{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T18:09:53Z","timestamp":1764785393105,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,5,12]],"date-time":"2024-05-12T00:00:00Z","timestamp":1715472000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["52272365"],"award-info":[{"award-number":["52272365"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>During the braking process of electric vehicles, both the regenerative braking system (RBS) and anti-lock braking system (ABS) modulate the hydraulic braking force, leading to control conflict that impacts the effectiveness and real-time capability of coordinated control. Aiming to enhance the coordinated control effectiveness of RBS and ABS within the electro-hydraulic composite braking system, this paper proposes a coordinated control strategy based on explicit model predictive control (eMPC-CCS). Initially, a comprehensive braking control framework is established, combining offline adaptive control law generation, online optimized control law application, and state compensation to effectively coordinate braking force through the electro-hydraulic system. During offline processing, eMPC generates a real-time-oriented state feedback control law based on real-world micro trip segments, improving the adaptiveness of the braking strategy across different driving conditions. In the online implementation, the developed three-dimensional eMPC control laws, corresponding to current driving conditions, are invoked, thereby enhancing the potential for real-time braking strategy implementation. Moreover, the state error compensator is integrated into eMPC-CCS, yielding a state gain matrix that optimizes the vehicle braking status and ensures robustness across diverse braking conditions. Lastly, simulation evaluation and hardware-in-the-loop (HIL) testing manifest that the proposed eMPC-CCS effectively coordinates the regenerative and hydraulic braking systems, outperforming other CCSs in terms of braking energy recovery and real-time capability.<\/jats:p>","DOI":"10.3390\/s24103076","type":"journal-article","created":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T11:18:17Z","timestamp":1715599097000},"page":"3076","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["RBS and ABS Coordinated Control Strategy Based on Explicit Model Predictive Control"],"prefix":"10.3390","volume":"24","author":[{"given":"Liang","family":"Chu","sequence":"first","affiliation":[{"name":"State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinwei","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiqi","family":"Guo","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zewei","family":"Jiang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shibo","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiming","family":"Du","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yilin","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2068-908X","authenticated-orcid":false,"given":"Chong","family":"Guo","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Li, N., Jiang, J., Sun, F., Ye, M., Ning, X., and Chen, P. (2022). A cooperative control strategy for a hydraulic regenerative braking system based on chassis domain control. Electronics, 11.","DOI":"10.3390\/electronics11244212"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Deemyad, T., Moeller, R., and Sebastian, A. (2020, January 2\u20133). Chassis design and analysis of an autonomous ground vehicle (AGV) using genetic algorithm. Proceedings of the 2020 IEEE Intermountain Engineering, Technology and Computing (IETC), Orem, UT, USA.","DOI":"10.1109\/IETC47856.2020.9249180"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"117365","DOI":"10.1016\/j.energy.2020.117365","article-title":"Life cycle assessment of fuel cell, electric and internal combustion engine vehicles under different fuel scenarios and driving mileages in China","volume":"198","author":"Yang","year":"2020","journal-title":"Energy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"122750","DOI":"10.1016\/j.energy.2021.122750","article-title":"A novel electro-hydraulic compound braking system coordinated control strategy for a four-wheel-drive pure electric vehicle driven by dual motors","volume":"241","author":"Tang","year":"2022","journal-title":"Energy"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1592","DOI":"10.4271\/2020-01-0846","article-title":"Integrated regenerative braking system and anti-lock braking system for hybrid electric vehicles & battery electric vehicles","volume":"2","author":"Yao","year":"2020","journal-title":"SAE Int. J. Adv. Curr. Pract. Mobil."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2371","DOI":"10.1177\/0954407021996906","article-title":"A review on braking control and optimization techniques for electric vehicle","volume":"235","author":"Jamadar","year":"2021","journal-title":"Proc. Inst. Mech. Eng. Part D J. Autom. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"76671","DOI":"10.1109\/ACCESS.2020.2990349","article-title":"Regenerative braking control strategy for electric vehicles based on optimization of switched reluctance generator drive system","volume":"8","author":"Zhu","year":"2020","journal-title":"IEEE Access"},{"key":"ref_8","first-page":"22","article-title":"Development of Real-time Simulator for Vehicle Electric Brake System","volume":"16","author":"Cheon","year":"2019","journal-title":"J. Drive Control"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"104324","DOI":"10.1016\/j.conengprac.2020.104324","article-title":"Coordinated control strategy of electro-hydraulic braking for energy regeneration","volume":"96","author":"Pei","year":"2020","journal-title":"Control Eng. Pract."