Calibration of the Hall Measurement System for a 6-DOF Precision Stage Using Self-Adaptive Hybrid TLBO
<p>The configuration of the 6-DOF precision stage.</p> "> Figure 2
<p>The structure of the designed Hall sensor.</p> "> Figure 3
<p>Part of Hall sensor array.</p> "> Figure 4
<p>The layout of the capacitance sensors.</p> "> Figure 5
<p>The precision stage.</p> "> Figure 6
<p>The dimension figure of the investigated stage.</p> "> Figure 7
<p>The angular assembly errors of the Hall sensor array.</p> "> Figure 8
<p>The flow chart of the self-adaptive hybrid TLBO.</p> "> Figure 9
<p>The displacements of the stage measured by the interferometers in X, Y, Rz directions (<b>a</b>–<b>c</b>) and the outputs of the Hall sensors A, B, C (<b>d</b>–<b>f</b>).</p> "> Figure 10
<p>The output errors of the Hall sensor array with the designed parameters using Model (15) when the stage is on a different vertical level.</p> "> Figure 11
<p>The output errors in horizontal 3-DOFs with the optimized parameters using Model (30).</p> "> Figure 12
<p>The output errors in horizontal 3-DOFs with the optimized parameters using Model (31).</p> ">
Abstract
:1. Introduction
2. System Configuration
3. Model Establishment
3.1. The Decoupling Model of the Hall Sensor Array
3.2. The Calibration Model of the Hall Sensor Array
4. Self-Adaptive Hybrid TLBO Algorithm
4.1. Original TLBO
4.1.1. Teacher Phase
4.1.2. Learner Phase
4.2. Self-Adaptive Hybrid TLBO
5. Experiments and Analysis
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A
Setting | DOF | /μm | /μm | /μm |
---|---|---|---|---|
Z = 0 | Y | 0.87 | 0.52 | 0.26 |
Rx = 0 | X | 0.27 | −0.05 | 0.78 |
Ry = 0 | Rz | 0.63 | 0.29 | 2.31 |
Z = −250 μm | Y | 1.32 | 0.33 | 0.45 |
Rx = 0 | X | 0.89 | −0.24 | 0.93 |
Ry = 0 | Rz | 1.05 | 0.58 | 0.86 |
Z = +250 μm | Y | −0.93 | 1.60 | 1.92 |
Rx = 0 | X | −0.82 | 1.23 | 0.39 |
Ry = 0 | Rz | 0.99 | 1.11 | 1.17 |
Z = −150 μm | Y | −0.33 | 1.90 | 0.12 |
Rx = 0 | X | −1.10 | −0.95 | 1.18 |
Ry = 0 | Rz | 0.09 | 0.41 | −0.94 |
Z = +150μm | Y | 0.01 | 2.15 | 1.11 |
Rx = 0 | X | −0.48 | −0.15 | −1.10 |
Ry = 0 | Rz | 0.41 | 0.15 | 0.81 |
Z = −50 μm | Y | 2.77 | 1.99 | −2.80 |
Rx = 0 | X | 1.97 | 1.23 | −0.09 |
Ry = 0 | Rz | 1.79 | 1.37 | 1.51 |
Z = +50 μm | Y | −0.66 | 1.27 | 0.07 |
Rx = 0 | X | 0.53 | 0.40 | 0.17 |
Ry = 0 | Rz | 1.91 | 0.48 | −0.89 |
Z = 0 | Y | −0.99 | −0.44 | 0.11 |
Rx = −500 μrad | X | 0.39 | 0.10 | 0.23 |
Ry = 0 | Rz | 1.11 | 0.93 | −0.09 |
Z = 0 | Y | 1.28 | 1.23 | −0.57 |
Rx = +500 μrad | X | 1.09 | 1.05 | 0.09 |
Ry = 0 | Rz | 0.49 | 0.94 | −1.47 |
Z = 0 | Y | 0.31 | 0.81 | 3.11 |
Rx = −250 μrad | X | −1.17 | −0.54 | 2.38 |
