Vibration control of flexible rotors based on modeling of magnetic saturation and full-dimensional observers

Using active magnetic bearings (AMB) for vibration control of flexible rotor systems is a significant focus of current research. Existing studies show that displacement sensors are prone to interference from the high-frequency magnetic fields of bearing coils, while sensors placed too far from the bearings can cause discrepancies in the observed positions of the flexible rotor. To address these issues, this paper optimizes the extended Kalman observer and derives it to suit magnetic bearing systems. By considering the dynamic variations in the magnetic permeability of ferromagnetic materials, the nonlinear magnetic force modeling of a 16-pole electromagnetic bearing is achieved, and an electromechanical-magnetic integrated model of the magnetic bearing-flexible rotor system is established. The modified observer, combined with the displacement measurements from sensor nodes, enables the observation of all nodes in the rotor system. Based on the observed displacements, a linear active disturbance rejection controller (LADRC) is introduced to predict external disturbances and calculate the required control current. The proposed method leverages the observed vibrations of all flexible rotor nodes to design the controller, maintaining the modeling accuracy of magnetic force under magnetic saturation within 5% while ensuring high computational efficiency. The analytical expressions support real-time computations for the controller. Under working conditions with process noise, measurement noise, and disturbances, the optimized nonlinear extended state observer (ESO) successfully completes various control tasks, maintaining an observation error within 10 µm. This enables the active disturbance rejection controller to smoothly guide the rotor through the first critical speed, demonstrating the effectiveness of the proposed method.