{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T15:35:27Z","timestamp":1784820927439,"version":"3.55.0"},"reference-count":31,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T00:00:00Z","timestamp":1637625600000},"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 addresses the problem of robust sensor faults detection and isolation in the air-path system of heavy-duty diesel engines, which has not been completely considered in the literature. Calibration or the total failure of a sensor can cause sensor faults. In the worst-case scenario, the engines can be totally damaged by the sensor faults. For this purpose, a second-order sliding mode observer is proposed to reconstruct the sensor faults in the presence of unknown external disturbances. To this aim, the concept of the equivalent output error injection method and the linear matrix inequality (LMI) tool are utilized to minimize the effects of uncertainties and disturbances on the reconstructed fault signals. The simulation results verify the performance and robustness of the proposed method. By reconstructing the sensor faults, the whole system can be prevented from failing before the corrupted sensor measurements are used by the controller.<\/jats:p>","DOI":"10.3390\/s21237788","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T01:45:02Z","timestamp":1638323102000},"page":"7788","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Dependable Sensor Fault Reconstruction in Air-Path System of Heavy-Duty Diesel Engines"],"prefix":"10.3390","volume":"21","author":[{"given":"Ashkan","family":"Taherkhani","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5131-3419","authenticated-orcid":false,"given":"Farhad","family":"Bayat","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5676-1875","authenticated-orcid":false,"given":"Saleh","family":"Mobayen","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, Iran"},{"name":"Future Technology Research Center, National Yunlin University of Science and Technology, Yunlin 64002, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1271-8488","authenticated-orcid":false,"given":"Andrzej","family":"Bartoszewicz","sequence":"additional","affiliation":[{"name":"Institute of Automatic Control, Lodz University of Technology, 90924 Lodz, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Nguyen, N.P., Mung, N.X., Thanh Ha, L.N.N., Huynh, T.T., and Hong, S.K. (2020). Finite-Time Attitude Fault Tolerant Control of Quadcopter System via Neural Networks. Mathematics, 8.","DOI":"10.3390\/math8091541"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"e12174","DOI":"10.1002\/2050-7038.12174","article-title":"Wind turbines sustainable power generation subject to sensor faults: Observer-based MPC approach","volume":"30","author":"Ghanbarpour","year":"2020","journal-title":"Int. Trans. Electr. Energy Syst."},{"key":"ref_3","first-page":"3045","article-title":"Open-switch fault detection in five-phase induction motor drives using model predictive control","volume":"65","author":"Duran","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.isatra.2018.03.014","article-title":"Adaptive super-twisting observer for fault reconstruction in electro-hydraulic systems","volume":"76","author":"Bahrami","year":"2018","journal-title":"ISA Trans."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Khan, A., Hwang, H., and Kim, H.S. (2021). Synthetic Data Augmentation and Deep Learning for the Fault Diagnosis of Rotating Machines. Mathematics, 9.","DOI":"10.3390\/math9182336"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"105802","DOI":"10.1016\/j.ijepes.2019.105802","article-title":"Dependable power extraction in wind turbines using model predictive fault tolerant control","volume":"118","author":"Ghanbarpour","year":"2020","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1109\/TAC.1971.1099826","article-title":"An introduction to observers","volume":"16","author":"Luenberger","year":"1971","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Alwi, H., Edwards, C., and Tan, C.P. (2011). Fault Detection and Fault-Tolerant Control Using Sliding Modes, Springer Science & Business Media.","DOI":"10.1007\/978-0-85729-650-4"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Thanh, H.L.N.N., Mung, N.X., Nguyen, N.P., and Phuong, N.T. (2020). Perturbation observer-based robust control using a multiple sliding surfaces for nonlinear systems with influences of matched and unmatched uncertainties. Mathematics, 8.","DOI":"10.3390\/math8081371"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1016\/S0005-1098(99)00177-6","article-title":"Sliding mode observers for fault detection and isolation","volume":"36","author":"Edwards","year":"2000","journal-title":"Automatica"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3096","DOI":"10.1049\/iet-gtd.2018.6736","article-title":"Wind turbines robust fault reconstruction using adaptive sliding mode observer","volume":"13","author":"Taherkhani","year":"2019","journal-title":"IET Gener. Transm. Distrib."