Ry = 0 | Rz | 0.30 | 1.09 | −0.79 |
Z = 0 | Y | 0.15 | 0.63 | −0.42 |
Rx = +250 μrad | X | 1.52 | 1.69 | −0.01 |
Ry = 0 | Rz | 0.61 | −0.54 | 0.61 |
Z = 0 | Y | −0.07 | 1.84 | 0.03 |
Rx = −100 μrad | X | 0.38 | −0.17 | −1.48 |
Ry = 0 | Rz | 1.71 | 0.28 | 0.46 |
Z = 0 | Y | 0.74 | 0.84 | 0.17 |
Rx = +100 μrad | X | 0.01 | −0.04 | −1.16 |
Ry = 0 | Rz | −0.04 | 1.03 | 2.93 |
Z = 0 | Y | 0.99 | 0.72 | −4.22 |
Rx = 0 | X | 0.63 | −0.11 | 1.10 |
Ry = −500 μrad | Rz | 0.71 | 0.18 | 0.76 |
Z = 0 | Y | 0.39 | −0.22 | 0.42 |
Rx = 0 | X | 1.70 | 1.90 | −0.96 |
Ry = +500 μrad | Rz | 0.02 | 0.02 | 0.36 |
Z = 0 | Y | −0.40 | 1.51 | −0.36 |
Rx = 0 | X | −0.31 | −0.97 | −4.79 |
Ry = −250 μrad | Rz | −1.09 | 0.07 | 0.96 |
Z = 0 | Y | −0.79 | −0.16 | −1.61 |
Rx = 0 | X | 2.93 | 1.01 | −0.21 |
Ry = +250 μrad | Rz | −0.92 | −0.10 | 1.66 |
Z = 0 | Y | 1.74 | 1.83 | 0.18 |
Rx = 0 | X | 1.73 | 0.58 | 0.08 |
Ry = −100 μrad | Rz | −0.09 | 0.11 | 0.30 |
Z = 0 | Y | −0.71 | 0.24 | 1.09 |
Rx = 0 | X | 1.07 | 0.53 | 1.81 |
Ry = +100μrad | Rz | 0.74 | 2.18 | −0.82 |
References
- Lee, C.B.; Lee, S.K. Multi-degree-of-freedom motion error measurement in an ultraprecision machine using laser encoder—Review. J. Mech. Sci. Technol. 2013, 27, 141–152. [Google Scholar] [CrossRef]
- Mura, A. Multi-dofs MEMS displacement sensors based on the Stewart platform theory. Microsyst. Technol. 2012, 18, 575–579. [Google Scholar] [CrossRef]
- Mura, A. Sensitivity analysis of a six degrees of freedom displacement measuring device. J. Mech. Eng. Sci. Proc. Inst. Mech. Eng. Part C 2014, 228, 158–168. [Google Scholar] [CrossRef]
- Allred, C.J.; Jolly, M.R.; Buckner, G.D. Real-time estimation of helicopter blade kinematics using integrated linear displacement sensors. Aerosp. Sci. Technol. 2015, 42, 274–286. [Google Scholar] [CrossRef]
- Kim, J.A.; Bae, E.W.; Kim, S.H.; Kwak, Y.K. Design methods for six-degree-of-freedom displacement measurement systems using cooperative targets. Precis. Eng. 2002, 26, 99–104. [Google Scholar] [CrossRef]
- Rhyu, S.H.; Jung, I.S.; Kwon, B.I. 2-D modeling and characteristic analysis of a magnetic position sensor. IEEE Trans. Magn. 2005, 41, 1828–1831. [Google Scholar] [CrossRef]
- Schott, C.; Racz, R.; Betschart, F.; Popovic, R.S. A new two-axis magnetic position sensor. In Proceedings of IEEE Sensors, Orlando, FL, USA, 12–14 June 2002; pp. 911–915.
- Han, X.T.; Cao, Q.L.; Wang, M. A linear Hall Effect displacement sensor using a stationary two-pair coil system. In Proceedings of the IEEE International Instrumentation and Measurement Technology Conference, Hangzhou, China, 10–12 May 2011; pp. 1342–1345.
