Lyapunov differential inequality, obviously provide conciseness and robustness in analysis/design/tuning and implementation while keeping the essence of the TSMC. Three simulated bench test examples, in which two of them have representatively numerical challenges and the other is a two-link rigid robotic manipulator with two input and two output (TITO) operational mode as a typical multi-degree interconnected nonlinear dynamics tool, are studied to demonstrate the effectiveness of the MFTSMC and employed to show the user-transparent procedure to facilitate the potential applications. The major MFTSMC performance includes (1) finite time (2.5±0.05 s) dynamic stabilization to equilibria in dealing with total physical model uncertainty and disturbance, (2) effective dynamic tracking and small steady state error 0±0.002, (3) robustness (zero sensitivity at state output against the unknown bounded internal uncertainty and external disturbance), (4) no singularity issue in the neighborhood of TSM σ=0, (5) stable chattering with low amplitude (±0.01) at frequency 50 mHz due to high gain used against disturbance d(t)=100+30sin(2πt)). The simulation results are similar to those from well-known nominal model-based approaches.