{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T01:25:48Z","timestamp":1766712348956,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T00:00:00Z","timestamp":1621555200000},"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>For pulse width modulation (PWM) inverter drives, an LC filter can cascade to a permanent magnet (PM) machine at inverter output to reduce PWM-reflected current harmonics. Because the LC filter causes resonance, the filter output current and voltage are required for the sensorless field-oriented control (FOC) drive. However, existing sensors and inverters are typically integrated inside commercial closed-form drives; it is not possible for these drives to obtain additional filter output signals. To resolve this integration issue, this paper proposes a sensorless LC filter state estimation using only the drive inside current sensors. The design principle of the LC filter is first introduced to remove PWM current harmonics. A dual-observer is then proposed to estimate the filter output current and voltage for the sensorless FOC drive. Compared to conventional model-based estimation, the proposed dual-observer demonstrates robust estimation performance under parameter error. The capacitor parameter error shows a negligible influence on the proposed observer estimation. The filter inductance error only affects the capacitor current estimation at high speed. The performance of the sensorless FOC drive using the proposed dual-observer is comparable to the same drive using external sensors for filter voltage and current measurement. All experiments are verified by a PM machine with only 130 \u03bcH phase inductance.<\/jats:p>","DOI":"10.3390\/s21113596","type":"journal-article","created":{"date-parts":[[2021,5,24]],"date-time":"2021-05-24T00:01:20Z","timestamp":1621814480000},"page":"3596","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Sensorless LC Filter Implementation for Permanent Magnet Machine Drive Using Observer-Based Voltage and Current Estimation"],"prefix":"10.3390","volume":"21","author":[{"given":"Chia-Ming","family":"Liang","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, National Taiwan University, No.1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi-Jen","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Taiwan University, No.1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3947-3115","authenticated-orcid":false,"given":"Jyun-You","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Taiwan University, No.1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7593-097X","authenticated-orcid":false,"given":"Guan-Ren","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Taiwan University, No.1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shih-Chin","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Taiwan University, No.1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6901","DOI":"10.3390\/s100706901","article-title":"Position and speed control of brushless DC motors using sensorless techniques and application trends","volume":"10","year":"2010","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Huh, N., Park, H.S., Lee, M.H., and Kim, J.M. (2019). Hybrid PWM Control for Regulating the High-Speed Operation of BLDC Motors and Expanding the Current Sensing Range of DC-link Single-Shunt. Energies, 12.","DOI":"10.3390\/en12224347"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Kim, H.J., Park, H.S., and Kim, J.M. (2020). Expansion of Operating Speed Range of High-Speed BLDC Motor Using Hybrid PWM Switching Method Considering Dead Time. Energies, 13.","DOI":"10.3390\/en13195212"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Coballes-Pantoja, J., Gomez-Fuentes, R., Noriega, J.R., and Garcia-Delgado, L.A. (2020). Parallel Loop Control for Torque and Angular Velocity of BLDC Motors with DTC Commutation. Electronics, 9.","DOI":"10.3390\/electronics9020279"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Yao, Y., Peng, F., and Huang, Y. (2018, January 23\u201327). In Proceedings of the Position and Capacitor Voltage Sensorless Control of High-Speed Surface-Mounted PMSM Drive with Output Filter. Proceedings of the 2018 IEEE Energy Conversion Congress and Exposition (ECCE), Portland, OR, USA.","DOI":"10.1109\/ECCE.2018.8557846"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Sikora, A., and Wozniak, M. (2021). Impact of Current Pulsation on BLDC Motor Parameters. Sensors, 21.","DOI":"10.3390\/s21020587"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1109\/TIA.2003.821665","article-title":"Novel vector control system using deadbeat-controlled PWM inverter with output LC filter","volume":"40","author":"Kojima","year":"2004","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1109\/TIA.2010.2101992","article-title":"Vector Control of Single-Phase Voltage-Source Converters Based on Fictive-Axis Emulation","volume":"47","author":"Bahrani","year":"2011","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1109\/TIE.2013.2238878","article-title":"Analysis, Design, and Experimental Verification of a Synchronous