- Manzin, A.; Nabaei, V. Modelling of micro-Hall sensors for magnetization imaging. J. Appl. Phys. 2014, 115. [Google Scholar] [CrossRef]
- Rajkumar, R.K.; Asenjo, A.; Panchal, V.; Manzin, A.; Iglesias-Freire, Ó.; Kazakova, O. Magnetic scanning gate microscopy of graphene Hall devices. J. Appl. Phys. 2014, 111, 172606-1–172606-6. [Google Scholar] [CrossRef]
- Xu, Y.; Pan, H.B.; He, S.Z.; Li, L. A highly sensitive CMOS digital Hall Sensor for low magnetic field applications. Sensors 2012, 12, 2162–2174. [Google Scholar] [CrossRef] [PubMed]
- Hyeonh, J.A.; Kyoung, R.K. 2D Hall sensor array for measuring the position of a magnet matrix. Int. J. Precis. Eng. Manuf. Green Technol. 2014, 1, 125–129. [Google Scholar]
- Kim, S.Y.; Choi, C.; Lee, K.; Lee, W. An improved rotor position estimation with vector—Tracking observer in PMSM drives with low-resolution Hall-effect sensors. IEEE Trans. Ind. Electron. 2011, 58, 4078–4086. [Google Scholar]
- Zhao, B.; Wang, L.; Tan, J.B. Design and Realization of a Three Degrees of Freedom Displacement Measurement System Composed of Hall Sensors Based on Magnetic Field Fitting by an Elliptic Function. Sensors 2015, 15, 22530–22546. [Google Scholar] [CrossRef] [PubMed]
- Kawato, Y.; Kim, W.J. Multi-degree-of-freedom precision position sensing and motion control using two-axis Hall-effect sensors. J. Dyn. Syst. Meas. Control 2006, 128, 980–988. [Google Scholar] [CrossRef]
- Kawato, Y.; Kim, W.J. A novel multi-DOF precision positioning methodology using two-axis Hall-effect sensors. In Proceedings of the American Control Conference, Portland, OR, USA, 8–10 June 2005.
- Sun, Y.T.; Hu, J.C.; Zhu, Y.; Chen, L.M. Study on fast and precise measurement of three-dimensional displacement using hall sensors. Adv. Mater. Res. 2013, 694–697, 1034–1038. [Google Scholar] [CrossRef]
- Brosillow, C. Inferential control of process. AIChE J. 1978, 24, 485–509. [Google Scholar]
- Prasad, V.; Schley, M.; Russo, L.P.; Bequetta, W. Product property and production rate control of styrene polymerization. J. Process Control 2002, 12, 353–372. [Google Scholar] [CrossRef]
- Zamprogna, E.; Barolo, M.; Seborg, D.E. Optimal selection of soft sensor inputs for batch distillation columns using principal component analysis. J. Process Control 2005, 15, 39–52. [Google Scholar] [CrossRef]
- Gonzaga, J.C.B.; Meleiro, L.A.C.; Kiang, C.; Filho, R.M. ANN-based soft-sensor for real-time process monitoring and control of an industrial polymerization process. Comput. Chem. Eng. 2009, 33, 43–49. [Google Scholar] [CrossRef]
- Liu, X.Q.; Li, K.; Mcafee, M.; Deng, J. ‘Soft-sensor’ for Real-time Monitoring of Melt Viscosity in Polymer Extrusion Process. In Proceedings of the 49th IEEE Conference on IEEE Decision and Control (CDC), Atlanta, GA, USA, 15–17 December 2010.
