{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:07:49Z","timestamp":1772294869227,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2020,8,31]],"date-time":"2020-08-31T00:00:00Z","timestamp":1598832000000},"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>In this paper, an actuator fault estimation technique is proposed for quadcopters under uncertainties. In previous studies, matching conditions were required for the observer design, but they were found to be complex for solving linear matrix inequalities (LMIs). To overcome these limitations, in this study, an improved intermediate estimator algorithm was applied to the quadcopter model, which can be used to estimate actuator faults and system states. The system stability was validated using Lyapunov theory. It was shown that system errors are uniformly ultimately bounded. To increase the accuracy of the proposed fault estimation algorithm, a magnitude order balance method was applied. Experiments were verified with four scenarios to show the effectiveness of the proposed algorithm. Two first scenarios were compared to show the effectiveness of the magnitude order balance method. The remaining scenarios were described to test the reliability of the presented method in the presence of multiple actuator faults. Different from previous studies on observer-based fault estimation, this proposal not only can estimate the fault magnitude of the roll, pitch, yaw, and thrust channel, but also can estimate the loss of control effectiveness of each actuator under uncertainties.<\/jats:p>","DOI":"10.3390\/s20174917","type":"journal-article","created":{"date-parts":[[2020,8,31]],"date-time":"2020-08-31T08:11:19Z","timestamp":1598861479000},"page":"4917","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Robust Fault Estimation Using the Intermediate Observer: Application to the Quadcopter"],"prefix":"10.3390","volume":"20","author":[{"given":"Ngoc Phi","family":"Nguyen","sequence":"first","affiliation":[{"name":"Department of Aerospace Engineering, Sejong University, Seoul 143-747 (05006), Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4575-5952","authenticated-orcid":false,"given":"Tuan Tu","family":"Huynh","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Yuan Ze University, No. 135, Yuandong Road, Zhongli, Taoyuan 320, Taiwan"},{"name":"Department of Electrical Electronic and Mechanical Engineering, Lac Hong University, No. 10, Huynh Van Nghe Road, Bien Hoa, Dong Nai 810000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1249-8005","authenticated-orcid":false,"given":"Xuan Phu","family":"Do","sequence":"additional","affiliation":[{"name":"MediRobotics Laboratory, Department of Machatronics and Sensor Systems Technology, Vietnamese-German University, Binh Duong 820000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5632-9399","authenticated-orcid":false,"given":"Nguyen","family":"Xuan Mung","sequence":"additional","affiliation":[{"name":"Department of Aerospace Engineering, Sejong University, Seoul 143-747 (05006), Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sung Kyung","family":"Hong","sequence":"additional","affiliation":[{"name":"Department of Aerospace Engineering, Sejong University, Seoul 143-747 (05006), Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,31]]},"reference":[{"key":"ref_1","first-page":"130","article-title":"Design and Implementation of a Real Time Wireless Quadcopter for Rescue Operations","volume":"5","author":"Gordon","year":"2016","journal-title":"Am. J. Eng. Res."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Eid, S.E., and Dol, S.S. (April, January 26). Design and development of lightweight-high endurance unmanned aerial vehicle for offshore search and rescue operation. Proceedings of the 2019 Advances in Science and Engineering Technology International Conference, Dubai, UAE.","DOI":"10.1109\/ICASET.2019.8714418"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.coastaleng.2016.03.011","article-title":"UAVs for coastal surveying","volume":"114","author":"Ian","year":"2016","journal-title":"Coast. