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

Quanmin Zhu (), Jianhua Zhang, Zhen Liu and Shuanghe Yu
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Quanmin Zhu: School of Engineering, University of the West of England, Frenchy Campus, Coldharbour Lane, Bristol BS16 1QY, UK
Jianhua Zhang: School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, China
Zhen Liu: School of Automation, Qingdao University, Qingdao 266071, China
Shuanghe Yu: College of Marine Electrical Engineering, Dalian Maritime University, Dalian 116026, China

Mathematics, 2025, vol. 13, issue 10, 1-23

Abstract: 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 + 30 sin ( 2 π t ) ). The simulation results are similar to those from well-known nominal model-based approaches.

Keywords: terminal sliding mode control (TSMC); model-free terminal sliding mode control (MFTSMC); Lyapunov stability; nonsingularity; total robustness; nonlinear dynamic systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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