{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T16:52:07Z","timestamp":1790268727368,"version":"4.1.0"},"reference-count":37,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,10,15]],"date-time":"2019-10-15T00:00:00Z","timestamp":1571097600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51777170"],"award-info":[{"award-number":["51777170"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of Shannxi Province","award":["2019JM-462"],"award-info":[{"award-number":["2019JM-462"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper proposes an adaptive backstepping control algorithm for electric braking systems with electromechanical actuators (EMAs). First, the ideal mathematical model of the EMA is established, and the nonlinear factors are analyzed, such as the deformation of the reduction gear. Subsequently, the actual mathematical model of the EMA is rebuilt by combining the ideal model and the nonlinear factors. To realize high performance braking pressure control, the backstepping control method is adopted to address the mismatched uncertainties in the electric braking system, and a radial basis function (RBF) neural network is established to estimate the nonlinear functions in the control system. The experimental results indicate that the proposed braking pressure control strategy can improve the servo performance of the electric braking system. In addition, the hardware-in-loop (HIL) experimental results show that the proposed EMA controller can satisfy the requirements of the aircraft antilock braking systems.<\/jats:p>","DOI":"10.3390\/a12100215","type":"journal-article","created":{"date-parts":[[2019,10,16]],"date-time":"2019-10-16T03:32:54Z","timestamp":1571196774000},"page":"215","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Backstepping Adaptive Neural Network Control for Electric Braking Systems of Aircrafts"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7584-0974","authenticated-orcid":false,"given":"Xi","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Automation, Northwestern Polytechnical University, Xi\u2019an 710129, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hui","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Automation, Northwestern Polytechnical University, Xi\u2019an 710129, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,15]]},"reference":[{"key":"ref_1","unstructured":"Tian, R.N., Jiao, Z.X., Huang, K.J., Liu, X.C., and Jing, G.H. (2016, January 12\u201314). Aircraft Anti-Skid braking control based on pressure servo control using high-speed on\/off valve. Proceedings of the 2016 IEEE Chinese Guidance, Navigation and Control Conference, Nanjing, China."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1044","DOI":"10.1109\/TFUZZ.2013.2241769","article-title":"Intelligent hybrid control system design for antilock braking systems using Self-Organizing Function-Link fuzzy cerebellar model articulation controller","volume":"21","author":"Lin","year":"2013","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1016\/j.engappai.2010.06.011","article-title":"Genetic fuzzy Self-Tuning PID controller for antilock braking systems","volume":"23","author":"Sharkawy","year":"2010","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1109\/TVT.2004.841552","article-title":"Iterative learning control of antilock braking of electric and hybrid vehicles","volume":"54","author":"Mi","year":"2005","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_5","unstructured":"Yuan, D.L., Wei, J., Qu, Y.H., and Wu, J.Z. (2013, January 26\u201328). Simulation of Hydraulic Brake Built-in Test System for a Certain UAV. Proceedings of the 32nd Chinese Control Conference, Xi\u2019an, China."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"126","DOI":"10.21629\/JSEE.2017.01.14","article-title":"Sensor Fault-Tolerant observer applied in UAV Anti-Skid braking control under control input constraint","volume":"28","author":"Sun","year":"2017","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.neucom.2012.12.019","article-title":"Fractional order sliding mode controller design for antilock braking systems","volume":"111","author":"Tang","year":"2013","journal-title":"Neurocomputing"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3523","DOI":"10.1109\/TIE.2011.2165453","article-title":"Over view of electric motor technologies used for more electric aircraft","volume":"59","author":"Cao","year":"2012","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1109\/TCST.2012.2229465","article-title":"Extremum-Seeking control of ABS braking in road vehicles with lateral force improvement","volume":"22","author":"Dincmen","year":"2014","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1109\/TVT.2015.2413451","article-title":"Uncertainty-Estimation-Based Approach to Antilock Braking Systems","volume":"65","author":"Patil","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1109\/TMECH.2014.2322629","article-title":"An ABS control strategy for commercial vehicle","volume":"20","author":"Zhang","year":"2015","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_12","first-page":"767","article-title":"A grey system modeling approach for Sliding-Mode control of antilock braking system","volume":"19","author":"Kayacan","year":"2009","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5197","DOI":"10.1016\/j.eswa.2013.03.012","article-title":"Adaptive Neuro-Fuzzy wheel slip control","volume":"40","author":"Velimir","year":"2013","journal-title":"Expert Syst. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Zhang, X., and Lin, H. (2018, January 25\u201327). UAV Anti-Skid Braking System Simulation. Proceedings of the 2018 37th Chinese Control Conference, Wuhan, China.","DOI":"10.23919\/ChiCC.2018.8483585"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1049\/iet-est.2016.0023","article-title":"Braking force control strategy for electric vehicles with load variation and wheel slip considerations","volume":"7","author":"Wei","year":"2017","journal-title":"IET Electr. Syst. Transp."