{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T07:38:12Z","timestamp":1761896292246,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2016,6,14]],"date-time":"2016-06-14T00:00:00Z","timestamp":1465862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Chinese National Science Foundation","doi-asserted-by":"publisher","award":["51405097"],"award-info":[{"award-number":["51405097"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Scientific Research Innovation Foundation in Harbin Institute of Technology","award":["HIT.NSRIF.2015031"],"award-info":[{"award-number":["HIT.NSRIF.2015031"]}]},{"name":"The State Key Program of National Natural Science of China","award":["51537002"],"award-info":[{"award-number":["51537002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To determine the planar motion of a 6-DOF precision stage, a measurement system based on three Hall sensors is adopted to obtain the X, Y, Rz motions of the stage. The machining and assembly errors in the actual mechanical system, which are difficult to measure directly, cause the parameters in the model of the Hall measurement system to deviate from their designed values. Additionally, the vertical movement of the stage will render the measurement model nonlinear. To guarantee the accuracy of the measurement, the parameters in the measurement model should be estimated and the nonlinearity compensated. In this paper, a novel approach based on self-adaptive hybrid TLBO (teaching-learning-based-optimization) is proposed to estimate the parameters in the Hall measurement model. The influences of zero deviations and vertical movements on the measurement accuracy are analyzed and compensated. The effectiveness of the proposed method is validated by experimental results obtained on a 6-DOF precision stage. Thanks to parameter estimation and calibration, the measurement error of the Hall sensor array is reduced to 6 micrometers.<\/jats:p>","DOI":"10.3390\/s16060872","type":"journal-article","created":{"date-parts":[[2016,6,14]],"date-time":"2016-06-14T11:12:12Z","timestamp":1465902732000},"page":"872","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Calibration of the Hall Measurement System for a 6-DOF Precision Stage Using Self-Adaptive Hybrid TLBO"],"prefix":"10.3390","volume":"16","author":[{"given":"Zhenyu","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Control Science and Engineering, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Control Science and Engineering, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Ultra-Precision Optoelectronic Instrumentation Engineering Centre, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenxian","family":"Fu","sequence":"additional","affiliation":[{"name":"Department of Control Science and Engineering, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shenmin","family":"Song","sequence":"additional","affiliation":[{"name":"Department of Control Science and Engineering, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiubin","family":"Tan","sequence":"additional","affiliation":[{"name":"Ultra-Precision Optoelectronic Instrumentation Engineering Centre, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,6,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/s12206-012-1217-6","article-title":"Multi-degree-of-freedom motion error measurement in an ultraprecision machine using laser encoder\u2014Review","volume":"27","author":"Lee","year":"2013","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1007\/s00542-012-1470-8","article-title":"Multi-dofs MEMS displacement sensors based on the Stewart platform theory","volume":"18","author":"Mura","year":"2012","journal-title":"Microsyst. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1177\/0954406213482071","article-title":"Sensitivity analysis of a six degrees of freedom displacement measuring device","volume":"228","author":"Mura","year":"2014","journal-title":"J. Mech. Eng. Sci. Proc. Inst. Mech. Eng. Part C"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.ast.2014.11.012","article-title":"Real-time estimation of helicopter blade kinematics using integrated linear displacement sensors","volume":"42","author":"Allred","year":"2015","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S0141-6359(01)00105-2","article-title":"Design methods for six-degree-of-freedom displacement measurement systems using cooperative targets","volume":"26","author":"Kim","year":"2002","journal-title":"Precis. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1828","DOI":"10.1109\/TMAG.2005.846494","article-title":"2-D modeling and characteristic analysis of a magnetic position sensor","volume":"41","author":"Rhyu","year":"2005","journal-title":"IEEE Trans. Magn."},{"key":"ref_7","unstructured":"Schott, C., Racz, R., Betschart, F., and Popovic, R.S. (2002, January 12\u201314). A new two-axis magnetic position sensor. Proceedings of IEEE Sensors, Orlando, FL, USA."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Han, X.T., Cao, Q.L., and Wang, M. (2011, January 10\u201312). A linear Hall Effect displacement sensor using a stationary two-pair coil system. Proceedings of the IEEE International Instrumentation and Measurement Technology Conference, Hangzhou, China.","DOI":"10.1109\/IMTC.2011.5944143"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Manzin, A., and Nabaei, V. (2014). Modelling of micro-Hall sensors for magnetization imaging. J. Appl. Phys., 115.","DOI":"10.1063\/1.4862090"},{"key":"ref_10","first-page":"172606-1","article-title":"Magnetic scanning gate microscopy of graphene Hall devices","volume":"111","author":"Rajkumar","year":"2014","journal-title":"J. Appl. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2162","DOI":"10.3390\/s120202162","article-title":"A highly sensitive CMOS digital Hall Sensor for low magnetic field applications","volume":"12","author":"Xu","year":"2012","journal-title":"Sensors"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/s40684-014-0017-0","article-title":"2D Hall sensor array for measuring the position of a magnet matrix","volume":"1","author":"Hyeonh","year":"2014","journal-title":"Int. J. Precis. Eng. Manuf. Green Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4078","DOI":"10.1109\/TIE.2010.2098367","article-title":"An improved rotor position estimation with vector\u2014Tracking observer in PMSM drives with low-resolution Hall-effect sensors","volume":"58","author":"Kim","year":"2011","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"22530","DOI":"10.3390\/s150922530","article-title":"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","volume":"15","author":"Zhao","year":"2015","journal-title":"Sensors"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"980","DOI":"10.1115\/1.2363201","article-title":"Multi-degree-of-freedom precision position sensing and motion control using two-axis Hall-effect sensors","volume":"128","author":"Kawato","year":"2006","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"ref_16","unstructured":"Kawato, Y., and Kim, W.J. (2005, January 8\u201310). A novel multi-DOF precision positioning methodology using two-axis Hall-effect sensors. Proceedings of the American Control Conference, Portland, OR, USA."