Robust Controller Design for AMB Levitation Recovery Alexander H. Pesch Department of Engineering Hofstra University
Jerzy T. Sawicki The Center for Rotating Machinery Dynamics and Control Department of Mechanical Engineering Cleveland State University
15th International Symposium on Magnetic Bearings August 3-6, 2016 Kitakyushu, Japan
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Introduction Problem AMBs are still not utilized widely. End users are fearful of loss of levitation. Robust control methods provide robustness only around the operating point. Solution A control method is proposed which seeks to guarantee automatic relevitation in the case of an acute external fault. The control method accounts for touchdown (TD) bearing forces on the rotor and current saturation limits at large deflections.
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μ-synthesis Controller Design for Normal AMB Performance and Levitation Recovery Generalized μ-synthesis
Structured Singular Value
(M )
1 inf{ () : det( I M ) 0, Δ}
μ-synthesis Control Problem min ( M ) K
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Îź-synthesis Controller Design for Normal AMB Performance and Levitation Recovery For Basic AMB Performance
Performance Controller
For Levitation Recovery
Recovery Controller
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Experimental Test Rig Photograph
Configuration
Basic Information • • • • • • •
2 Radial AMBs 1 Thrust AMB 1 Disk DC Motor Flexible Motor Coupling Rolling Element TD Bearings 190 µm gap
• Experiments at 2000 RPM
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Drop Test and Simulation for TD Bearing Force Bounding
Orbit
Time Response
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Drop Test and Simulation for TD Bearing Force Bounding
Simulated TD Force Frequency Spectrum
TD Force Bound Transfer Function
WTD
1.382 104 s 5.052 104 s 2 3748 s 1.01 106
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AMB Controller Synthesis Parameters and Results Parametric Uncertainties Parameter 1st Natural Frequency* 2nd Natural Frequency* Current Stiffness Position Stiffness Running Speed
Type Complex Complex Real Real Real
Range ±3% ±5% ±5% ±20% ±100%
Performance Weights Signal Position Position TD Force
Weight WP1 WP2 WTD
Units
Cont.
0.03125 s 1.834 s 16.5
µm-1
Perf.
2.632 107 s 1.336 s 253.9
µm-1
Rec.
N
Rec.
1.382 104 s 5.052 104 s 2 3748 s 1.01 106
Bode Plot of μ-synthesized Controllers
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Fault Recovery Experiments Experiment • Speed = 2000 RPM • Power cut at 1 s • Power restored at 3 s • Switching scheme: • Recovery controller triggered at ±100 µm • Automatically switches back if inside ±100 µm
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Conclusions Summary A novel levitation recovery AMB control scheme has been proposed and experimentally demonstrated. The levitation recovery controller is designed with model based μ-synthesis considering TD bearing forces and corresponding deflections. Such a control scheme may lead to more widespread use of AMBs in industry. Future Work This method can be improved with a more rigorous TD bearing force bounding. The improved bounding can be from a sophisticated TD bearing model or experimental TD force data. 10
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