- Elmas, C.; Zelaya-De, L.P.H. Applilcation of a full-oirder extended Luenberger observer for a position sensorless operation of a switched reluctance motor drive. IEEE Proc. Control Theory Appl. 1996, 143, 401–408. [Google Scholar] [CrossRef]
- Szabat, K.; Tran-Van, T.; Kaminski, M. A Modified Fuzzy Luenberger Observer for a Two-Mass Drive System. IEEE Trans. Ind. Inform. 2015, 11, 531–539. [Google Scholar] [CrossRef]
- Shirai, H.; Kageyama, Y.; Ohuchi, A.; Takaya, T.; Nishida, M. On-line Parameter Estimation of Interior Permanent Magnet Synchronous Motor using an Extended Kalman Filter. J. Electr. Eng. Technol. 2014, 9, 600–608. [Google Scholar]
- Rajamani, R.; Hedrick, J.K. Adaptive Observer for Active Automotive Suspensions. In Proceedings of the American Control Conference, San Francisco, CA, USA, 2–4 June 1993; pp. 706–710.
- Lim, T.M.; Cheng, S. Parameter estimation and statistical analysis on frequency-dependent active control forces. Mech. Syst. Signal Process. 2007, 21, 2112–2124. [Google Scholar] [CrossRef]
- Holland, J.H. Adaptation in Natural and Artificial Systems; MIT Press: Cambridge, MA, USA, 1992. [Google Scholar]
- Das, S.; Suganthan, P.N. Differential Evolution: A Survey of the State-of-the-Art. IEEE Trans. Evolut. Comput. 2011, 15, 4–31. [Google Scholar] [CrossRef]
- Kennedy, J.; Eberhart, R. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks, Perth, WA, USA, 27 Novemebr–1 December 1995; pp. 1942–1948.
- Rao, R.V.; Savsani, V.J.; Vakharia, D.P. Teaching-Learning-Based Optimization: A novel method for constrained mechanical design optimization problems. Comput.-Aided Des. 2011, 43, 303–315. [Google Scholar] [CrossRef]
- Rao, R.V.; Savsani, V.J.; Vakharia, D.P. Teaching-Learning-Based Optimization: An optimization method for continuous non-linear large scale problems. Inf. Sci. 2012, 183, 1–15. [Google Scholar] [CrossRef]
- Neri, F.; Mininno, E.; Iacca, G. Compact Particle Swarm Optimization. Inf. Sci. 2013, 239, 96–121. [Google Scholar] [CrossRef]
- Niu, Q.; Zhang, H.Y.; Li, K. An improved TLBO with elite strategy for parameters identification of PEM fuel cell and solar cell models. Int. J. Hydrog. Energy 2014, 39, 3837–3857. [Google Scholar] [CrossRef]
- Niknam, T.; Azizipanah-Abarghooee, R.; Narimani, M.R. A new multi objective optimization approach based on TLBO for location of automatic voltage regulators in distribution systems. Eng. Appl. Artif. Intell. 2012, 25, 1577–1588. [Google Scholar] [CrossRef]
- Ghasemi, M.; Taghizadeh, M.; Ghavidel, S.; Aghaei, J.; Abbasian, A. Solving optimal reactive power dispatch problem using a novel teaching-learning-based optimization algorithm. Eng. Appl. Artif. Intell. 2015, 39, 100–108. [Google Scholar] [CrossRef]
- Chen, Y.M. A 3-DOF Precision Position Sensing Using Linear Hall Sensors. Master’s Thesis, Harbin Institute of Technology, Harbin, China, June 2014. [Google Scholar]
- Kennedy, J. Bare bones particle swarms. Swarm Intelligence Symposium. In Proceedings of the IEEE Swarm Intelligence Symposium, Indianapolis, IN, USA, 24–26 April 2003; pp. 80–87.