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1034","DOI":"10.4028\/www.scientific.net\/AMR.694-697.1034","article-title":"Study on fast and precise measurement of three-dimensional displacement using hall sensors","volume":"694\u2013697","author":"Sun","year":"2013","journal-title":"Adv. Mater. Res."},{"key":"ref_18","first-page":"485","article-title":"Inferential control of process","volume":"24","author":"Brosillow","year":"1978","journal-title":"AIChE J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/S0959-1524(01)00044-0","article-title":"Product property and production rate control of styrene polymerization","volume":"12","author":"Prasad","year":"2002","journal-title":"J. Process Control"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.jprocont.2004.04.006","article-title":"Optimal selection of soft sensor inputs for batch distillation columns using principal component analysis","volume":"15","author":"Zamprogna","year":"2005","journal-title":"J. Process Control"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.compchemeng.2008.05.019","article-title":"ANN-based soft-sensor for real-time process monitoring and control of an industrial polymerization process","volume":"33","author":"Gonzaga","year":"2009","journal-title":"Comput. Chem. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Liu, X.Q., Li, K., Mcafee, M., and Deng, J. (2010, January 15\u201317). \u2018Soft-sensor\u2019 for Real-time Monitoring of Melt Viscosity in Polymer Extrusion Process. Proceedings of the 49th IEEE Conference on IEEE Decision and Control (CDC), Atlanta, GA, USA.","DOI":"10.1109\/CDC.2010.5717800"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1049\/ip-cta:19960421","article-title":"Applilcation of a full-oirder extended Luenberger observer for a position sensorless operation of a switched reluctance motor drive","volume":"143","author":"Elmas","year":"1996","journal-title":"IEEE Proc. Control Theory Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TII.2014.2327912","article-title":"A Modified Fuzzy Luenberger Observer for a Two-Mass Drive System","volume":"11","author":"Szabat","year":"2015","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"600","DOI":"10.5370\/JEET.2014.9.2.600","article-title":"On-line Parameter Estimation of Interior Permanent Magnet Synchronous Motor using an Extended Kalman Filter","volume":"9","author":"Shirai","year":"2014","journal-title":"J. Electr. Eng. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Rajamani, R., and Hedrick, J.K. (1993, January 2\u20134). Adaptive Observer for Active Automotive Suspensions. Proceedings of the American Control Conference, San Francisco, CA, USA.","DOI":"10.23919\/ACC.1993.4792951"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2112","DOI":"10.1016\/j.ymssp.2006.09.005","article-title":"Parameter estimation and statistical analysis on frequency-dependent active control forces","volume":"21","author":"Lim","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Holland, J.H. (1992). Adaptation in Natural and Artificial Systems, MIT Press.","DOI":"10.7551\/mitpress\/1090.001.0001"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/TEVC.2010.2059031","article-title":"Differential Evolution: A Survey of the State-of-the-Art","volume":"15","author":"Das","year":"2011","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_30","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the IEEE International Conference on Neural Networks, Perth, WA, USA."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.cad.2010.12.015","article-title":"Teaching-Learning-Based Optimization: A novel method for constrained mechanical design optimization problems","volume":"43","author":"Rao","year":"2011","journal-title":"Comput.-Aided Des."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2011.08.006","article-title":"Teaching-Learning-Based Optimization: An optimization method for continuous non-linear large scale problems","volume":"183","author":"Rao","year":"2012","journal-title":"Inf. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.ins.2013.03.026","article-title":"Compact Particle Swarm Optimization","volume":"239","author":"Neri","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3837","DOI":"10.1016\/j.ijhydene.2013.12.110","article-title":"An improved TLBO with elite strategy for parameters identification of PEM fuel cell and solar cell models","volume":"39","author":"Niu","year":"2014","journal-title":"Int. J. Hydrog. Energy"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1577","DOI":"10.1016\/j.engappai.2012.07.004","article-title":"A new multi objective optimization approach based on TLBO for location of automatic voltage regulators in distribution systems","volume":"25","author":"Niknam","year":"2012","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.engappai.2014.12.001","article-title":"Solving optimal reactive power dispatch problem using a novel teaching-learning-based optimization algorithm","volume":"39","author":"Ghasemi","year":"2015","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_37","unstructured":"Chen, Y.M. (2014). A 3-DOF Precision Position Sensing Using Linear Hall Sensors. [Master\u2019s Thesis, Harbin Institute of Technology]."},{"key":"ref_38","unstructured":"Kennedy, J. (2003, January 24\u201326). Bare bones particle swarms. Swarm Intelligence Symposium. Proceedings of the IEEE Swarm Intelligence Symposium, Indianapolis, IN, USA."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.ejor.2008.02.035","article-title":"Bare bones differential evolution","volume":"196","author":"Omran","year":"2009","journal-title":"Eur. J. Oper. Res."},{"key":"ref_40","first-page":"1785","article-title":"Self-adaptive differential evolution algorithm for numerical optimization","volume":"2","author":"Qin","year":"2005","journal-title":"IEEE Congr. Evolut. Comput. Proc."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/6\/872\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:25:25Z","timestamp":1760210725000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/6\/872"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,14]]},"references-count":40,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2016,6]]}},"alternative-id":["s16060872"],"URL":"https:\/\/doi.org\/10.3390\/s16060872","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2016,6,14]]}}}