Finite-Time Sliding Mode Adaptive Control for Unknown Nonlinear Beam System With Neural Network Disturbance Observer

This paper proposes a finite-time sliding mode adaptive tracking control strategy with a neural network disturbance observer to address problems of inertia uncertainties, unknown external disturbances, singularity, and chattering. First, an accurate mathematical model of the Bernoulli-Euler beam system is constructed using an in-domain constraint strategy for surface-mounted sensors. Next, a novel finite-time disturbance observer based on the Radial Basis Function (RBF) neural network is designed to handle uncertainties, enabling fast response. In addition, a novel integral sliding surface is designed to resolve the singularity issue in terminal sliding mode. Finally, an adaptive terminal sliding mode controller is developed based on the finite-time disturbance observer and integral sliding surface to ensure finite-time convergence of tracking errors; its stability is rigorously analyzed. Simulation and experimental results demonstrate that the proposed sliding mode control strategy achieves superior tracking performance and finite-time stability compared to traditional methods in industrial beam systems. Note to Practitioners—The motivation of this paper is the vibration control problem of beam systems. Existing methods have limitations in improving system accuracy and addressing convergence time issues, primarily due to the difficulty in accurately estimating disturbances and system uncertainties. To address this, a finite-time sliding mode adaptive tracking control strategy based on neural network approximation is proposed. By applying an in-domain control strategy with sensors mounted on the Bernoulli-Euler beam equation, an accurate mathematical model of the beam system is constructed to achieve finite-time adaptive sliding mode control. The system uncertainties and unknown disturbances are treated as a lumped disturbance. Utilizing the universal approximation capability of the RBF neural network, a finite-time neural network disturbance observer is designed for compensation. Additionally, a norm-based adaptive law is designed to avoid redundant weight calculations, thereby improving computational efficiency. To mitigate the chattering effect of sliding mode control, a nonlinear gain function is applied, avoiding the singularity issue of terminal sliding mode control and enhancing the system’s tracking performance. The feasibility of the proposed method is verified through both simulation and physical experiments; however, the system has not yet been tested in actual production environments. In future research, the focus will be on improving the accuracy of the finite-time strategy and integrating data-driven approaches to build models for specific engineering applications.