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Research Papers

Nonlinear Analysis for Influence of Parametric Uncertainty on the Stability of Rotor System With Active Magnetic Bearing Using Feedback Linearization

[+] Author and Article Information
Junya Kato

Department of Mechanical Systems Engineering,
Nagoya University,
Furo-cho,
Chikusa-ku 464-8603, Nagoya, Japan

Tsuyoshi Inoue

Mem. ASME
Department of Mechanical Systems Engineering,
Nagoya University,
Furo-cho, Chikusa-ku,
Nagoya 464-8603, Japan
e-mail: inoue.tsuyoshi@nagoya-u.jp

Kentaro Takagi, Shota Yabui

Department of Mechanical Systems Engineering,
Nagoya University,
Furo-cho, Chikusa-ku
Nagoya 464-8603, Japan

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 30, 2017; final manuscript received April 24, 2018; published online May 28, 2018. Assoc. Editor: Firdaus Udwadia.

J. Comput. Nonlinear Dynam 13(7), 071004 (May 28, 2018) (9 pages) Paper No: CND-17-1531; doi: 10.1115/1.4040128 History: Received November 30, 2017; Revised April 24, 2018

Active magnetic bearing (AMB) is the device to support and control rotating shaft. Feedback linearization is one of the methods to compensate the system nonlinearity, and it is often used in the control of AMB. Some parameters in the electromagnetic force model have often been ignored or their parametric uncertainty from the nominal values has been calibrated; however, their influence on the stability has not been investigated. In this paper, the influence of the parametric uncertainty in the electromagnetic force model on the stability of AMB is investigated. The equilibrium positions and their stability are investigated and clarified analytically. Furthermore, the choice of the parameter value for improving the stability of AMB with feedback linearization is proposed, and its effectiveness is explained analytically. It is shown that the proposed choice of the parameter value also reduces the remained nonlinearity significantly. The validity of theoretical results and proposed choice of the parameter value are confirmed by experiment.

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Figures

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Fig. 3

Block diagram of closed loop system with both PD feedback and feedback linearization

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Fig. 2

AMB configuration and four electromagnets in xbfybf-plane

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Fig. 1

Schematic of 2DOF vertical rotor system supported by AMB

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Fig. 4

Magnetic force Fx for the displacement xbf in the AMB system with feedback linearization shown for various cases of parametric uncertainty Δδ in the AMB model

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Fig. 5

Equilibrium position xbf0 for the parametric uncertainty Δδ in the AMB model with feedback linearization

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Fig. 6

Magnetic force Fx for the displacement xbf in the AMB system without feedback linearization shown for various cases of parametric uncertainty Δδ in the AMB model

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Fig. 12

Photo of experimental setup to investigate the region of attraction of the trivial equilibrium position xbf0z

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Fig. 13

Experimental method to investigate the region of attraction of the trivial equilibrium position xbf0z

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Fig. 8

Comparison of the cases with and without feedback linearization on the remained nonlinearity: case with actual magnetic constant is δ = 0.23, and tuning to δ̂ = 0 in the AMB model

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Fig. 9

Initial value responses from various initial positions xbf(0)

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Fig. 10

Initial value responses with various values of parametric uncertainty Δδ

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Fig. 7

Equilibrium position xbf0 for the parametric uncertainty Δδ in the AMB model without feedback linearization

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Fig. 11

Experimental system

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Fig. 14

Experimental result of the region of attraction of the trivial equilibrium position xbf0z in theAMB system with feedback linearization. It corresponds to the theoretical result shown in Fig. 5.

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Fig. 15

Experimental result of the region of attraction of the trivial equilibrium position xbf0z in the AMB system without feedback linearization. It corresponds to the theoretical result shown in Fig. 7.

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Fig. 16

Comparison of static magnetic forces between the cases with and without feedback linearization when the value of Δδ is tuned to the critical value of stability

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Fig. 17

Resonance curves of the experimental results and the influence of value δ̂ in the AMB model of feedback linearization controller

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