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Kingston, D., Rasmussen, S., and Humphrey, L. (2016, January 19\u201322). Automated UAV tasks for search and surveillance. Proceedings of the 2016 IEEE Conference on Control Applications Part of 2016 IEEE Multi-Conference on Systems and Control, Buenos Aires, Argentina.","DOI":"10.1109\/CCA.2016.7587813"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.rse.2017.04.007","article-title":"UAV lidar and hyperspectral fusion for forest monitoring in the southwestern USA","volume":"195","author":"Tenmuulen","year":"2017","journal-title":"Remote Sens. Environ."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Krause, S., Sanders, T.G., Mund, J.-P., and Greve, K. (2019). UAV-Based Photogrammetric Tree Height Measurement for Intensive Forest Monitoring. Remote Sens., 11.","DOI":"10.3390\/rs11070758"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhang, M., Li, H., Xia, G., Zhao, W., Rem, S., and Wang, C. (2018, January 8\u20139). Research on the Application of Deep Learning Target Detection of Engineering Vehicles in the Patrol and Inspection for Military Optical Cable Lines by UAV. Proceedings of the 2018 11th International Symposium on Computational Intelligence and Design (ISCID), Hangzhou, China.","DOI":"10.1109\/ISCID.2018.00029"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Butt, A., Shah, S.I.A., and Zaheer, Q. (2019, January 21\u201322). Weapon Launch System Design of Anti-Terrorist UAV. Proceedings of the 2019 International Conference on Engineering and Emerging Technologies, Lahore, Pakistan.","DOI":"10.1109\/CEET1.2019.8711832"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Brossard, J., Bensoussan, D., Landry, R., and Hammami, M. (2019, January 11\u201314). Robustness studies on quadrotor control. Proceedings of the 2019 International Conference on Unmanned Aircraft Systems, Atlanta, GA, USA.","DOI":"10.1109\/ICUAS.2019.8798198"},{"key":"ref_10","first-page":"79","article-title":"An application of mu-synthesis for control of a small air vehicle and simulation results","volume":"14","author":"Mystkowski","year":"2012","journal-title":"J. Vibroeng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s10778-018-0876-0","article-title":"A Flight Control System for Small Unmanned Aerial Vehicle","volume":"54","author":"Tunik","year":"2018","journal-title":"Int. Appl. Mech."},{"key":"ref_12","first-page":"1","article-title":"Fault tolerant control of a quadrotor using L1 adaptive control","volume":"4","author":"Xu","year":"2016","journal-title":"Int. J. Intell. Unmanned Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"082003","DOI":"10.1088\/1742-6596\/570\/8\/082003","article-title":"Feedback linearization approach for standard and fault tolerant control: Application to a quadrotor UAV testbed","volume":"570","author":"Ghandour","year":"2014","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_14","unstructured":"Li, T., Zhang, Y., and Gordon, B.W. (2012, January 29\u201331). Nonlinear fault-tolerant control of a quadrotor UAV based on sliding mode control technique. Proceedings of the 8th IFAC Symposium of Fault Detection, Supervision and Safety of Technical Processes, Mexico city, Mexico."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10846-012-9650-4","article-title":"A diagnostic thau observer for a class of unmanned vehicles","volume":"67","author":"Freddi","year":"2012","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_16","unstructured":"Freddi, A., Longhi, S., and Monteri\u00f9, A. (2009, January 19\u201320). A model-based fault diagnosis system for a mini-quadrotor. Proceedings of the 7th Workshop on Advanced Control and Diagnosis, Zielona Gora, Poland."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Freddi, A., Longhi, S., and Monteriu, A. (2020, January 4\u20137). Actuator fault detection system for a mini-quadrotor. Proceedings of the 2010 IEEE International Symposium on Industrial Electronics, Bari, Italy.","DOI":"10.1109\/ISIE.2010.5637750"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Aguilar-Sierra, H., Flores, G., Salazar, S., and Lozano, R. (2013, January 28\u201331). Fault estimation for a quad-rotor MAV using a polynominal observer. Proceedings of the 2013 International Conference on Unmanned Aircraft Systems, Atlanta, GA, USA.","DOI":"10.1109\/ICUAS.2013.6564753"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s10846-012-9757-7","article-title":"Experimental test of a two-stage Kalman filter for actuator fault detection and diagnosis of an unmanned quadrotor helicopter","volume":"70","author":"Amoozgar","year":"2013","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s10846-017-0535-4","article-title":"Active