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Research Papers: Gas Turbines: Structures and Dynamics

Active Vibration Control of the Flexible Rotor to Pass the First Bending Critical Speed in High Energy Density Magnetically Suspended Motor

[+] Author and Article Information
Enqiong Tang

Science and Technology on Inertial Laboratory,
Beihang University,
Shining Building 403, Xueyuan Road,
Beijing 100191, China
e-mail: tang.forever@163.com

Jiancheng Fang

Professor
Science and Technology on Inertial Laboratory,
Beihang University,
Shining Building 403, Xueyuan Road,
Beijing 100191, China
e-mail: fangjiancheng@buaa.edu.cn

Shiqiang Zheng

Science and Technology on Inertial Laboratory,
Beihang University,
Shining Building 403, Xueyuan Road,
Beijing 100191, China
e-mail: zhengshiqiang@buaa.edu.cn

Dikai Jiang

18th Institute of China Academy of Launch Vehicle Technology,
Nandahongmen Road No.1,
Beijing 100076, China
e-mail: jdk_2008@126.com

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received December 7, 2014; final manuscript received March 1, 2015; published online May 12, 2015. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(11), 112501 (Nov 01, 2015) (9 pages) Paper No: GTP-14-1652; doi: 10.1115/1.4030264 History: Received December 07, 2014; Revised March 01, 2015; Online May 12, 2015

In order to minimizing the rotor displacement and the amplifier current mainly caused by the unbalance forces when the flexible rotor passes the first bending critical speed, the optimal controller is presented in this paper. The accurate modeling method for the flexible rotor based on the sine sweeping measurements is investigated. The design of the Kalman estimator and the choice of the variance matrix elements have been described. The optimal state feedback regulator with an integral controller has been used for stabilizing the system and the determination of the weight matrices has been investigated in detail. The influences of the specific elements of the weight matrices on the resonance peak of the flexible rotor when passing the first bending critical speed are analyzed. Finally, the running up test of the flexible rotor is implemented and the result shows the effectiveness of linear quadratic Gaussian (LQG) controller minimizing the rotor displacement and the amplifier current nearby the first bending critical speed. Furthermore, the comparison between the proportional-integral-differential (PID) controller with phase lead compensator and the LQG controller verifies the superiority of LQG controller in reducing the amplifier currents.

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Figures

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Fig. 1

The sketch map of the magnetically suspended motor

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Fig. 2

The block diagram of the rotor-AMB system

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Fig. 3

The finite element model of the rotor

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Fig. 4

The bending mode shape of the flexible rotor

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Fig. 5

Schematic diagram of switching power amplifier

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Fig. 6

The saturation characteristics of the amplifier current

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Fig. 7

Frequency characteristics of power amplifier from amplifier reference input to amplifier current output

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Fig. 8

Bode plots from amplifier reference input to displacement sensor output in the x direction

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Fig. 9

Structure of the LQG controller

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Fig. 10

The experimental system of the 100 kW magnetically suspended motor

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Fig. 11

Amplifier current and rotor displacement sampled by DSP

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Fig. 12

Influence of estimation algorithm on amplifier current and rotor displacement; (a) amplifier current and (b) rotor displacement

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Fig. 13

The estimated value of x0, x1, and x2 obtained by Kalman filtering algorithm

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Fig. 14

LQG controller and integral feedback of control deviation

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Fig. 15

Influence of diagonal weighting matrices Q and R on step response (rotor at standstill, reference position step is 50 μm in one axis). (a) q44, (b) q55, and (c) r11.

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Fig. 16

Influence of diagonal weighting matrices Q and R on response of the sine sweeping signal. (a) q22 and (b) q77.

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Fig. 17

The response to the sine sweeping signal near the bending mode frequency with different controller

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Fig. 18

The synchronous vibration amplitude of the amplifier current and the displacement in run-up test of the flexible rotor with different controller

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