Elliptic Motions and Control of Rotors Suspending in Active Magnetic Bearings

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Xiao-Dong Yang ◽  
Hua-Zhen An ◽  
Ying-Jing Qian ◽  
Wei Zhang ◽  
Ming-Hui Yao
Keyword(s):  
Phase Portrait ◽  
Vibration Suppression ◽  
Multiple Scales ◽  
Free Vibrations ◽  
Magnetic Bearings ◽  
Pd Controller ◽  
Active Magnetic Bearings ◽  
Energy Ratios ◽  
And Control ◽  
Two Degree Of Freedom

The nonlinear dynamics of rotors suspending in the active magnetic bearings (AMBs) with eight pole pairs are investigated. The nonlinear governing equations of two degree-of-freedom (2DOF) are obtained considering the rotor with proportional–derivative (PD) controller. By studying the conservative free vibrations of the general 2DOF nonlinear systems, three types of motions are found, namely, in-unison modal motions, elliptic modal motions, and quasi-periodic motions. The method of multiple scales is used to obtain the amplitude-phase portrait to demonstrate the three types of motions by introducing the energy ratios and phase differences. It is found that in-unison modal motions do not exist due to the symmetry feature of the rotors in the AMBs. The effect of the PD controller and damping to the vibration suppression is discussed by the idea of the rolled-up amplitude-phase portrait.

The μ Approach to Control of Active Magnetic Bearings

2002 ◽  
Vol 124 (3) ◽  
pp. 566-570 ◽  
Author(s):  
R. L. Fittro ◽  
C. R. Knospe
Keyword(s):  
Laboratory Test ◽  
Rotating Machinery ◽  
Vibration Response ◽  
Experimental Results ◽  
Magnetic Bearings ◽  
Pd Controller ◽  
Active Magnetic Bearings ◽  
Test Rig ◽  
Rotor Vibration ◽  
Multivariable Controller

Many important industrial problems in the control of rotating machinery with active magnetic bearings concern the minimization of the rotor vibration response to poorly characterized disturbances at a single or several shaft locations, these typically not corresponding to those of a sensor or actuator. Herein, we examine experimental results of a multivariable controller obtained via μ synthesis with a laboratory test rig. These indicate that a significant improvement in performance can be obtained with a multivariable μ controller over that achieved with an optimal decentralized PD controller.

The μ Approach to Control of Active Magnetic Bearings

2000 ◽  
Author(s):  
Roger L. Fittro ◽  
Carl R. Knospe
Keyword(s):  
Laboratory Test ◽  
Rotating Machinery ◽  
Vibration Response ◽  
Experimental Results ◽  
Magnetic Bearings ◽  
Pd Controller ◽  
Active Magnetic Bearings ◽  
Test Rig ◽  
Rotor Vibration ◽  
Multivariable Controller

Many important industrial problems in the control of rotating machinery with active magnetic bearings concern the minimization of the rotor vibration response to poorly characterized disturbances at a single or several shaft locations, these typically not corresponding to those of a sensor or actuator. Herein, we examine experimental results of a multivariable controller obtained via μ synthesis with a laboratory test rig. These indicate that a significant improvement in performance can be obtained with a multivariable μ controller over that achieved with an optimal decentralized PD controller.

Modeling and Vibration Control of a Flexible Rotor by Using Magnetic Bearings

2011 ◽  
Author(s):  
Takuya Nomoto ◽  
Daisuke Hunakoshi ◽  
Toru Watanabe ◽  
Kazuto Seto
Keyword(s):  
Control System ◽  
Control Method ◽  
Design Procedure ◽  
Modeling Method ◽  
Magnetic Bearings ◽  
Active Magnetic Bearings ◽  
Flexible Rotor ◽  
Modeling And Control ◽  
Elastic Modes ◽  
And Control

This paper presents a new modeling method and a control system design procedure for a flexible rotor with many elastic modes using active magnetic bearings. The purpose of our research is to let the rotor rotate passing over the 1st and the 2nd critical speeds caused by flexible modes. To achieve this, it is necessary to control motion and vibration of the flexible rotor simultaneously. The new modeling method named as Extended Reduced Order Physical Model is presented to express its motion and vibration uniformly. By using transfer function of flexible rotor-Active Magnetic Bearings system, we designed a Local Jerk Feedback Control system and conducted stability discrimination with root locus. In order to evaluate this modeling and control method, levitation experimentation is conducted.

On Nonlinear Motions of Two-Degree-of-Freedom Nonlinear Systems with Repeated Linearized Natural Frequencies

2019 ◽  
Vol 29 (10) ◽  
pp. 1950132
Author(s):  
Hua-Zhen An ◽  
Xiao-Dong Yang ◽  
Feng Liang ◽  
Wei Zhang ◽  
Tian-Zhi Yang ◽  
...  
Keyword(s):  
Natural Frequencies ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Phase Portraits ◽  
Chaotic Motions ◽  
Nonlinear Parameters ◽  
Energy Ratios ◽  
Two Degree Of Freedom ◽  
Nonlinear Motions ◽  
Phase Differences

In this paper, we investigate systematically the vibration of a typical 2DOF nonlinear system with repeated linearized natural frequencies. By application of Descartes’ rule of signs, we demonstrate that there are 14 types of roots describing different modal motions for varying nonlinear parameters. The method of multiple scales is used to obtain the amplitude-phase portraits by introducing the energy ratios and phase differences. The typical nonlinear in-unison and elliptic out-of-unison modal motions are located for the 14 types of roots and then validated by numerical simulations. It is found that the normal in-unison modal motions, elliptic out-of-unison modal motions are analogous to the polarization of classical optic theory. Further, some kinds of periodic and chaotic motions under out-of-unison and in-unison excitations are investigated numerically. The result of this study offers a detailed discussion of nonlinear modal motions and responses of 2DOF systems with cubic nonlinear terms.

Sign in / Sign up

Export Citation Format

Share Document