Eigenvalue assignment for stabilizing unstable conical modes of rigid rotor-active magnetic bearing system over high rotational speed range

Abstract

Conventional centralized proportional-integral-derivative (PID) control methods manipulate the feedback gains in prescribed forms until they achieve the desired control performance, but they have often failed to stabilize the lightlydamped and unstable conical modes, among the rigid body modes, of the rigid rotor-AMB system with large gyroscopic effect over high rotational speed range. In this study, an eigenvalue assignment for decoupled translational and conical modes is proposed in the complex domain to yield a unique PID controller in a closed form, preserving isotropic bearing characteristics. The eigenvalue assignment necessitates the constraints required for decoupling of two modal equations related to translational and conical whirl motions from the complex equation of motion written in the center of gravity coordinates of the rigid rotor. A flywheel energy storage system is taken as a simulation example in order to demonstrate the validity and effectiveness of the proposed eigenvalue assignment. The simulation results show that the eigenvalue assignment algorithm is superior to conventional control methods at systematically ensuring sufficient stability margins for the lightlydamped and unstable conical modes with unique, explicit gain-scheduled PID controller with respect to the rotational speed.