A Novel Piecewise Frequency Control Strategy Based on Fractional-Order Filter for Coordinating Vibration Isolation and Positioning of Supporting System
Abstract
:1. Introduction
2. Description of PFC Strategy for VIP
3. Effects of AVI and Positioning Controls
3.1. Effect of AVF on AVI
3.2. Effect of RPF on Positioning
3.3. Interaction of AVI and Positioning
4. Analysis and Optimization of PFC
4.1. PFC Based on IOFs
4.2. PFC Based on FOFs
- (1)
- Phase margin = PM ≥ 40°;
- (2)
- Gain margin = GM ≥ 15 dB;
- (3)
- Vibration transmissibility: max() ≤ 5 dB and the amplitude crossover frequency is close to 10 Hz;
- (4)
- Positioning transmissibility: max() ≤ −75 dB when the frequency is smaller than 2 Hz, otherwise max () ≤ −60 dB.
5. Experimental Verification
5.1. Experimental Setup
5.2. Experimental Results
5.3. Discussion
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Symbol | Property | Value |
---|---|---|
m1 | Mass of payload | 2 kg |
m2 | Mass of base | 2.2 kg |
k2 | Stiffness constant | 9.59 KN/m |
c2 | Damping coefficient | 20 Ns/m |
f | Inherent frequency | 10.5 Hz |
Ga | Voice coil motor (VCM) gain | 3.17 N/V |
Ge | Eddy-current sensor gain | 0.421 mm/V |
Cut-Off Frequency | Gain Margin and Phase Crossover Frequency | Phase Margin and Gain Crossover Frequency |
---|---|---|
flp = 10 Hz & fhp = 1.6 Hz | 15.5 dB @ 1.98 Hz | 34.2° @ 6.11 Hz |
flp = 15 Hz & fhp = 1.6 Hz | 15.6 dB @ 1.96 Hz | 40.3° @ 5.96 Hz |
flp = 29 Hz & fhp = 1.6 Hz (Traditional control) | 15.7 dB @ 1.95 Hz | 42.6° @ 5.74 Hz 125° @ 18.2 Hz 108° @ 29.5 Hz |
flp = 29 Hz & fhp = 3 Hz | 6.42 dB @ 4.33 Hz | 19.5° @ 6.1 Hz 141° @ 17.2 Hz 103° @ 28.2 Hz |
flp = 29 Hz & fhp = 4 Hz | 0.734 dB @ 6.21 Hz | 2.33° @ 6.41 Hz 156° @ 16.5 Hz 99.6° @ 27.2 Hz |
Cut-Off Frequency | AVI Performance | Positioning Performance |
---|---|---|
flp = 10 Hz & fhp = 1.6 Hz | Maximum value: 10.84 dB @ 7.03 Hz Cross-frequency: 9.57 Hz | Maximum value: −48.7 dB @ 7.22 Hz |
flp = 15 Hz & fhp = 1.6 Hz | Maximum value: 8.89 dB @ 7.52 Hz Cross-frequency: 10.16 Hz | Maximum value: −51.41 dB @ 7.52 Hz |
flp = 29 Hz & fhp = 1.6 Hz (Traditional control) | Maximum value: 3.93 dB @ 7.91 Hz Cross-frequency: 11.23 Hz | Maximum value: −58.37 dB @ 7.72 Hz |
flp = 29 Hz & fhp = 3 Hz | Maximum value: 8.98 dB @ 8.24 Hz Cross-frequency: 12.5 Hz | Maximum value: −55.36 dB @ 8.89 Hz |
flp = 29 Hz & fhp = 4 Hz | Maximum value: 10.06 dB @ 13.07 Hz Cross-frequency: 13.57 Hz | Maximum value: −52.15 dB @ 10.06 Hz |
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Tao, Y.; Jiang, W.; Han, B.; Li, X.; Luo, Y.; Zeng, L. A Novel Piecewise Frequency Control Strategy Based on Fractional-Order Filter for Coordinating Vibration Isolation and Positioning of Supporting System. Sensors 2020, 20, 5307. https://doi.org/10.3390/s20185307
Tao Y, Jiang W, Han B, Li X, Luo Y, Zeng L. A Novel Piecewise Frequency Control Strategy Based on Fractional-Order Filter for Coordinating Vibration Isolation and Positioning of Supporting System. Sensors. 2020; 20(18):5307. https://doi.org/10.3390/s20185307
Chicago/Turabian StyleTao, Yeying, Wei Jiang, Bin Han, Xiaoqing Li, Ying Luo, and Lizhan Zeng. 2020. "A Novel Piecewise Frequency Control Strategy Based on Fractional-Order Filter for Coordinating Vibration Isolation and Positioning of Supporting System" Sensors 20, no. 18: 5307. https://doi.org/10.3390/s20185307
APA StyleTao, Y., Jiang, W., Han, B., Li, X., Luo, Y., & Zeng, L. (2020). A Novel Piecewise Frequency Control Strategy Based on Fractional-Order Filter for Coordinating Vibration Isolation and Positioning of Supporting System. Sensors, 20(18), 5307. https://doi.org/10.3390/s20185307