{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:01:48Z","timestamp":1760144508748,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,4,12]],"date-time":"2024-04-12T00:00:00Z","timestamp":1712880000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents the design and the non-linearity optimization of a new vertical non-contact angle sensor based on the electromagnetic induction principle. The proposed sensor consists of a stator part (with one solenoidal excitation coil and three sinusoidal receiver coils) and a rotor part (with six rectangular metal sheets). The receiver coil was designed based on the differential principle, which eliminates the effect of the excitation coil on the induced voltage of the receiver coil, and essentially decouples the excitation field from the eddy current field. Moreover, the induced voltages in the three receiver coils are three-phase sinusoidal signals with a phase difference of 10\u00b0, which are linearized by CLARK transformation. To minimize the sensor non-linearity, the Plackett\u2013Burman technique was used, which identified the stator radius and the rotor blade thickness as the key factors affecting the sensor linearity. Then, the particle swarm algorithm with decreasing inertia weights was utilized to optimize the sensor linearity. A sensor prototype was made and tested in the laboratory, where the experimental results showed that the sensor non-linearity was only 0.648% and 0.645% in the clockwise and counterclockwise directions, respectively. Notably, the non-linearity of the sensor was less than \u22120.696% at different speeds.<\/jats:p>","DOI":"10.3390\/s24082469","type":"journal-article","created":{"date-parts":[[2024,4,12]],"date-time":"2024-04-12T03:34:37Z","timestamp":1712892877000},"page":"2469","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Design and Non-Linearity Optimization of a Vertical Brushless Electric Power Steering Angle Sensor"],"prefix":"10.3390","volume":"24","author":[{"given":"Jie","family":"Chen","sequence":"first","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanling","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/j.measurement.2019.03.064","article-title":"A review of micromachined sensors for automotive applications","volume":"140","author":"Mohankumar","year":"2019","journal-title":"Measurement"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Liu, Y. (2020, January 14\u201316). Design and implementation of the angle measurement system for position detecting of one launcher. Proceedings of the 2020 IEEE 2nd International Conference on Civil Aviation Safety and Information Technology (ICCASIT), Weihai, China.","DOI":"10.1109\/ICCASIT50869.2020.9368823"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1109\/TIM.2009.2024367","article-title":"Joint-Angle Measurement Using Accelerometers and Gyroscopes\u2014A Survey","volume":"59","author":"Cheng","year":"2010","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"7195","DOI":"10.1109\/JSEN.2020.3045461","article-title":"Technologies and Applications of Angle Sensors: A Review","volume":"21","author":"Kumar","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_5","unstructured":"Gasulla, M., Li, X., Meijer, G.C.M., van der Ham, L., and Spronck, J.W. (2002, January 12\u201314). A contactless capacitive angular-position sensor. Proceedings of the SENSORS 2002 IEEE, Orlando, FL, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1275","DOI":"10.1109\/TIM.2019.2908508","article-title":"A Noncontact Angle Sensor Based on Eddy Current Technique","volume":"69","author":"Kumar","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"108865","DOI":"10.1016\/j.vacuum.2019.108865","article-title":"Design and parameter optimization of contactless vertical inductive angle sensor","volume":"169","author":"Li","year":"2019","journal-title":"Vacuum"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Othman, A., Hamzah, N., Hussain, Z., and Baharudin, R. (2016, January 25\u201327). Design and development of an adjustable angle sensor based on rotary potentiometer for measuring finger flexion. Proceedings of the 2016 6th IEEE International Conference on Control System, Computing and Engineering (ICCSCE), Penang, Malaysia.","DOI":"10.1109\/ICCSCE.2016.7893640"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5728","DOI":"10.1109\/TIE.2017.2677308","article-title":"A Wide-Range Capacitive Sensor for Linear and Angular Displacement Measurement","volume":"64","author":"Anandan","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1109\/TIM.2016.2640458","article-title":"A Driver State Detection System\u2014Combining a Capacitive Hand Detection Sensor with Physiological Sensors","volume":"66","author":"Mosa","year":"2017","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"10253","DOI":"10.1109\/JSEN.2019.2929538","article-title":"Improved Capacitive Sensor for Combined Angular and Linear Displacement