Parametric Stability Analysis of Active Magnetic Bearing Supported Rotor System With a Novel Control Law Subject to Periodic Base Motion

Active magnetic bearings (AMBs) are being continuously explored for industrial applications mainly because of their friction-free operation. However, if a rotor-shaft-AMB system is used in applications such as turbo engine of an aircraft or in the propeller shaft of a ship, it would be subject to parametric excitation because of the moving base of the system. Parametric excitation is known to cause instability in systems. This paper addresses the issue of such flexible rotor-AMB system and performs the parametric stability analysis. A novel control law based on the constitutive relationship of a viscoelastic material called the four-element control law is developed. Because of the presence of periodic base motion terms in the system state matrix, the system can be classified as a linear periodic system. Thus, the stability analysis is carried out using Floquet-Liapunov theory on stability of periodic system, for which an approximate state transition matrix is first found and stability of the system is then decided based on the absolute value of eigenvalue. Three different base motions (roll, pitch, and yaw) were considered for evaluating the performance of the proposed control law. Simulation results reveal that the proposed control law has better stability characteristics than the proportional-integral-derivative (PID) control law.