Complex modal space control of rigid and flexible rotors supported by active magnetic bearings

Abstract

Active magnetic bearing (AMB) has been recently applied to high performance rotating machineries such as flywheel energy storage system, momentum wheel and turbo-machinery, because the AMB can support high speed rotors with many promising advantages over conventional rolling-element and fluid-film bearings such as no mechanical contact between rotor and stator, low power loss, elimination of lubrication and adjustability of bearing force characteristics. The AMB is inherently unstable due to the pre-magnetization of electro-magnets, and thus decentralized proportional-integral-derivative (PID) feedback control has been widely adopted for stable and reliable operation of the rotors supported by a pair of active magnetic bearing systems. High performance rotor-AMB system has increasingly demanded higher rated rotational speed so that the control problems related to the stability and the vibration become dominant. The present study develops practical complex PD control methods such as an eigenvalue assignment and an optimal isotropic PD control for the rigid and flexible rotor-AMB systems, respectively, which can facilitate the high-speed operation of the rotor by solving the associated stability and vibration problems.Because of the AMBs’ limited specific bearing capacity compared with that of the conventional bearings, the dynamic behavior of a rotor supported by AMBs is often dominated by the rigid body modes including the translational and conical modes, which are normally well separated in frequency from higher flexural bending modes. The gyroscopic moment itself is conservative and is not a destabilizing factor. However, it has been reported that the decentralized PID control were not successful for high speed operation of a rigid rotor-AMB system with a strong gyroscopic effect due to the instability of the conical modes caused by phase-lagged electro-magnetic control force. To solve this problem, an eigenvalue assignment for decoupled translational and co...