{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T17:55:31Z","timestamp":1775757331447,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,6,12]],"date-time":"2022-06-12T00:00:00Z","timestamp":1654992000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Major National Scientific Instrument and Equipment Development Project of China","award":["2017YFF0105304"],"award-info":[{"award-number":["2017YFF0105304"]}]},{"name":"Major National Scientific Instrument and Equipment Development Project of China","award":["20200401117GX"],"award-info":[{"award-number":["20200401117GX"]}]},{"name":"Key Research and Development Project of Science and Technology Development Plan of Jilin Provincial of China","award":["2017YFF0105304"],"award-info":[{"award-number":["2017YFF0105304"]}]},{"name":"Key Research and Development Project of Science and Technology Development Plan of Jilin Provincial of China","award":["20200401117GX"],"award-info":[{"award-number":["20200401117GX"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Photoelectric encoders are widely used in high-precision measurement fields such as industry and aerospace because of their high precision and reliability. In order to improve the subdivision accuracy of moir\u00e9 grating signals, a particle swarm optimization compensation model for grating the subdivision error of a photoelectric encoder based on parallel iteration is proposed. In the paper, an adaptive subdivision method of a particle swarm search domain based on the honeycomb structure is proposed, and a raster signal subdivision error compensation model based on the multi-swarm particle swarm optimization algorithm based on parallel iteration is established. The optimization algorithm can effectively improve the convergence speed and system accuracy of traditional particle swarm optimization. Finally, according to the subdivision error compensation algorithm, the subdivision error of the grating system caused by the sinusoidal error in the system is quickly corrected by taking advantage of the high-speed parallel processing of the FPGA pipeline architecture. The design experiment uses a 25-bit photoelectric encoder to verify the subdivision error algorithm. The experimental results show that the actual dynamic subdivision error can be reduced to \u00bd before compensation, and the static subdivision error can be reduced from 1.264\u2033 to 0.487\u2033 before detection.<\/jats:p>","DOI":"10.3390\/s22124456","type":"journal-article","created":{"date-parts":[[2022,6,13]],"date-time":"2022-06-13T02:01:44Z","timestamp":1655085704000},"page":"4456","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Research on Particle Swarm Compensation Method for Subdivision Error Optimization of Photoelectric Encoder Based on Parallel Iteration"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4659-8875","authenticated-orcid":false,"given":"Han","family":"Hou","sequence":"first","affiliation":[{"name":"Mechanical Engineering Faculty, Changchun University of Science and Technology, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guohua","family":"Cao","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Faculty, Changchun University of Science and Technology, Changchun 130022, China"},{"name":"Chongqing Research Institute, Changchun University of Science and Technology, No. 618 Liangjiang Avenue, Chongqing 401135, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongchang","family":"Ding","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Faculty, Changchun University of Science and Technology, Changchun 130022, China"},{"name":"Chongqing Research Institute, Changchun University of Science and Technology, No. 618 Liangjiang Avenue, Chongqing 401135, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kun","family":"Li","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Faculty, Changchun University of Science and Technology, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.3788\/OPE.20122002.0379","article-title":"Errors and precision analysis of subdivision signals for photoelectric angle encoder","volume":"20","author":"Wang","year":"2012","journal-title":"Opt. Precis. Eng."},{"key":"ref_2","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_3","doi-asserted-by":"crossref","first-page":"6586","DOI":"10.1109\/JSEN.2016.2588981","article-title":"Novel analog ratio-metric optical rotary encoder for avionic applications","volume":"16","author":"Tameh","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"967034","DOI":"10.1155\/2015\/967034","article-title":"Subdivision error analysis and compensation for photoelectric angle encoder in a telescope control system","volume":"2015","author":"Su","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1109\/TIE.2013.2247013","article-title":"Improved angular displacement estimation based on Hall-effect sensors for driving a brushless permanent-magnet motor","volume":"61","author":"Yang","year":"2014","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.sna.2016.05.026","article-title":"Study on array of photo-detector based absolute rotary encoder","volume":"246","author":"Das","year":"2016","journal-title":"Sens. Actuators A Phys."},{"key":"ref_7","first-page":"27","article-title":"An absolute rotary position sensor based on cylindrical coordinate color space transformation","volume":"213","author":"Stupar","year":"2015","journal-title":"Sens. Actuators A Phys."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wang, Y., Liu, Y., Yan, X., Chen, X., and Lv, H. (2011, January 6\u201318). Compensation of moire fringe sinusoidal deviation in photoelectrical encoder based on tunable filter. Proceedings of the 2011 Symposium on Photonics and Optoelectronics (SOPO), Wuhan, China.","DOI":"10.1109\/SOPO.2011.5780483"},{"key":"ref_9","first-page":"45","article-title":"Subdivision and direction judgment of grating Moire fringes","volume":"34","author":"Anguo","year":"2007","journal-title":"Opto Electron. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"379","DOI":"10.3788\/OPE.20122002.0379","article-title":"Analysis of the error and accuracy of the subdivision signal of the photoelectric shaft encoder","volume":"20","author":"Xianjun","year":"2012","journal-title":"Opt. Precis. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1117\/1.1523943","article-title":"High-performance absolute rotary encoder using muhitrack and M-code","volume":"42","author":"Matszoe","year":"2003","journal-title":"Opt. Eng."},{"key":"ref_12","first-page":"104","article-title":"A new optical encoder","volume":"11","author":"Luo","year":"2003","journal-title":"Opt. Precis. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"013609-1","DOI":"10.1117\/1.1829093","article-title":"Optimizing design of high-resolution optical encoder using a poin-source light-emitting diode with slits","volume":"44","author":"Matsuzoe","year":"2005","journal-title":"Opt. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.3788\/OPE.20192709.2053","article-title":"Measurement of spindle radial movement error with circular grating and autocollimator","volume":"27","author":"Zhifeng","year":"2019","journal-title":"Opt. Precis. Eng."},{"key":"ref_15","first-page":"605","article-title":"Subdivision error compensation method of small photoelectric encoder","volume":"25","author":"Ying","year":"2011","journal-title":"J. Electron. Meas. Instrum."},{"key":"ref_16","first-page":"124","article-title":"A new error compensation method in linear encoder using phase shifted grating","volume":"2740","author":"Song","year":"1999","journal-title":"SPIE"},{"key":"ref_17","first-page":"57","article-title":"Study on quadrature error real-time compensation for grating Moir\u00e9 signal","volume":"38","author":"Shuliang","year":"2017","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1284","DOI":"10.1049\/iet-cds.2019.0150","article-title":"Design of a precise subdivision system for gratings using a modified CORDIC algorithm","volume":"13","author":"Zhu","year":"2019","journal-title":"IET Circuits Devices Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"14820","DOI":"10.1109\/ACCESS.2020.2966004","article-title":"Research on Sinusoidal Error Compensation of Moir\u00e9 Signal Using Particle Swarm Optimization","volume":"8","author":"Zhu","year":"2020","journal-title":"IEEE Access"},{"key":"ref_20","first-page":"194","article-title":"Automatic compensation of sine deviation for grating fringe photoelectric signal","volume":"33","author":"Gao","year":"2013","journal-title":"J. Opt."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/12\/4456\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:28:32Z","timestamp":1760138912000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/12\/4456"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,12]]},"references-count":20,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["s22124456"],"URL":"https:\/\/doi.org\/10.3390\/s22124456","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,12]]}}}