Cross-Feedback Stabilization of the Digitally Controlled Magnetic Bearing

Abstract

A method of stabilizing a high speed rotor supported by magnetic bearings is presented. The magnetic bearing is controlled by a digital controller with rotationally synchronized interruption. The main problem with the rotating disc is the cross-coupling effect caused by the gyroscopic or inductive forces which sometimes make the high speed rotor unstable. Standard PID control is carried out with constant time interval interruption, while the rotational interrupt subroutine performs the cross-coupling feedback. The cross-feedback in the x-y directions well compensates for the undesirable coupling effect. This scheme is applied to a four-mass, two-bearing rotor system and its capability is tested.

Optimal control of the magnetic bearings for a flywheel energy storage system

“…Note that the last term in (8) corresponds to the final future state and the coupling matrices are given by…”

“…It is also recognized that the spinning rotor under the magnetic suspension may experience two kinds of whirl modes. The conical whirl mode gives rise to the gyroscopic forces to twist the rotor, thereby severely affecting stability of the rotor if not properly controlled [8]. The translatory whirl mode constrains the rotor to synchronous motion in the radial direction so as to suppress the gyroscopic rotation, which has been extensively used in industry [3,9,10].…”

Analysis and Control of Flywheel Energy Storage Systems

“…In reality, the spinning rotor under the magnetic suspension may experience two kinds of whirl modes. The conical whirl mode gives rise to the gyroscopic forces to twist the rotor, thereby severely affecting stability of the rotor if not properly controlled (Okada et al, 1992;Williams et al, 1990). The translatory whirl mode constrains the rotor to synchronous motion in the radial direction so as to suppress the gyroscopic rotation, which has been extensively used in industry (Tomizuka et al, 1992;Tsao et al, 2000).…”

Whirling Modes Stability Criterion for a Magnetically Suspended Flywheel Rotor With Significant Gyroscopic Effects and Bending Modes

“…Gyroscopic effects are mainly characterized by the forward tilt whirling (nutation) and backward tilt whirling (precession) modes [15]- [17]. Like the rigid body mode, the first bending mode splits with rotor speed, forming the first bending forward whirl (BFW) and first bending backward whirl (BBW) [13], [14].…”