{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T12:59:35Z","timestamp":1780577975954,"version":"3.54.1"},"reference-count":30,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2017,12,6]],"date-time":"2017-12-06T00:00:00Z","timestamp":1512518400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Nos. 61773159, 61473117, 61733004 and 61503131."],"award-info":[{"award-number":["Nos. 61773159, 61473117, 61733004 and 61503131."]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Scientific Research Fund of the Hunan Provincial Education Department","award":["Nos. 16A058 and 17B073."],"award-info":[{"award-number":["Nos. 16A058 and 17B073."]}]},{"name":"Hunan Provincial Natural Science Foundation of China","award":["Nos. 2017JJ4031 and 2016JJ5012."],"award-info":[{"award-number":["Nos. 2017JJ4031 and 2016JJ5012."]}]},{"DOI":"10.13039\/100009377","name":"Hunan Province Education Department","doi-asserted-by":"publisher","award":["No. 13CY018."],"award-info":[{"award-number":["No. 13CY018."]}],"id":[{"id":"10.13039\/100009377","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Teaching Reform Fund of Hunan Province Education Department under Grant","award":["No. 400."],"award-info":[{"award-number":["No. 400."]}]},{"name":"Teaching Reform of Degree and Postgraduate Education Fund of Hunan University of Technology","award":["No. JG1604."],"award-info":[{"award-number":["No. JG1604."]}]},{"name":"Key Laboratory for Electric Drive Control and Intelligent Equipment of Hunan Province","award":["No. 2016TP1018."],"award-info":[{"award-number":["No. 2016TP1018."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper proposes a new scheme of reconstructing current sensor faults and estimating unknown load disturbance for a permanent magnet synchronous motor (PMSM)-driven system. First, the original PMSM system is transformed into two subsystems; the first subsystem has unknown system load disturbances, which are unrelated to sensor faults, and the second subsystem has sensor faults, but is free from unknown load disturbances. Introducing a new state variable, the augmented subsystem that has sensor faults can be transformed into having actuator faults. Second, two sliding mode observers (SMOs) are designed: the unknown load disturbance is estimated by the first SMO in the subsystem, which has unknown load disturbance, and the sensor faults can be reconstructed using the second SMO in the augmented subsystem, which has sensor faults. The gains of the proposed SMOs and their stability analysis are developed via the solution of linear matrix inequality (LMI). Finally, the effectiveness of the proposed scheme was verified by simulations and experiments. The results demonstrate that the proposed scheme can reconstruct current sensor faults and estimate unknown load disturbance for the PMSM-driven system.<\/jats:p>","DOI":"10.3390\/s17122833","type":"journal-article","created":{"date-parts":[[2017,12,6]],"date-time":"2017-12-06T11:29:36Z","timestamp":1512559776000},"page":"2833","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["Sliding Mode Observer-Based Current Sensor Fault Reconstruction and Unknown Load Disturbance Estimation for PMSM Driven System"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4265-9631","authenticated-orcid":false,"given":"Kaihui","family":"Zhao","sequence":"first","affiliation":[{"name":"College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7876-9915","authenticated-orcid":false,"given":"Peng","family":"Li","sequence":"additional","affiliation":[{"name":"College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9800-3984","authenticated-orcid":false,"given":"Changfan","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiangfei","family":"Li","sequence":"additional","affiliation":[{"name":"College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"He","sequence":"additional","affiliation":[{"name":"College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China"},{"name":"College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha 410000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuliang","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Shandong Polytechnic, Jinan 250104, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.conengprac.2016.10.004","article-title":"Sensorless algorithm for sustaining controllability of IPMSM drive in electric vehicle after resolver fault","volume":"58","author":"Jarzebowicz","year":"2017","journal-title":"Control Eng. Prac."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1434","DOI":"10.1049\/el.2016.2198","article-title":"Current sensor fault detection and isolation method for PMSM drives, using average normalised currents","volume":"52","author":"Jlassi","year":"2016","journal-title":"Electron. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1206","DOI":"10.1109\/TIA.2013.2271992","article-title":"A New Approach for Current Sensor Fault Diagnosis in PMSG Drives for Wind Energy Conversion Systems","volume":"50","author":"Freire","year":"2014","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_4","first-page":"1","article-title":"Fault Reconstruction Based on Sliding Mode Observer for Current Sensors of PMSM","volume":"2016","author":"Zhang","year":"2016","journal-title":"J. Sens."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Huang, G., Luo, Y.P., Zhang, C.F., He, J., and Huang, Y.S. (2016). Current sensor fault reconstruction for PMSM drives. Sensors, 16.","DOI":"10.3390\/s16020178"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"11027","DOI":"10.3390\/s150511027","article-title":"Current Sensor Fault Diagnosis Based on a Sliding Mode Observer for PMSM Driven Systems","volume":"15","author":"Huang","year":"2015","journal-title":"Sensors"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.6113\/JPE.2016.16.3.1012","article-title":"Sensor Fault Detection, Localization, and System Reconfiguration with a Sliding Mode Observer and Adaptive Threshold of PMSM","volume":"16","author":"Abderrezak","year":"2016","journal-title":"J. Power Electron."