- Omran, M.G.H.; Engelbrecht, A.P.; Salman, A. Bare bones differential evolution. Eur. J. Oper. Res. 2009, 196, 128–139. [Google Scholar] [CrossRef]
- Qin, A.K.; Suganthan, P.N. Self-adaptive differential evolution algorithm for numerical optimization. IEEE Congr. Evolut. Comput. Proc. 2005, 2, 1785–1791. [Google Scholar]
Parameter | ||||||
Value | 0.1975 m | 0.1975 m | 0.36 m | 0.1975 m | 0.4 m | 0.42 m |
Parameter | ||||||
Value | 1 | 1 | 1 | 0° | 0° | 0° |
DOF | X | Y | Rz |
---|---|---|---|
RMSE | 27.8795 μm | 44.1243 μm | 89.2927 μrad |
Peak error | 61.2092 μm | 119.9458 μm | 221.5275 μrad |
Parameter | ||||||
Lower range | 0.1475 m | 0.1475 m | 0.26 m | 0.1475 m | 0.3 m | 0.32 m |
Upper range | 0.2475 m | 0.2475 m | 0.46 m | 0.2475 m | 0.5 m | 0.52 m |
Parameter | ||||||
Lower range | 0.78 | 0.65 | 0.72 | −8° | −8° | −8° |
Upper range | 0.98 | 0.85 | 0.92 | 8° | 8° | 8° |
DOF | X | Y | Rz |
---|---|---|---|
RMSE | 2.1896 μm | 4.2560 μm | 2.9176 μrad |
Peak error | 10.6451 μm | 19.2473 μm | 15.0316 μrad |
Parameter | |||||
Lower range | −5000 | −5000 | 0 | −5000 | −5000 |
Upper range | 0 | 0 | 5000 | 0 | 0 |
Parameter | |||||
Lower range | −5000 | −5000 | −5000 | 0 | |
Upper range | 0 | 0 | 0 | 5000 |
DOF | Z/μm | Rx/μrad | Ry/μrad | |
---|---|---|---|---|
NO. | ||||
1 | 0 | 0 | 0 | |
2 | 250 | 0 | 0 | |
3 | −250 | 0 | 0 | |
4 | 150 | 0 | 0 | |
5 | −150 | 0 | 0 | |
6 | 50 | 0 | 0 | |
7 | −50 | 0 | 0 | |
8 | 0 | 500 | 0 | |
9 | 0 | −500 | 0 | |
10 | 0 | 250 | 0 | |
11 | 0 | −250 | 0 | |
12 | 0 | 100 | 0 | |
13 | 0 | −100 | 0 | |
14 | 0 | 0 | 500 | |
15 | 0 | 0 | −500 | |
16 | 0 | 0 | 250 | |
17 | 0 | 0 | −250 | |
18 | 0 | 0 | 100 | |
19 | 0 | 0 | −100 |
Parameter | ||||||
Value | 0.1944 m | 0.2173 m | 0.3293m | 0.1979 m | 0.3381 m | 0.3555 m |
Parameter | ||||||
Value | −188.1873 | −69.7432 | 14.8664 | 0.8671 | ||
Parameter | ||||||
Value | −156.5783 | −56.7511 | −55.0764 | 0.7049 | ||
Parameter | ||||||
Value | −178.1902 | −63.4133 | 12.7241 | 0.8632 | ||
Parameter | ||||||
Value | 0.0145° | 0.4143° | −0.0561° |
DOF | X | Y | Rz |
---|---|---|---|
RMSE | 1.3919 μm | 1.5381 μm | 2.3057 μrad |
Peak error | 6.6368 μm | 5.9375 μm | 9.6300 μrad |
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Chen, Z.; Liu, Y.; Fu, Z.; Song, S.; Tan, J. Calibration of the Hall Measurement System for a 6-DOF Precision Stage Using Self-Adaptive Hybrid TLBO. Sensors 2016, 16, 872. https://doi.org/10.3390/s16060872
Chen Z, Liu Y, Fu Z, Song S, Tan J. Calibration of the Hall Measurement System for a 6-DOF Precision Stage Using Self-Adaptive Hybrid TLBO. Sensors. 2016; 16(6):872. https://doi.org/10.3390/s16060872
Chicago/Turabian StyleChen, Zhenyu, Yang Liu, Zhenxian Fu, Shenmin Song, and Jiubin Tan. 2016. "Calibration of the Hall Measurement System for a 6-DOF Precision Stage Using Self-Adaptive Hybrid TLBO" Sensors 16, no. 6: 872. https://doi.org/10.3390/s16060872