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Robust Control Design and Optimization for Under-Actuated Mechanical Systems Considering Fuzzy Uncertainties

Year: 2025
Type: article
Abstract: This paper addresses the robust control problem for under-actuated mechanical systems subject to uncertainties. The key challenge lies in achieving precise control with insufficient degrees of freedom while maintaining robustness against system uncertainties. We propose a novel control framework that characterizes bounded, time-varying uncertainties through fuzzy set theory, leading to a fuzzy dynamical system formulation. The main contributions are threefold: (1) the development of a deterministic robust controller that eschews traditional IF-THEN rules while guaranteeing system stability through a Lyapunov–Minimax analysis; (2) the formulation of a performance optimization scheme that minimizes both fuzzy system average performance and control costs, with proven existence and uniqueness of the analytical solution; and (3) the establishment of stability conditions using the Lyapunov theory for time-varying systems with bounded uncertainties. The theoretical framework is validated through both numerical simulations and experimental implementation on a linear motor-driven inverted pendulum system. The experimental results demonstrate significant performance improvements over conventional approaches: the optimal robust controller achieves 34.89% and 29.20% reductions in cart position and pendulum angle errors, respectively, from the initial conditions. A comparative analysis with traditional PD control shows a reduction in steady-state errors from 0.00318 m to 0.00057 m for the cart position and from 0.01117 rad to 0.00055 rad for the pendulum angle, validating the effectiveness of the proposed methodology.
Source: Processes
DOI: 10.3390/pr13030609
Authors: Xiaofei Chen, Jie Fang, Jiandong Li
Language: English
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4407812345
FWCI: 2.447
Cites: 38
Cited by: 6
Related to: 10