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"77","DOI":"10.3901\/CJME.2011.02.277","article-title":"Design and Dynamics Analysis of Anti-Skid Braking System for Aircraft with Four-Wheel Bogie Landing Gears","volume":"24","author":"Zhang","year":"2011","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1869","DOI":"10.2514\/1.C032242","article-title":"Antiskid braking control with on\/off valves for aircraft applications","volume":"50","author":"Huang","year":"2013","journal-title":"J. Aircr."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"142","DOI":"10.23919\/TEMS.2018.8326461","article-title":"Fuzzy sliding mode control based on longitudinal force estimation for Electro-Mechanical braking systems using BLDC motor","volume":"2","author":"Peng","year":"2018","journal-title":"CES Trans. Electr. Mach. Syst."},{"key":"ref_19","first-page":"1139","article-title":"Enhanced stability dynamic surface control for aircraft antiskid braking system using electromechanical actuator","volume":"38","author":"Li","year":"2016","journal-title":"Syst. Eng. Electron."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Ju, J.Y., Zhao, Y.R., Zhang, C.R., and Liu, Y.F. (2018). Vibration suppression of a flexible-joint robot based on parameter identification and fuzzy PID control. Algorithms, 11.","DOI":"10.3390\/a11110189"},{"key":"ref_21","first-page":"1037","article-title":"Backstepping Power Fast Terminal Siding Mode Control for Missile Borne Electric Rudder","volume":"36","author":"Lv","year":"2016","journal-title":"Trans. Beijing Inst. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Liang, B., Zhu, Y.Q., Li, Y.R., He, P.J., and Li, W.L. (2017). Adaptive Nonsingular Fast Terminal Sliding Mode Control for Braking Systems with Electro-Mechanical Actuators Based on Radial Basis Function. Energies, 10.","DOI":"10.3390\/en10101637"},{"key":"ref_23","first-page":"1439","article-title":"Sliding-Mode Extremum-Seeking control for All-Electric active braking system in unmanned aerial vehicle","volume":"32","author":"Chen","year":"2015","journal-title":"Control Theory Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2826","DOI":"10.1109\/TIE.2013.2276775","article-title":"Realization of Anti-Lock Braking Strategy for Electric Scooters","volume":"61","author":"Lin","year":"2014","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"79244","DOI":"10.1109\/ACCESS.2019.2923532","article-title":"Impacts of Misalignments on Mesh Behaviors of Face-Hobbed Hypoid Gear Considering System Deformation","volume":"7","author":"Yang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"33344","DOI":"10.1109\/ACCESS.2018.2847737","article-title":"The Effects of Blank Geometry on Gear Rolling for Large Gear Modules: Experiments and Finite Element Simulations","volume":"6","author":"Khodaee","year":"2019","journal-title":"IEEE Access"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Saeed, A., Siddiq, M., Mustafa, S.H., Jawed, U., and Shahid, L. (2019, January 9\u201310). Validation of Hertz Theory in order to increase the efficiency of gear element (Plastic and Fiber). Proceedings of the 2019 International Conference on Information Science and Communication Technology (ICISCT), Karachi, Pakistan.","DOI":"10.1109\/CISCT.2019.8777415"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1109\/TVT.2007.905251","article-title":"Clamp-Force Estimation for a Brake-by-Wire System: A Sensor-Fusion Approach","volume":"57","author":"Saric","year":"2008","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1156","DOI":"10.1016\/j.mechatronics.2011.07.006","article-title":"Novel clamping force control for electric parking brake systems","volume":"21","author":"Lee","year":"2011","journal-title":"Mechatronics"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3205","DOI":"10.1109\/TVT.2010.2043696","article-title":"Clamping-Force Control for Electromechanical Brake","volume":"59","author":"Jo","year":"2010","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1109\/TII.2012.2223478","article-title":"The Adaptive Backstepping Control of Permanent Magnet Synchronous Motor Supplied by Current Source Inverter","volume":"9","author":"Morawiec","year":"2013","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2470","DOI":"10.1109\/TMECH.2018.2864187","article-title":"Gain-Adaptive Robust Backstepping Position Control of a BLDC Motor System","volume":"23","author":"Ba","year":"2018","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1109\/TAC.2016.2570140","article-title":"Adaptive backstepping quantized control for a class of nonlinear systems","volume":"62","author":"Yu","year":"2017","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1109\/JSEE.2015.00063","article-title":"Adaptive backstepping-based NTSM control for unmatched uncertain nonlinear systems","volume":"26","author":"Zheng","year":"2015","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_35","first-page":"5740","article-title":"Adaptive RBF Network Based Direct Voltage Control for Interior PMSM Based Vehicles","volume":"67","author":"Chaoui","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_36","first-page":"2013","article-title":"Research on the RBF-PID control method for the motor actuator used in a UHV GIS disconnector","volume":"16","author":"Shi","year":"2019","journal-title":"J. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/S1007-0214(05)70069-9","article-title":"Improvement and parallelism of K-Means clustering algorithm","volume":"10","author":"Tian","year":"2005","journal-title":"Tsinghua Sci. Technol."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/10\/215\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:26:38Z","timestamp":1760189198000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/10\/215"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,15]]},"references-count":37,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2019,10]]}},"alternative-id":["a12100215"],"URL":"https:\/\/doi.org\/10.3390\/a12100215","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,15]]}}}