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TECHNICAL PAPERS

Constrained Control Design for Magnetic Bearing Systems

[+] Author and Article Information
Tingshu Hu

Department of Electrical and Computer Engineering,  University of Massachusetts Lowell, Lowell, MA 01854tingshu@ece.ucsb.edu

Zongli Lin

Charels L. Brown Department of Electrical and Computer Engineering, University of Virginia, P.O. Box 400743, Charlottesville, VA 22904-4743zl5y@virginia.edu

Wei Jiang

Department of Mechanical and Aerospace Engineering, University of Virginia, P.O. Box 400746, Charlottesville, VA 22904-4743wj2b@virginia.edu

Paul E. Allaire

Department of Electrical and Aerospace Engineering, University of Virginia, P.O. Box 400746, Charlottesville, VA 22904-4743pea@virginia.edu

J. Dyn. Sys., Meas., Control 127(4), 601-616 (Jan 24, 2005) (16 pages) doi:10.1115/1.2101850 History: Received April 18, 2003; Revised January 24, 2005

We study control problems in magnetic bearing systems that are subject to both input and state constraints. Apart from the usual restrictions on voltages and currents in the circuit systems, most magnetic bearing systems are subject to a severe state constraint: the motion of the rotor (the suspended object) is only allowed in an extremely small airgap, otherwise the collision of the rotor and the stator would cause severe damages. Traditional methods for avoiding a collision include increasing the airgap and increasing the currents, which would usually result in unnecessarily large capacity of power supply and power loss. In this paper we present a systematic approach for dealing with all the input and state constraints by using some recently developed tools for constrained control design. Issues on the stability region, robustness, disturbance rejections, and transient response are addressed. We hope that by dealing with the constraints properly, safety operation can be ensured with relatively small currents and power consumption. Experiments on the balance beam test rig in our laboratory show that the design techniques are effective.

Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

The beam balancing test rig

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Figure 2

An illustration diagram for the test rig

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Figure 3

The stability region under Ib=0.5A and a valid estimate

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Figure 4

The stability region under Ib=0.1A and an invalid estimate

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Figure 5

The stability regions under Ib=0.1A and 0.5 A

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Figure 6

The estimated stability region and the actual stability region: Ib=0.5A

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Figure 7

The estimated stability region and the actual stability region: Ib=0.1A

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Figure 8

Experimental results: time responses of θ,I1, and I2 under Ib=0.5A

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Figure 9

Experimental results: time responses of θ,I1, and I2 under Ib=0.1A

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Figure 10

Experimental results: time responses of θ under parameter changes for Ib=0.1A

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Figure 11

Simulation: time responses of θ,I1, and I2 of the exact system

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Figure 12

Simulation: unstable responses under actuator uncertainties

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Figure 13

Experimental results: stable time responses of θ,I1, and I2

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Figure 14

Stability regions under different feedback laws: Ib=0.1

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Figure 15

Experimental results: time responses of θ under control laws 23,40,41

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Figure 16

Experimental results: time responses of I1 under control laws 23,40,41

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Figure 17

Experimental result: time responses of I2 under control laws 23,40,41

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