Super Twisting Sliding Mode Control with Compensated Current Controller Dynamics on Active Magnetic Bearings with Large Air Gap
Abstract
:1. Introduction
2. Mathematical Modeling
2.1. Modelling of AMBs
2.2. Integrating the Current Controller Dynamics
- PI Controller: with the controller gain and the time constant tuned according to the modulus optimum criterion.
- H-bridge Voltage Amplifier: with the time constant where is the PWM frequency of the H-bride.
- Current Sensor: with its time constant , where is the sensors sampling frequency.
- Coil: with is resistance R, inductance L, gain and its electric time constant .
3. Controller Design
4. Results and Discussion
4.1. Test Bench Design
4.2. Experiment Current Controlled
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
reference displacement in x-direction | |
x | displacement in x-direction |
initial rotor displacement in x-direction | |
reference displacement in y-direction | |
y | displacement in y-direction |
initial rotor displacement in y-direction | |
control error | |
u | controller output |
i | current |
bias current | |
f | force |
permeability of vacuum | |
permeability of iron | |
n | number of windings in a coil |
cross-section area | |
angle between the legs of the AMB | |
length of the iron | |
s | magnetic air gap |
nominal magnetic air gap | |
magnetic flux | |
field energy | |
volume in the air gap | |
magnetic flux density in the air gap | |
magnetic field in the air gap | |
k | machine constant |
force/current factor | |
force/displacement factor | |
v | velocity |
m | mass of the rotor |
L | inductance |
R | resistance |
time constant | |
state vector | |
sliding variable | |
controller gain | |
c | controller gain |
b | controller gain |
* | control reference |
x | in x direction |
y | in x direction |
+ | in positive direction |
− | in negative direction |
R | state space description in controllability form |
Appendix B
Parameter | Symbol | Value | Unit |
---|---|---|---|
number of poles | 8 | - | |
angle between pole and axis | rad | ||
coil windings | n | 96 | - |
maximum voltage | 24 | V | |
maximum current | 5 | A | |
bias current | A | ||
sampling frequency position sensor | 2 | kHz | |
sampling frequency current sensor | 10 | kHz | |
PWM frequency | 20 | kHz | |
controller gain | C | - | |
sliding surface gains | S | - |
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Axis | Mean Error in % | Max Error in % | Max Error in mm | Settling Time in s |
---|---|---|---|---|
x | 0.9 | 21.18 | 0.21 | 0.7 |
y | 0.44 | 15.42 | 0.15 | 0.7 |
Axis | Mean Error in % | Max Error in % | Max Error in mm | Settling Time in s |
---|---|---|---|---|
x | 0.007 | 1.86 | 0.018 | 0.6 |
y | 0.03 | 1.86 | 0.018 | 0.6 |
Axis | Mean Error in % | Max Error in % | Max Error in mm | Settling Time in s |
---|---|---|---|---|
x | 0.14 | 12.32 | 0.12 | 0.6 |
y | 0.11 | 14.48 | 0.14 | 0.6 |
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Vennemann, J.; Brasse, R.; König, N.; Nienhaus, M.; Grasso, E. Super Twisting Sliding Mode Control with Compensated Current Controller Dynamics on Active Magnetic Bearings with Large Air Gap. Electronics 2023, 12, 950. https://doi.org/10.3390/electronics12040950
Vennemann J, Brasse R, König N, Nienhaus M, Grasso E. Super Twisting Sliding Mode Control with Compensated Current Controller Dynamics on Active Magnetic Bearings with Large Air Gap. Electronics. 2023; 12(4):950. https://doi.org/10.3390/electronics12040950
Chicago/Turabian StyleVennemann, Jonah, Romain Brasse, Niklas König, Matthias Nienhaus, and Emanuele Grasso. 2023. "Super Twisting Sliding Mode Control with Compensated Current Controller Dynamics on Active Magnetic Bearings with Large Air Gap" Electronics 12, no. 4: 950. https://doi.org/10.3390/electronics12040950
APA StyleVennemann, J., Brasse, R., König, N., Nienhaus, M., & Grasso, E. (2023). Super Twisting Sliding Mode Control with Compensated Current Controller Dynamics on Active Magnetic Bearings with Large Air Gap. Electronics, 12(4), 950. https://doi.org/10.3390/electronics12040950