Rotation Modes Stability Analysis and Phase Compensation for Magnetically Suspended Flywheel Systems with Cross Feedback Controller and Time Delay

Abstract

This paper analyzes the effects of time delay on the stability of the rotation modes for the magnetically suspended flywheel (MSFW) with strong gyroscopic effects. A multi-input multioutput system is converted into a single-input single-output control system with complex coefficient by variable reconstruction, and the stability equivalence of the systems before and after variable reconstruction is proven. For the rotation modes, the stability limits and corresponding vibration frequencies are found as a function of nondimensional magnetic stiffness and damping and nondimensional parameters of rotor speed and time delay. Additionally, the relationship between cross feedback control system stability and time delay is investigated. And an effective phase compensation method based on cross-channel is further presented. Simulation and experimental results are presented to demonstrate the correctness of the stability analysis method and the superiority of the phase compensation strategy.

A single neuron PID control method based on Smith predictor for active balancing control of rotor with time-delay

“…However, the control law is only applicable to rigid rotor rather than to flexible rotor. Ren et al analyzed the effects of time-delay on the stability of the rotation modes for the magnetically suspended flywheel (MSFW) with strong gyroscopic effects, and they presented an effective phase compensation method based on cross-channel [4]. However, this idea only applies the method of solving nonlinear dynamic systems without time-delay to time-delay systems; this method requires that the time-delay system is a weak linear system.…”

“…Therefore, in the current work we aimed to propose a new method to overcome the influence of time-delay on system. The main objectives of this study were four folds: (1) establish the dynamic model of flexible rotor by simplification and abstraction of high speed rotor; (2) build the Smith predictor of flexible rotor with time-delay to eliminate the influence of time-delay factor in the system; (3) design a single neuron PID control method based on Smith predictor to adjust the parameters of the PID controller adaptively; (4)…”

Study on stability and rotating speed stable region of magnetically suspended rigid rotors using extended Nyquist criterion and gain-stable region theory

“…In recent decades, many control strategies have been applied to MSRs, such as decentralized PID [2][3][4], decentralized PID plus cross-feedback [5,6], centralized PID plus cross-feedback [1,[7][8][9][10], adaptive control [11], robust control [12,13], inverse control [14,15] and optimal control [16][17][18][19]. Among these control methods, centralized PID plus cross-feedback control is widely used in industrial applications because it is simple and convenient to implement.…”