},{"key":"ref_10","unstructured":"Sardarmehni, T., and Heydari, A. (2015, January 28\u201330). Optimal switching in anti-lock brake systems of ground vehicles based on approximate dynamic programming. Proceedings of the Dynamic Systems and Control Conference, Columbus, OH, USA."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"103167","DOI":"10.1109\/ACCESS.2021.3098807","article-title":"Parameterized energy-optimal regenerative braking strategy for connected and autonomous electrified vehicles: A real-time dynamic programming approach","volume":"9","author":"Kim","year":"2021","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Wang, W., Yang, C., Han, L., Zhang, Z., and Liu, J. (2019, January 12\u201314). An effective regenerative braking strategy based on the combination algorithm of particle swarm optimization and ant colony optimization for electrical vehicle. Proceedings of the 2019 IEEE 28th International Symposium on Industrial Electronics (ISIE), Vancouver, BC, Canada.","DOI":"10.1109\/ISIE.2019.8781183"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2531","DOI":"10.1007\/s11831-021-09694-4","article-title":"Particle swarm optimization algorithm and its applications: A systematic review","volume":"29","author":"Gad","year":"2022","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1504\/IJVS.2013.055025","article-title":"Modelling and PID control of antilock braking system with wheel slip reduction to improve braking performance","volume":"6","author":"Aparow","year":"2013","journal-title":"Int. J. Veh. Saf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1177\/0954407019864229","article-title":"Electromechanical composite brake control for two in-wheel motors drive electric vehicle with single motor failure","volume":"234","author":"Zhang","year":"2020","journal-title":"Proc. Inst. Mech. Eng. Part D J. Autom. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.56038\/ejrnd.v2i2.21","article-title":"Optimization with Genetic Algorithm of Linear Quadratic Regulator Controller for Active Trailer Braking System","volume":"2","author":"Karali","year":"2022","journal-title":"Eur. J. Res. Dev."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Jin, H., Xu, H., and Wang, S. (2021, January 15\u201317). The electromechanical brake control strategy based on linear quadratic regulator. Proceedings of the Tenth International Symposium on Precision Mechanical Measurements, Qingdao, China.","DOI":"10.1117\/12.2611016"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Dou, J., Cui, G., Li, S., Zheng, S., Zhu, X., and Yu, Z. (2017, January 17\u201318). Research on the Composite Braking Control of Electric Vehicle. Proceedings of the 2017 2nd International Conference on Automation, Mechanical and Electrical Engineering (AMEE 2017), Shenzhen, China.","DOI":"10.2991\/amee-17.2017.2"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"162467","DOI":"10.1109\/ACCESS.2020.3021193","article-title":"Research on anti-lock braking control strategy of distributed-driven electric vehicle","volume":"8","author":"Yu","year":"2020","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"100292","DOI":"10.1016\/j.etran.2023.100292","article-title":"Brake-by-wire system for passenger cars: A review of structure, control, key technologies, and application in X-by-wire chassis","volume":"18","author":"Zhang","year":"2023","journal-title":"eTransportation"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"11344","DOI":"10.1016\/j.ifacol.2020.12.543","article-title":"Reducing the computational effort of MPC with closed-loop optimal sequences of affine laws","volume":"53","author":"Pannocchia","year":"2020","journal-title":"IFAC-PapersOnLine"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.mechatronics.2016.05.006","article-title":"Nonlinear MPC-based slip control for electric vehicles with vehicle safety constraints","volume":"38","author":"Yuan","year":"2016","journal-title":"Mechatronics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1244","DOI":"10.1109\/TTE.2023.3269602","article-title":"Autonomous high-speed overtaking of intelligent chassis using fast iterative model predictive control","volume":"10","author":"Chu","year":"2024","journal-title":"IEEE Trans. Transp. Electrif."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3644","DOI":"10.1109\/TIV.2024.3352171","article-title":"Real-Time High-Precision Nonlinear Tracking Control of Autonomous Vehicles Using Fast Iterative Model Predictive Control","volume":"9","author":"Meng","year":"2024","journal-title":"IEEE Trans. Intell. Veh."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0005-1098(01)00174-1","article-title":"The explicit linear quadratic regulator for constrained systems","volume":"38","author":"Bemporad","year":"2002","journal-title":"Automatica"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1918","DOI":"10.1002\/aic.11965","article-title":"Perspectives in multiparametric programming and explicit model predictive control","volume":"55","author":"Pistikopoulos","year":"2009","journal-title":"AIChE J."