Sliding-Mode Vibration Control of Flexible Structures via Physics-Informed Neural Network-Based Modeling

This study establishes an integrated modeling and control framework for vibration suppression in large flexible structures. We propose a Physics-Informed Neural Network methodology that accurately identifies mass, damping, and stiffness parameters by incorporating dual physics-informed loss terms: equation of dynamics errors and natural frequency constraints. This approach enables high-fidelity dynamic modeling of complex flexible systems. Building upon this model, we design a terminal sliding mode control strategy with mathematically proven finite-time convergence through Lyapunov stability analysis. Numerical simulations confirm the controller's performance, achieving rapid vibration attenuation with minimal settling time. Experimental validation using cantilever beam data demonstrates the practical efficacy of the proposed methodology under realistic conditions.