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 o...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/10/1559 |
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| Summary: | 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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.5</mn><mo>±</mo><mn>0.05</mn></mrow></semantics></math></inline-formula> s) dynamic stabilization to equilibria in dealing with total physical model uncertainty and disturbance, (2) effective dynamic tracking and small steady state error <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>±</mo><mn>0.002</mn></mrow></semantics></math></inline-formula>, (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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>σ</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, (5) stable chattering with low amplitude (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>±</mo><mn>0.01</mn></mrow></semantics></math></inline-formula>) at frequency 50 mHz due to high gain used against disturbance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>100</mn><mo>+</mo><mn>30</mn><mi>sin</mi><mo stretchy="false">(</mo><mn>2</mn><mi>π</mi><mi>t</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>). The simulation results are similar to those from well-known nominal model-based approaches. |
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| ISSN: | 2227-7390 |