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Bemporad, A., Morari, M., Dua, V., and Pistikopoulos, E.N. (2000, January 28\u201330). The explicit solution of model predictive control via multiparametric quadratic programming. Proceedings of the 2000 IEEE American Control Conference, ACC (IEEE Cat. No.00CH36334), Chicago, IL, USA.","DOI":"10.1109\/ACC.2000.876624"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Gupta, A., and Falcone, P. (2018, January 4\u20137). Low-Complexity Explicit MPC Controller for Vehicle Lateral Motion Control. Proceedings of the 2018 21st IEEE International Conference on Intelligent Transportation Systems (ITSC), Maui, HI, USA.","DOI":"10.1109\/ITSC.2018.8569902"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1109\/TFUZZ.2020.2965868","article-title":"Hardware-in-the-loop test of an open-loop fuzzy control method for decoupled electrohydraulic antilock braking system","volume":"29","author":"Aksjonov","year":"2020","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1513","DOI":"10.1109\/TNNLS.2013.2276571","article-title":"Adaptive optimal control of unknown constrained-input systems using policy iteration and neural networks","volume":"24","author":"Modares","year":"2013","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3131","DOI":"10.1109\/TNNLS.2021.3051030","article-title":"Observer-based neuro-adaptive optimized control of strict-feedback nonlinear systems with state constraints","volume":"33","author":"Li","year":"2021","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"76524","DOI":"10.1109\/ACCESS.2023.3297274","article-title":"Steady-State Error Compensation for Reinforcement Learning-Based Control of Power Electronic Systems","volume":"11","author":"Weber","year":"2023","journal-title":"IEEE Access"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"11193","DOI":"10.1109\/TPEL.2020.2979122","article-title":"Multiobjective finite control set model predictive control using novel delay compensation technique for PMSM","volume":"35","author":"Han","year":"2020","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4223","DOI":"10.1109\/TMTT.2021.3081119","article-title":"Comparative analysis of machine learning techniques for temperature compensation in microwave sensors","volume":"69","author":"Kazemi","year":"2021","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1002\/acs.2411","article-title":"Simple adaptive control\u2014A stable direct model reference adaptive control methodology\u2013brief survey","volume":"28","author":"Barkana","year":"2014","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2752","DOI":"10.1109\/TMECH.2015.2409893","article-title":"A practical nonlinear adaptive control of hydraulic servomechanisms with periodic-like disturbances","volume":"20","author":"Yao","year":"2015","journal-title":"IEEE\/AsmE Trans. Mechatron."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1476","DOI":"10.1109\/TCYB.2015.2447153","article-title":"Fuzzy adaptive control design and discretization for a class of nonlinear uncertain systems","volume":"46","author":"Zhao","year":"2015","journal-title":"IEEE Trans. Cybern."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2874","DOI":"10.1109\/TPEL.2018.2842743","article-title":"Robustness improvement of FCS-MPTC for induction machine drives using disturbance feedforward compensation technique","volume":"34","author":"Yan","year":"2018","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"120756","DOI":"10.1016\/j.apenergy.2023.120756","article-title":"Feedforward-based decoupling control of air supply for vehicular fuel cell system: Methodology and experimental validation","volume":"335","author":"Zeng","year":"2023","journal-title":"Appl. Energy"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.automatica.2019.03.022","article-title":"Barrier Lyapunov functions-based command filtered output feedback control for full-state constrained nonlinear systems","volume":"105","author":"Yu","year":"2019","journal-title":"Automatica"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"107769","DOI":"10.1016\/j.ymssp.2021.107769","article-title":"Output feedback backstepping control of hydraulic actuators with valve dynamics compensation","volume":"158","author":"Deng","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"0036850419877762","DOI":"10.1177\/0036850419877762","article-title":"Research on braking energy recovery strategy of electric vehicle based on ECE regulation and I curve","volume":"103","author":"Li","year":"2020","journal-title":"Sci. Prog."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1021\/ie100245z","article-title":"Recent advances in explicit multiparametric nonlinear model predictive control","volume":"50","author":"Pistikopoulos","year":"2011","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Grancharova, J.A., and Johansen, T.A. (2012). Explicit Nonlinear Model Predictive Control: Theory and Applications, Springer.","DOI":"10.1007\/978-3-642-28780-0"},{"key":"ref_45","unstructured":"Pacejka, H.B. (2012). Tire and Vehicle Dynamics, Butterworth Heinemann."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Bardawil, C., Daher, N., and Shammas, E. (2020, January 1\u20133). Applying the Similarity Method on Pacejka\u2019s Magic Formula to Estimate the Maximum Longitudinal Tire-Road Friction Coefficient. Proceedings of the 2020 American Control Conference (ACC), Denver, CO, USA.","DOI":"10.23919\/ACC45564.2020.9147264"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Chang, H., Pistikopoulos, E.N., and Astolfi, A. (2013, January 17\u201319). Robust multi-parametric model predictive control for discrete-time LPV systems. Proceedings of the American Control Conference, Washington, DC, USA.","DOI":"10.1109\/ACC.2013.6579875"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Ventre, A.G. (2023). Calculus and Linear Algebra: Fundamentals and Applications, Springer.","DOI":"10.1007\/978-3-031-20549-1"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Olumuyiwa, O., and Chen, Y. (2022). Virtual CANBUS and Ethernet Switching in Future Smart Cars Using Hybrid Architecture. Electronics, 11.","DOI":"10.3390\/electronics11213428"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/10\/3076\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:41:11Z","timestamp":1760107271000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/10\/3076"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,12]]},"references-count":49,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["s24103076"],"URL":"https:\/\/doi.org\/10.3390\/s24103076","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2024,5,12]]}}}