Reference Frame Voltage Control for Single-Phase Inverters","volume":"61","author":"Monfared","year":"2014","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Yen, S.H., Tang, P.C., Lin, Y.C., and Lin, C.Y. (2019). A Sensorless and Low-Gain Brushless DC Motor Controller Using a Simplified Dynamic Force Compensator for Robot Arm Application. Sensors, 19.","DOI":"10.3390\/s19143171"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1850","DOI":"10.1109\/TPEL.2011.2168427","article-title":"Generalized Closed-Loop Control Schemes with Embedded Virtual Impedances for Voltage Source Converters with LC or LCL Filters","volume":"27","author":"He","year":"2012","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7394","DOI":"10.1109\/TPEL.2016.2632065","article-title":"Stability Analysis and Controller Synthesis for Single-Loop Voltage-Controlled VSIs","volume":"32","author":"Wang","year":"2017","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2237","DOI":"10.1109\/TIE.2012.2193864","article-title":"Full-Feedforward Schemes of Grid Voltages for a Three-Phase LCL-Type Grid-Connected Inverter","volume":"60","author":"Li","year":"2013","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1109\/TIE.2011.2141093","article-title":"Active Damping of Output LC Filter Resonance for Vector-Controlled VSI-Fed AC Motor Drives","volume":"59","author":"Hatua","year":"2012","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1109\/TIA.2018.2868552","article-title":"Discrete-Time Voltage Controller for Voltage Source Converters with LC Filter Based on State-Space Models","volume":"55","author":"Kim","year":"2019","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1109\/TIE.2016.2625238","article-title":"Model Predictive Control for Power Converters and Drives: Advances and Trends","volume":"64","author":"Vazquez","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1188","DOI":"10.1109\/TIE.2006.878314","article-title":"Sensorless Control of Induction Motor Drives Equipped with Inverter Output Filter","volume":"53","author":"Salomaki","year":"2006","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1109\/TIA.2007.912765","article-title":"Influence of Inverter Output Filter on Maximum Torque and Speed of PMSM Drives","volume":"44","author":"Hinkkanen","year":"2008","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5993","DOI":"10.1109\/TIE.2015.2424391","article-title":"Full-State Feedback Equivalent Controller for Active Damping in LCL-Filtered Grid-Connected Inverters Using a Reduced Number of Sensors","volume":"62","author":"Busada","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1109\/TIA.2006.889738","article-title":"Modeling, Simulation, and Test of a Three-Level Voltage-Source Inverter with Output LC Filter and Direct Torque Control","volume":"43","author":"Sapin","year":"2007","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Hsu, C., Yang, S., and Chen, J. (October, January 29). Implementation of Low Inductance Permanent Magnet Machine Drive with LC Filter for Field Oriented Control. Proceedings of the 2019 IEEE Energy Conversion Congress and Exposition (ECCE), Baltimore, MD, USA.","DOI":"10.1109\/ECCE.2019.8913165"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1109\/TIA.2013.2266892","article-title":"Regions of Active Damping Control for LCL Filters","volume":"50","author":"Parker","year":"2014","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_23","unstructured":"Wang, T.C.Y., Zhihong, Y., Gautam, S., and Xiaoming, Y. (2003, January 15\u201319). Output filter design for a grid-interconnected three-phase inverter. Proceedings of the IEEE 34th Annual Conference on Power Electronics Specialist, PESC \u201803, Acapulco, Mexico."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Ahmed, K.H., Finney, S.J., and Williams, B.W. (June, January 29). Passive Filter Design for Three-Phase Inverter Interfacing in Distributed Generation. Proceedings of the 2007 Compatibility in Power Electronics, Gdansk, Poland.","DOI":"10.1109\/CPE.2007.4296511"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1109\/TIA.2015.2480852","article-title":"Inverter Nonlinear Error Compensation Using Feedback Gains and Self-Tuning Estimated Current Error in Adaptive Full-Order Observer","volume":"52","author":"Sun","year":"2016","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"692","DOI":"10.1016\/j.energy.2013.05.052","article-title":"Performance evaluation of directly photovoltaic powered DC PM (direct current permanent magnet) motor\u2014Propeller thrust system","volume":"57","author":"Atlam","year":"2013","journal-title":"Energy"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/11\/3596\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:05:41Z","timestamp":1760162741000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/11\/3596"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,21]]},"references-count":26,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["s21113596"],"URL":"https:\/\/doi.org\/10.3390\/s21113596","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2021,5,21]]}}}