{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T09:22:31Z","timestamp":1775467351293,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,9,27]],"date-time":"2018-09-27T00:00:00Z","timestamp":1538006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["P2-0028"],"award-info":[{"award-number":["P2-0028"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Velocity measurement by an incremental encoder is an important issue for advanced motion control applications such as robotics. In this paper, we deal with a kind of MT-type velocity estimation method. Though the conventional MT method is well known and has been well proven in practice, it requires execution of an arithmetic division operation that prevents an efficient implementation on low-cost FPGA-based control platforms. Thus, we propose a divisionless MT-type algorithm, which can provide a similar performance in velocity estimation accuracy as the conventional method, but requiring significantly less FPGA resources, since it implements only simple arithmetic operations such as addition, subtraction, and multiplication, that can be implemented more easily on the processing hardware. Furthermore, the algorithm is fast in execution, thus, it provides the output in only a few clock cycles. Though the proposed algorithm can be described in a recursive form, the stability of the estimation process is not jeopardized, although it is an important issue in this case. Hence, the algorithm is introduced in a form which assures stability in a wide speed range. We show the implementation of the algorithm on the experimental FPGA platform. The experimental results validated the proposed divisionless MT-type algorithm fully for accurate velocity estimation.<\/jats:p>","DOI":"10.3390\/s18103250","type":"journal-article","created":{"date-parts":[[2018,9,28]],"date-time":"2018-09-28T02:54:54Z","timestamp":1538103294000},"page":"3250","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Accurate FPGA-Based Velocity Measurement with an Incremental Encoder by a Fast Generalized Divisionless MT-Type Algorithm"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4802-168X","authenticated-orcid":false,"given":"Ale\u0161","family":"Hace","sequence":"first","affiliation":[{"name":"Institute of Robotics, Faculty of Electrical Engineering and Computer Science, University of Maribor, Koro\u0161ka cesta 46, SI-2000 Maribor, Slovenia"}]},{"given":"Milan","family":"\u010curkovi\u010d","sequence":"additional","affiliation":[{"name":"Institute of Robotics, Faculty of Electrical Engineering and Computer Science, University of Maribor, Koro\u0161ka cesta 46, SI-2000 Maribor, Slovenia"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1109\/3516.491410","article-title":"Motion Control for Advanced Mechatronics","volume":"1","author":"Ohnishi","year":"1996","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1109\/TIE.2008.2003208","article-title":"A Wide-Range Velocity Measurement Method for Motion Control","volume":"56","author":"Tsuji","year":"2009","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1162","DOI":"10.1109\/TRO.2013.2265631","article-title":"Precision Control of Modular Robot Manipulators: The VDC Approach With Embedded FPGA","volume":"29","author":"Zhu","year":"2013","journal-title":"IEEE Trans. Robot."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1109\/TMECH.2018.2805863","article-title":"Evaluation of Velocity Estimation Methods Based on Their Effect on Haptic Device Performance","volume":"23","author":"Chawda","year":"2018","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Kennel, R.M. (2006, January 8\u201312). Why Do Incremental Encoders Do a Reasonably Good Job in Electrical Drives with Digital Control?. Proceedings of the Conference Record of the 2006 IEEE Industry Applications Conference Forty-First IAS Annual Meeting, Tampa, FL, USA.","DOI":"10.1109\/IAS.2006.256635"},{"key":"ref_6","unstructured":"Kennel, R.M. (2005, January 2\u20136). Encoders for simultaneous sensing of position and speed in electrical drives with digital control. Proceedings of the Conference Record of the 2005 Industry Applications Conference Fourtieth IAS Annual Meeting, Kowloon, Hong Kong, China."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1109\/TMECH.2013.2241778","article-title":"Pseudo-Sensorless High-Performance Bilateral Teleoperation by Sliding-Mode Control and FPGA","volume":"19","author":"Hace","year":"2014","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1109\/19.948308","article-title":"Performance Analysis and Compensation of M\/T-Type Digital Tachometers","volume":"50","author":"Kavanagh","year":"2001","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Petrella, R., Tursini, M., Peretti, L., and Zigliotto, M. (2007, January 10\u201312). Speed Measurement Algorithms for Low-Resolution Incremental Encoder Equipped Drives: A Comparative Analysis. Proceedings of the 2007 International Aegean Conference on Electrical Machines and Power Electronics, Bodrum, Turkey.","DOI":"10.1109\/ACEMP.2007.4510607"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1109\/TIE.1982.356665","article-title":"A Microprocessor-Controlled High-Accuracy Wide-Range Speed Regulator for Motor Drives","volume":"IE-29","author":"Ohmae","year":"1982","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1109\/41.315274","article-title":"Extremely Wide-Range Speed Measurement Using a Double-Buffered Method","volume":"41","author":"Prokin","year":"1994","journal-title":"IEEE Trans. Ind. Elecron."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1191\/0142331204tm114oa","article-title":"An Enhanced Constant Sample-Time Digital Tachometer Through Oversampling","volume":"26","author":"Kavanagh","year":"2004","journal-title":"Trans. Inst. Meas. Control."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Pu, J.-T., and Wang, H. (2012, January 7\u201312). A Novel Variable M\/T Method for Speed Measurement with High Precision. Proceedings of the 2nd International Conference on Electronic & Mechanical Engineering and Information Technology (EMEIT-2012), Liaoning, China.","DOI":"10.2991\/emeit.2012.411"},{"key":"ref_14","unstructured":"Hachiya, K., and Ohmae, T. (2007, January 2\u20135). Digital Speed Control System for a Motor Using Two Speed Detection Methods of an Incremental Encoder. Proceedings of the 2007 European Conference on Power Electronics and Applications, Aalborg, Denmark."