Complementary Cooperation of Dual Power Circuits to Drive Active Magnetic Bearings
Abstract
:1. Introduction
2. Design of Dual Cooperative Drive Circuit (DC2)
2.1. Digital Drive Mode (DDM)
2.2. Analog Drive Mode (ADM)
3. Pulse Width Modulation-Tuning Processors (PWM-TPs)
- Step 1
- Based on the step-wise reference shown in Section 4, the gain, , with respect to proportional action at PI controller is tuned from zero to infinity.
- Step 2
- As is tuned from zero to , the steady-state errors are all decreased gradually. By contrast, as is tuned from to infinity, the corresponding steady-state errors are all increased gradually.
- Step 3
- It is concluded that is the gain finally chosen.
- Step 4
- Secondly, the gain, , with respect to the integral action at PI controller is tuned from zero to infinity.
- Step 5
- It is observed that the steady-state errors are altered from negative values to positive values as from zero to infinity while is fixed. Therefore, is chosen since the corresponding steady-state errors are approximated to zero.
- Step 1
- Based on the step-wise reference shown in Section 4, the gain, , with respect to proportional action at PI controller is tuned from zero to infinity.
- Step 2
- As is tuned from zero to , the steady-state errors are all decreased gradually. By contrast, as is tuned from to infinity, the corresponding steady-state errors are all increased gradually.
- Step 3
- Different from the DDM, as , the tracking errors of output current would be more than the threshold such that ADM is cut off and then switched to DDM. In this case, we finally choose to prevent any potential switch to DDM.
- Step 4
- Secondly, the gain, , with respect to the integral action at PI controller is tuned from zero to infinity.
- Step 5
- It is observed that the steady-state errors are altered from negative values to positive values as from zero to infinity while is fixed. Therefore, is chosen since the corresponding steady-state errors are approximated to zero.
3.1. PWM-TP for DDM
3.2. PWM-TP for ADM
4. Simulations
5. Experiments
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
List of Abbreviations
ADM | Analog Driving Mode |
AMB | Active Magnetic Bearing |
CS | Current Sensor |
DAC | Digital to Analog Converter |
DC | Direct Current |
DC2 | Dual Cooperative Drive Circuit |
DDM | Digital Driving Mode |
DSP | Digital Signal Processor |
EMI | Electromagnetic Interference |
Imp. | Improvement |
IC | Integrated Circuit |
LPF | Low Pass Filter |
MUX | Multiplexer |
MOSFET | Metal-Oxide-Semiconductor Field-Effect Transistor |
OP | Observation Point |
PA | Power Amplifier |
PD | Power Dissipation |
PI | Proportional–Integral |
PID | Proportional–Integral–Derivative |
PPACR | Peak-to-Peak Amplitude of Current Ripple |
PWM | Pulse Width Modulation |
PWM-TP | Pulse Width Modulation-Tuning Processor |
SLH | Switch-Linear Hybrid |
TE | Tracking Error |
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Parameters | Value |
---|---|
Solver Type | Variable-step |
Numerical Method | ode23t |
Supply Voltage to AMB | 40 VDC |
PWM Switching Frequency | 22 kHz |
Threshold to Switch Operation Mode | 0.03 V |
Threshold of Multiplexer | 3.005 V |
Gate-source threshold voltage of MOSFET | 3 V |
Drain-source on Resistance of MOSFET | 0.028 |
Channel Modulation of MOSFET | 0.01 |
Gate-source voltage for R_DS (on) | 10 V |
Drain current for R_DS (on) | 75 A |
Transresistance of Current Sensor | 1 |
P Gain of PWM-TP under DDM | 300 |
I Gain of PWM-TP under DDM | 1000 |
P Gain of PWM-TP under ADM | 90 |
I Gain of PWM-TP under ADM | 300 |
Resistance of AMB coil | 0.9 |
Inductance of AMB coil | 13 mH |
A: Amplitude of | Two-State PA (DDM) | Three-State PA | DC2 | |||
---|---|---|---|---|---|---|
B: TE (mA) | C: Error C = B/A (%) | D: TE (mA) | E: Error E = D/A (%) | F: TE (mA) | G: Error G = F/A (%) | |
0.01 | 13.36 | 133.600 | 5.49 | 54.900 | 1.46 | 14.600 |
0.30 | 6.78 | 2.260 | 5.43 | 1.810 | 0.87 | 0.290 |
0.50 | 3.77 | 0.754 | 2.36 | 0.472 | 0.56 | 0.112 |
0.80 | 1.72 | 0.215 | 5.36 | 0.670 | 0.11 | 0.014 |
1.00 | 0.30 | 0.030 | 1.41 | 0.140 | 0.79 | 0.079 |
1.50 | 5.21 | 0.347 | 3.29 | 0.219 | 1.86 | 0.124 |
Amplitude of | Two-State PA (DDM) | Three-State PA | DC2 | ||
---|---|---|---|---|---|
A: PPACR (mA) | D: PPACR (mA) | E: Imp. E = (A − D)/A | F: PPACR (mA) | F: Imp. F = (A − F)/A | |
0.01 | 31.4 | 2.4 | 92.36% | 1.7 | 94.59% |
0.30 | 30.5 | 4.6 | 84.92% | 3.4 | 88.85% |
0.50 | 30.0 | 5.5 | 81.67% | 4.2 | 86.00% |
0.80 | 29.3 | 5.8 | 80.20% | 5.2 | 82.25% |
1.00 | 28.9 | 6.3 | 78.20% | 5.8 | 79.93% |
1.50 | 27.7 | 7.5 | 72.92% | 7.2 | 74.01% |
Amplitude of | Two-State PA (DDM) | Three-State PA | DC2 | ||
---|---|---|---|---|---|
A: PD (mW) | B: PD (mW) | C: Imp. C = (A − B)/A | D: PD (mW) | E: Imp. E = (A − D)/A | |
0.01 | 0.02 | <0.01 | 95.59% | <0.01 | 96.80% |
0.30 | 3.93 | 0.50 | 87.28% | 0.84 | 78.63% |
0.50 | 10.99 | 1.68 | 84.71% | 2.65 | 75.89% |
0.80 | 28.42 | 6.09 | 78.57% | 8.15 | 71.32% |
1.00 | 44.69 | 11.20 | 74.94% | 14.08 | 68.49% |
1.50 | 102.06 | 32.76 | 69.90% | 39.69 | 61.11% |
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Chiu, H.-L.; Tsai, N.-C. Complementary Cooperation of Dual Power Circuits to Drive Active Magnetic Bearings. Appl. Sci. 2018, 8, 1270. https://doi.org/10.3390/app8081270
Chiu H-L, Tsai N-C. Complementary Cooperation of Dual Power Circuits to Drive Active Magnetic Bearings. Applied Sciences. 2018; 8(8):1270. https://doi.org/10.3390/app8081270
Chicago/Turabian StyleChiu, Hsin-Lin, and Nan-Chyuan Tsai. 2018. "Complementary Cooperation of Dual Power Circuits to Drive Active Magnetic Bearings" Applied Sciences 8, no. 8: 1270. https://doi.org/10.3390/app8081270