Nonlinear Lyapunov-based control of a misaligned heteropolar magnetic bearing system

The dynamic behavior of an active magnetic bearing (AMB) mounted rotor was investigated through an analytical study conducted as part of this research work. A biased AMB model was developed, in which six electromagnets were supplied with a bias current I-0, and their respective control currents. The magnetic load was obtained through a differentiated driving mode based on the virtual displacement principle. Motion equations were formulated, and simulations were performed to investigate the dynamic response of the misaligned AMB mounted on a high-speed rotor, considering rigid body motion, elastic motion, gyroscopic effect, shear deformation effect, and internal damping. Subsequently, a nonlinear novel direct Lyapunov-based controller derived from an energetic approach was applied and compared to an optimal regulator based on Hamilton-Jacobi-Bellman (HJB) equations. The Linear Quadratic Riccati (LQR) method required less energy, as expected, but the Lyapunov method was more efficient and demonstrated its ability to asymptotically control the plant instability as well as the misalignment effect. Finally, the method was applied to a milling machine spindle, and the controller was still able not only to handle the cutting forces generating disturbances but also to overcome the defect effect without any oscillation.