Sensing","volume":"19","author":"Kumar","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1109\/JSEN.2008.918717","article-title":"Integrated Optical Sensor in a Digital Microfluidic Platform","volume":"8","author":"Luan","year":"2008","journal-title":"IEEE Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1109\/JSEN.2017.2770176","article-title":"Fiber Bragg Grating Goniometer for Joint Angle Measurement","volume":"18","author":"Umesh","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2675","DOI":"10.1109\/JSEN.2018.2794822","article-title":"Design and Realization of an Optical Rotary Sensor","volume":"18","author":"Das","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.sna.2015.11.022","article-title":"Design and fabrication of an innovative three-axis Hall sensor","volume":"237","author":"Wouters","year":"2016","journal-title":"Sens. Actuat. A Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2419","DOI":"10.1109\/TIM.2019.2959294","article-title":"Design, Modeling, and Experimental Verification of a Hall-Effect-Based Linear Instrumentation System for through-shaft Angle Sensing","volume":"69","author":"Sontakke","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1109\/20.846218","article-title":"Circular displacement sensor using magnetostrictive amorphous wires","volume":"36","author":"Fosalau","year":"2000","journal-title":"IEEE Trans. Magn."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"GMoreton, Meydan, T., and Williams, P. (2016). A Novel Magnetostrictive Curvature Sensor Employing Flexible, Figure-of-Eight Sensing Coils. IEEE Trans. Magn., 52, 2500604.","DOI":"10.1109\/TMAG.2016.2520828"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.sna.2013.01.040","article-title":"A novel absolute angular position sensor based on electromagnetism","volume":"194","author":"Zhang","year":"2013","journal-title":"Sens. Actuat. A Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3702","DOI":"10.1109\/20.952694","article-title":"Electromagnetic finite element analysis for designing high frequency inductive position sensors","volume":"37","author":"Huang","year":"2001","journal-title":"IEEE Trans. Magn."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1109\/TIM.2014.2348631","article-title":"Analysis and Validation of a Planar High-Frequency Contactless Absolute Inductive Position Sensor","volume":"64","author":"Aschenbrenner","year":"2015","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"160878","DOI":"10.1109\/ACCESS.2021.3131344","article-title":"A Contactless Planar Inductive Sensor for Absolute Angular Displacement Measurement","volume":"9","author":"Gao","year":"2021","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3947","DOI":"10.1109\/JSEN.2015.2404349","article-title":"An Inductive Angular Displacement Sensor Based on Planar Coil and Contrate Rotor","volume":"15","author":"Tang","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"10217","DOI":"10.1109\/JSEN.2018.2874065","article-title":"A Flexible, Planar-Coil-Based Sensor for Through-Shaft Angle Sensing","volume":"18","author":"Anandan","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1109\/JSEN.2017.2780835","article-title":"Design and Development of a New Non-Contact Inductive Displacement Sensor","volume":"18","author":"Babu","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4111","DOI":"10.3390\/s140304111","article-title":"Nonlinearity analysis and parameters optimization for an inductive angle sensor","volume":"14","author":"Ye","year":"2014","journal-title":"Sensors"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1795","DOI":"10.1109\/TIM.2018.2810698","article-title":"Analysis of a Linearizing Direct Digitizer With Phase-Error Compensation for TMR Angular Position Sensor","volume":"67","author":"Bhaskarrao","year":"2018","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1631\/jzus.A0820564","article-title":"Parameters optimization and nonlinearity analysis of grating eddy current displacement sensor using neural network and genetic algorithm","volume":"10","author":"Qi","year":"2009","journal-title":"J. Zhejiang Univ.-Sci. A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.measurement.2013.11.017","article-title":"Optimization of inductive angle sensor using response surface methodology and finite element method","volume":"48","author":"Ye","year":"2014","journal-title":"Measurement"},{"key":"ref_30","first-page":"8372","article-title":"Subdivided Error Correction Method for Photoelectric Axis Angular Displacement Encoder Based on Particle Swarm Optimization","volume":"69","author":"Gao","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/8\/2469\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:26:46Z","timestamp":1760106406000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/8\/2469"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,12]]},"references-count":30,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["s24082469"],"URL":"https:\/\/doi.org\/10.3390\/s24082469","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2024,4,12]]}}}