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"551","DOI":"10.3233\/JAE-160090","article-title":"Current sensor fault diagnosis and adaptive fault-tolerant control of PMSM drive system based on differential algebraic method","volume":"53","author":"Li","year":"2017","journal-title":"Int. J. Appl. Electromagn. Mech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1002\/rnc.3597","article-title":"Integrated fault estimation and fault-tolerant control for uncertain Lipschitz nonlinear systems","volume":"27","author":"Lan","year":"2017","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.isatra.2016.12.001","article-title":"Multiple incipient sensor faults diagnosis with application to high-speed railway traction devices","volume":"67","author":"Wu","year":"2017","journal-title":"ISA Trans."},{"key":"ref_11","first-page":"759","article-title":"Observer-based sensor fault estimation in nonlinear systems","volume":"230","author":"Valibeygi","year":"2016","journal-title":"Proc. Inst. Mech. Eng. Part I"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1478","DOI":"10.1002\/asjc.1249","article-title":"Adaptive Fuzzy Descriptor Sliding Mode Observer-based Sensor Fault Estimation for Uncertain Nonlinear Systems","volume":"18","author":"Shahnazi","year":"2016","journal-title":"Asian J. Control"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.ins.2016.05.016","article-title":"Simultaneous fault diagnosis for robot manipulators with actuator and sensor faults","volume":"366","author":"Ma","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1002\/acs.2556","article-title":"Adaptive sensor and actuator fault estimation for a class of uncertain Lipschitz nonlinear systems","volume":"30","author":"Defoort","year":"2016","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1002\/asjc.867","article-title":"FDI Design for Uncertain Nonlinear Systems with Both Actuator and Sensor Faults","volume":"17","author":"Yang","year":"2015","journal-title":"Asian J. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2206","DOI":"10.1002\/asjc.1123","article-title":"Actuator and Sensor Fault Reconstructions for Uncertain Lipschitz Nonlinear Systems Based on H\u221e Observers","volume":"17","author":"Li","year":"2015","journal-title":"Asian J. Control"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1098","DOI":"10.1109\/TCST.2014.2361869","article-title":"Adaptive Second-Order Sliding Mode Observer-Based Fault Reconstruction for PEM Fuel Cell Air-Feed System","volume":"23","author":"Laghrouche","year":"2015","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1995","DOI":"10.1016\/j.jfranklin.2012.12.018","article-title":"High-gain observer with sliding mode for nonlinear state estimation and fault reconstruction","volume":"351","author":"Veluvolu","year":"2014","journal-title":"J. Frankl. Inst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1049\/iet-cta.2013.0593","article-title":"Higher-order sliding mode observer for estimation of tyre friction in ground vehicles","volume":"8","author":"Rath","year":"2014","journal-title":"IET Control Theory Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1296","DOI":"10.1002\/asjc.987","article-title":"Robust Sliding Mode Observer based Fault Estimation for Certain Class of Uncertain Nonlinear Systems","volume":"17","author":"Zhang","year":"2015","journal-title":"Asian J. Control"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1364","DOI":"10.1049\/iet-cta.2014.0096","article-title":"Simultaneous robust actuator and sensor fault estimation for uncertain non-linear Lipschitz systems","volume":"8","author":"Zhang","year":"2014","journal-title":"IET Control Theory Appl."},{"key":"ref_22","unstructured":"Haitham, A.R., Atif, I., and Jaroslaw, G. (2012). High Performance Control of AC Drives with Matlab\/Simulink Models, Wiley."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1785","DOI":"10.1002\/rnc.1545","article-title":"H\u221e sliding mode observers for uncertain nonlinear Lipschitz systems with fault estimation synthesis","volume":"20","author":"Raoufi","year":"2010","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_24","unstructured":"Yu, L. (2002). Robust Control-Linear Matrix Inequality Processing Method, TsingHua University Press."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/s00034-008-9035-x","article-title":"Fault reconstruction for Lipschitz nonlinear descriptor systems via linear matrix inequality approach","volume":"27","author":"Gao","year":"2008","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1080\/00207720701847638","article-title":"Sliding mode observers: a survey","volume":"39","author":"Spurgeon","year":"2008","journal-title":"Int. J. Syst. Sci."},{"key":"ref_27","unstructured":"Kok, Y.H., Raoufi, R., and Kwong, R.H.S. (2013, January 9\u201311). Fault-Tolerant Control Using H\u221e Sliding Mode Observer. Proceedings of the 2nd International Conference on Control and Fault-Tolerant Systems (Systol), Nice, France."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/276386","article-title":"LMI-Based Sliding Mode Observers for Incipient Faults Detection in Nonlinear System","volume":"2012","author":"Zhang","year":"2012","journal-title":"J. Appl. Math."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"He, J., and Zhang, C.F. (2012). On Observer-based Robust Fault Detection and Reconstruction for Nonlinear Systems, China Light Industry Press.","DOI":"10.1155\/2012\/451843"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"23119","DOI":"10.3390\/s141223119","article-title":"Online Fault Detection of Permanent Magnet Demagnetization for IPMSMs by Nonsingular Fast Terminal-Sliding-Mode Observer","volume":"14","author":"Zhao","year":"2014","journal-title":"Sensors"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/12\/2833\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:52:52Z","timestamp":1760208772000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/12\/2833"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,6]]},"references-count":30,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2017,12]]}},"alternative-id":["s17122833"],"URL":"https:\/\/doi.org\/10.3390\/s17122833","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12,6]]}}}