Modeling and Vibration Suppression of Rotating Machines Using the Sparse Identification of Nonlinear Dynamics and Terminal Sliding Mode Control

This paper presents a novel physics-based data-driven approach for reconstructing the nonlinear governing equations and suppressing vibrations in vertical-shaft rotary machines during transient motion. We first identify the key nonlinear terms using a physics-based methodology. Subsequently, a data-driven approach, known as the Sparse Identification of Nonlinear Dynamical Systems (SINDy), is employed to reconstruct the nonlinear governing equations of a typical rotary machine. After validating the model, a robust nonlinear controller is designed using the terminal sliding mode control (TSMC) technique to reduce lateral vibrations in the machine’s shaft. Extensive experimental tests on a laboratory-scale rotary system confirm the stability and robustness of the proposed approach. The results also demonstrate that the proposed method significantly reduces lateral vibrations in rotary machines.