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1049\/iet-epa.2018.5232","article-title":"Second order sliding mode observer of linear induction motor","volume":"13","author":"Zhang","year":"2019","journal-title":"IET Electr. Power Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"25232","DOI":"10.1109\/ACCESS.2018.2872792","article-title":"Accelerated adaptive second order super-twisting sliding mode observer","volume":"7","author":"Lin","year":"2018","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1016\/S0005-1098(97)00209-4","article-title":"Robust exact differentiation via sliding mode technique","volume":"34","author":"Levant","year":"1998","journal-title":"Automatica"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2085","DOI":"10.1109\/TAC.2007.908319","article-title":"Analysis of chattering in systems with second-order sliding modes","volume":"52","author":"Boiko","year":"2007","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.matcom.2018.03.004","article-title":"Adaptive super twisting extended state observer based sliding mode control for diesel engine air path subject to matched and unmatched disturbance","volume":"151","author":"Mohamed","year":"2018","journal-title":"Math. Comput. Simul."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.conengprac.2019.06.021","article-title":"Model predictive controller with average emissions constraints for diesel airpath","volume":"90","author":"Sankar","year":"2019","journal-title":"Control Eng. Pract."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.ifacol.2019.12.222","article-title":"Model predictive control of diesel engine air path with actuator delays","volume":"52","author":"Kekik","year":"2019","journal-title":"IFAC-PapersOnLine"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"104724","DOI":"10.1016\/j.conengprac.2021.104724","article-title":"Sliding mode control on receding horizon: Practical control design and application","volume":"109","author":"Yin","year":"2021","journal-title":"Control Eng. Pract."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"108718","DOI":"10.1016\/j.automatica.2019.108718","article-title":"Robust fault reconstruction for a class of nonlinear systems","volume":"113","author":"Chua","year":"2020","journal-title":"Automatica"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.isatra.2019.07.024","article-title":"Fault reconstruction using a terminal sliding mode observer for a class of second-order MIMO uncertain nonlinear systems","volume":"97","author":"Chu","year":"2020","journal-title":"ISA Trans."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.automatica.2019.03.008","article-title":"Fault reconstruction for Markovian jump systems with iterative adaptive observer","volume":"105","author":"Chen","year":"2019","journal-title":"Automatica"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1080\/00207179.2019.1590738","article-title":"Fault diagnosis in linear systems via sliding mode observers","volume":"94","author":"Zhirabok","year":"2019","journal-title":"Int. J. Control"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1109\/TAC.2010.2041996","article-title":"Robust fault reconstruction in uncertain linear systems using multiple sliding mode observers in cascade","volume":"55","author":"Tan","year":"2010","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5046","DOI":"10.1109\/TSMC.2019.2945998","article-title":"Sliding-mode observer-based fault reconstruction for TS fuzzy descriptor systems","volume":"51","author":"Li","year":"2019","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1007\/s12204-020-2196-x","article-title":"Fault Reconstruction for Lipschitz Nonlinear Systems Using Higher Terminal Sliding Mode Observer","volume":"25","author":"Dai","year":"2020","journal-title":"J. Shanghai Jiaotong Univ. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Mollenhauer, K., Tsch\u00f6ke, H., and Johnson, K.G. (2010). Handbook of Diesel Engines, Springer.","DOI":"10.1007\/978-3-540-89083-6"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Guzzella, L., and Onder, C. (2009). Introduction to Modeling and Control of Internal Combustion Engine Systems, Springer Science & Business Media.","DOI":"10.1007\/978-3-642-10775-7"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Eriksson, L., and Nielsen, L. (2014). Modeling and Control of Engines and Drivelines, John Wiley & Sons.","DOI":"10.1002\/9781118536186"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM.","DOI":"10.1137\/1.9781611970777"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1002\/rnc.723","article-title":"Sliding mode observers for robust detection and reconstruction of actuator and sensor faults","volume":"13","author":"Tan","year":"2003","journal-title":"Int. J. Robust Nonlinear Control IFAC-Affil. J."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/23\/7788\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:34:43Z","timestamp":1760168083000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/23\/7788"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,23]]},"references-count":31,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["s21237788"],"URL":"https:\/\/doi.org\/10.3390\/s21237788","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,23]]}}}