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1016\/j.micpro.2009.09.001","article-title":"A New Method for Digital Encoder Adaptive Velocity\/Acceleration Evaluation Using a TDC with Picosecond Accuracy","volume":"33","author":"Lygouras","year":"2009","journal-title":"Microprocess. Microsyst."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Chen, Y., Yang, M., Long, J., Xu, D., and Blaabjerg, F. (November, January 29). M\/T Method Based Incremental Encoder Velocity Measurement Error Analysis and Self-Adaptive Error Elimination Algorithm. Proceedings of the IECON 2017\u201443rd Annual Conference of the IEEE Industrial Electronics Society, Beijing, China.","DOI":"10.1109\/IECON.2017.8216350"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.mechatronics.2009.06.010","article-title":"Velocity and Acceleration Estimation for Optical Incremental Encoders","volume":"20","author":"Merry","year":"2010","journal-title":"Mechatronics"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zhu, W.-H. (2010, January 4\u20137). FPGA-Based Velocity Estimation for Control of Harmonic Drives. Proceedings of the 2010 IEEE International Conference on Mechatronics and Automation, Xi\u2019an, China.","DOI":"10.1109\/ICMA.2010.5589767"},{"key":"ref_19","unstructured":"Koren, I. (2002). Computer Arithmetic Algorithms, A K Peters, Ltd.. [2nd ed.]."},{"key":"ref_20","unstructured":"Hahn, T., Humphreys, J., Fritsch, A., and Greenstreet, D. (2018, July 26). Demystifying Digital Signal Processing (DSP) Programming: The Ease in Realizing Implementations with TI DSPs. Available online: http:\/\/www.ti.com\/lit\/wp\/spry281\/spry281.pdf."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1109\/TII.2011.2123908","article-title":"FPGAs in Industrial Control Applications","volume":"7","author":"Monmasson","year":"2011","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1109\/TII.2015.2431223","article-title":"Advanced Features and Industrial Applications of FPGAs\u2014A Review","volume":"11","author":"Moure","year":"2015","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"7263","DOI":"10.3390\/s100807263","article-title":"A Field Programmable Gate Array-Based Reconfigurable Smart-Sensor Network for Wireless Monitoring of New Generation Computer Numerically Controlled Machines","volume":"10","author":"Stiharu","year":"2010","journal-title":"Sensors"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"12235","DOI":"10.3390\/s120912235","article-title":"Sensor Systems Based on FPGAs and Their Applications: A Survey","volume":"12","author":"Braeken","year":"2012","journal-title":"Sensors"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"6247","DOI":"10.3390\/s140406247","article-title":"A Survey on FPGA-Based Sensor Systems: Towards Intelligent and Reconfigurable Low-Power Sensors for Computer Vision, Control and Signal Processing","volume":"14","author":"Jara","year":"2014","journal-title":"Sensors"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4335","DOI":"10.3390\/s110404335","article-title":"Fused Smart Sensor Network for Multi-Axis Forward Kinematics Estimation in Industrial Robots","volume":"11","year":"2011","journal-title":"Sensors"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.measurement.2016.04.031","article-title":"Improving the Performance of Incremental Encoders with Conditioning Circuits based on FPGA","volume":"90","year":"2016","journal-title":"Measurement"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Rodr\u00edguez Andina, J.J., De la Torre Arnanz, E., and Vald\u00e9s Pe\u00f1a, M.D. (2017). FPGAs\u2014Fundamentals, Advanced Features and Applications in Industrial Electronics, CRC Press.","DOI":"10.1201\/9781315162133"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1109\/MCS.2014.2308691","article-title":"FPGA Logic Devices for Precision Control\u2014An Application to Large Friction Actuators with Payloads","volume":"34","author":"Zhu","year":"2014","journal-title":"IEEE Control. Syst. Mag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1109\/TII.2013.2261080","article-title":"Binary Division Power Models for High-Level Power Estimation of FPGA-Based DSP Circuits","volume":"10","author":"Jovanovic","year":"2014","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Sutter, G., and Deschamps, J.P. (September, January 31). High speed fixed point dividers for FPGAs. Proceedings of the 2009 International Conference on Field Programmable Logic and Applications, Prague, Czech Republic.","DOI":"10.1109\/FPL.2009.5272492"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Deschamps, J.-P., Antoine Bioul, G.J., and Sutter, G.D. (2006). Synthesis of Arithmetic Circuits, John Wiley & Sons, Inc.","DOI":"10.1002\/0471741426"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Hace, A., and \u010curkovi\u010d, M. (2018). A Novel Divisionless MT-type Velocity Estimation Algorithm for Efficient FPGA Implementation. IEEE Access.","DOI":"10.1109\/ACCESS.2018.2867510"},{"key":"ref_34","first-page":"287","article-title":"Incremental Encoder in Electrical Drives: Modeling and Simulation","volume":"Volume 313","author":"Rudas","year":"2010","journal-title":"Computational Intelligence in Engineering. Studies in Computational Intelligence"},{"key":"ref_35","unstructured":"Tsai, M.-F., and Chen, C.-P. (2002, January 5\u20138). Design of a Quadrature Decoder\/Counter Interface IC for Motor Control Using CPLD. Proceedings of the IEEE 28th Annual Conference of the Industrial Electronics Society (IECON \u201902), Sevilla, Spain."},{"key":"ref_36","unstructured":"(2018, July 31). Digilent Nexys 2 Reference Manual. Available online: https:\/\/reference.digilentinc.com\/reference\/programmable-logic\/nexys-2\/reference-manual."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3250\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:22:47Z","timestamp":1760196167000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3250"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,27]]},"references-count":36,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,10]]}},"alternative-id":["s18103250"],"URL":"https:\/\/doi.org\/10.3390\/s18103250","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9,27]]}}}