fault-tolerant control of unmanned quadrotor helicopter using linear parameter varying technique","volume":"88","author":"Liu","year":"2017","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1007\/s10846-013-9921-8","article-title":"Robust fault diagnosis for quadrotor UAVs using adaptive Thau observer","volume":"73","author":"Cen","year":"2014","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Cen, Z., and Noura, H. (2013, January 9\u201311). An Adaptive Thau Observer for estimating the time-varying LOE fault of quadrotor actuators. Proceedings of the 2013 Conference on Control and Fault-Tolerant Systems (SysTol), Nice, France.","DOI":"10.1109\/SysTol.2013.6693918"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1109\/TII.2018.2865522","article-title":"Nonlinear High-Gain Observer-Based Diagnosis and Compensation for Actuator and Sensor Faults in a Quadrotor Unmanned Aerial Vehicle","volume":"15","author":"Ma","year":"2019","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.neucom.2016.10.076","article-title":"A neural network approach to simultaneous state and actuator fault estimation under unknown input decoupling","volume":"250","author":"Witczak","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s10846-018-0781-0","article-title":"Neural Network Based Adaptive Actuator Fault Detection Algorithm for Robot Manipulators","volume":"95","author":"Cho","year":"2019","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1080\/00207721.2012.724100","article-title":"Actuator fault estimation for a class of nonlinear descriptor systems","volume":"45","author":"Wang","year":"2014","journal-title":"Int. J. Syst. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1080\/00207179.2018.1484173","article-title":"A fault tolerant tracking control for a quadrotor UAV subject to simultaneous actuator faults and exogenous disturbances","volume":"93","author":"Mallavalli","year":"2018","journal-title":"Int. J. Control"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"33","DOI":"10.5772\/62224","article-title":"Actuator fault estimation and reconfiguration control for quad-rotor helicopter","volume":"13","author":"Chen","year":"2016","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_29","unstructured":"Bharani, K.P., Alwi, H., and Edwards, C. (2015, January 2\u20134). Fault reconstruction for a quadrotor using an LPV sliding mode observer. Proceedings of the 9th IFAC Symposium on Fault Detection Supervision and Safety for Technical Processes SAFEPROCESS 2015, Paris, France."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Nguyen, N.P., and Hong, S.K. (2018). Sliding Mode Thau Observer for Actuator Fault Diagnosis of Quadcopter UAVs. Appl. Sci., 8.","DOI":"10.3390\/app8101893"},{"key":"ref_31","first-page":"901","article-title":"Modeling and Control of a Quadrotor UAV with Aerodynamics Concepts","volume":"7","author":"Dong","year":"2013","journal-title":"World Acad. Sci. Eng. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zhang, Y., and Chamseddine, A. (2012). Fault tolerant flight control techniques with application to a quadrotor UAV testbed. Automatic Flight Control Systems-Latest Developments, Thomas Lombaerts, IntechOpen.","DOI":"10.5772\/38918"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2518","DOI":"10.1109\/TAC.2015.2491898","article-title":"Fault estimation for a class of nonlinear systems based on intermediate estimator","volume":"61","author":"Zhu","year":"2016","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_34","unstructured":"(2018, August 31). Editing\/Building with Eclipse on Windows. Available online: http:\/\/ardupilot.org\/dev\/docs\/editing-the-code-with-eclipse.html."},{"key":"ref_35","unstructured":"(2018, August 31). Telemetry. Available online: http:\/\/ardupilot.org\/copter\/docs\/common-telemetry-landingpage.html."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/17\/4917\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:04:59Z","timestamp":1760177099000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/17\/4917"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,31]]},"references-count":35,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["s20174917"],"URL":"https:\/\/doi.org\/10.3390\/s20174917","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,31]]}}}