Modelling and Stability Analysis for a Magnetically Levitated Slice Motor (MLSM) with Gyroscopic Effect and Non-Collocated Structure Based on the Extended Inverse Nyquist Stability Criterion
Abstract
:1. Introduction
2. Modelling of MLSM with Gyroscopic Effect and Non-Collocated Structure
2.1. Working Principle of the MLSM
2.2. Kinetics Analysis of the MLSM System Featured with Gyroscopic Effect
2.3. Description of the MLSM with Non-Collocated Structure
2.4. Analytical Model of the Controlled MLSM System with Gyroscopic Effect and Non-Collocated Structure
3. Extended Inverse Nyquist Stability Criterion in the Complex Domain
4. Stability Analysis on MLSM with Gyroscopic Effect and Non-Collocated Structure
- (1)
- When , the sufficient and necessary condition for the absolute stability is that the inverse Nyquist curve of the open-loop transfer function encloses counterclockwise once.
- (2)
- When , the sufficient and necessary condition for the absolute stability is that the inverse Nyquist curve of the open-loop transfer function encircles zero times.
5. Simulation and Experimental Results
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
MLSM | Magnetically levitated slice motor. |
MIMO | Multiple-input and multiple-output. |
SISO | Single-input and single-out. |
Suspension coils and driving coils. | |
Inclinations of rotor about x-, y-, and z-axes. | |
Spin velocity. | |
Mass of the rotor. | |
Moment of inertia of the rotor about Z-axis. | |
Moment of inertia of the rotor about X- and Y-axes. | |
Radial stiffness in x-and y-directions. | |
Tilting stiffness in x-and y-directions. | |
, | Total disturbance forces in -and -directions. |
Total disturbance moments in -and -directions. | |
Axial position of radial displacement sensors. | |
Equivalent application point of radial suspension force. | |
Center of gravity of rotor. | |
Distance of S with respect to N. | |
Distance of F with respect to N. | |
Parameters of the radial translational controllers. |
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Condition | Characteristic of the Inverse Nyquist Plot | |
---|---|---|
Symmetry about the imaginary axis | Turn clockwise from to with an infinite radius | |
Double root on the imaginary axis | Turn clockwise from to and clockwise at with an infinite radius, respectively | |
Two different roots on imaginary axis | Turn clockwise from to and clockwise at with an infinite radius, respectively |
Quantity | Value | Unit |
---|---|---|
Inner diameter of the rotor | 11 | mm |
Outer diameter of the rotor | 29 | mm |
Thickness of the rotor | 14 | mm |
Inner diameter of the stator | 36.5 | mm |
Outer diameter of the stator | 61.5 | mm |
Height of the stator | 54.26 | mm |
Phase of driving windings | 2 | // |
Poles of driving windings | 2 | // |
Phase of suspension windings | 2 | // |
Poles of suspension windings | 4 | // |
Parameter | Value | Parameter | Value |
---|---|---|---|
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Li, L.; Yu, Y.; Hu, L.; Ruan, X.; Su, R.; Fu, X. Modelling and Stability Analysis for a Magnetically Levitated Slice Motor (MLSM) with Gyroscopic Effect and Non-Collocated Structure Based on the Extended Inverse Nyquist Stability Criterion. Machines 2021, 9, 201. https://doi.org/10.3390/machines9090201
Li L, Yu Y, Hu L, Ruan X, Su R, Fu X. Modelling and Stability Analysis for a Magnetically Levitated Slice Motor (MLSM) with Gyroscopic Effect and Non-Collocated Structure Based on the Extended Inverse Nyquist Stability Criterion. Machines. 2021; 9(9):201. https://doi.org/10.3390/machines9090201
Chicago/Turabian StyleLi, Lingling, Yang Yu, Liang Hu, Xiaodong Ruan, Rui Su, and Xin Fu. 2021. "Modelling and Stability Analysis for a Magnetically Levitated Slice Motor (MLSM) with Gyroscopic Effect and Non-Collocated Structure Based on the Extended Inverse Nyquist Stability Criterion" Machines 9, no. 9: 201. https://doi.org/10.3390/machines9090201