{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T16:48:53Z","timestamp":1782406133590,"version":"3.54.5"},"reference-count":35,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2022,12,13]],"date-time":"2022-12-13T00:00:00Z","timestamp":1670889600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Fund of China","award":["52005345"],"award-info":[{"award-number":["52005345"]}]},{"name":"National Natural Science Fund of China","award":["52005344"],"award-info":[{"award-number":["52005344"]}]},{"name":"National Natural Science Fund of China","award":["2020YFC2006701"],"award-info":[{"award-number":["2020YFC2006701"]}]},{"name":"National Natural Science Fund of China","award":["LFGD2020002"],"award-info":[{"award-number":["LFGD2020002"]}]},{"name":"National Natural Science Fund of China","award":["2022JH1\/10400027"],"award-info":[{"award-number":["2022JH1\/10400027"]}]},{"name":"National Key Research and Development Project","award":["52005345"],"award-info":[{"award-number":["52005345"]}]},{"name":"National Key Research and Development Project","award":["52005344"],"award-info":[{"award-number":["52005344"]}]},{"name":"National Key Research and Development Project","award":["2020YFC2006701"],"award-info":[{"award-number":["2020YFC2006701"]}]},{"name":"National Key Research and Development Project","award":["LFGD2020002"],"award-info":[{"award-number":["LFGD2020002"]}]},{"name":"National Key Research and Development Project","award":["2022JH1\/10400027"],"award-info":[{"award-number":["2022JH1\/10400027"]}]},{"name":"Scientific Research Fund Project of Liaoning Provincial Department of Education","award":["52005345"],"award-info":[{"award-number":["52005345"]}]},{"name":"Scientific Research Fund Project of Liaoning Provincial Department of Education","award":["52005344"],"award-info":[{"award-number":["52005344"]}]},{"name":"Scientific Research Fund Project of Liaoning Provincial Department of Education","award":["2020YFC2006701"],"award-info":[{"award-number":["2020YFC2006701"]}]},{"name":"Scientific Research Fund Project of Liaoning Provincial Department of Education","award":["LFGD2020002"],"award-info":[{"award-number":["LFGD2020002"]}]},{"name":"Scientific Research Fund Project of Liaoning Provincial Department of Education","award":["2022JH1\/10400027"],"award-info":[{"award-number":["2022JH1\/10400027"]}]},{"name":"Major Project of the Ministry of Science and Technology of Liaoning Province","award":["52005345"],"award-info":[{"award-number":["52005345"]}]},{"name":"Major Project of the Ministry of Science and Technology of Liaoning Province","award":["52005344"],"award-info":[{"award-number":["52005344"]}]},{"name":"Major Project of the Ministry of Science and Technology of Liaoning Province","award":["2020YFC2006701"],"award-info":[{"award-number":["2020YFC2006701"]}]},{"name":"Major Project of the Ministry of Science and Technology of Liaoning Province","award":["LFGD2020002"],"award-info":[{"award-number":["LFGD2020002"]}]},{"name":"Major Project of the Ministry of Science and Technology of Liaoning Province","award":["2022JH1\/10400027"],"award-info":[{"award-number":["2022JH1\/10400027"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Under extreme working conditions such as high-speed driving on roads with a large road surface unevenness coefficient, turning on a road with a low road surface adhesion coefficient, and emergency acceleration and braking, a vehicle\u2019s stability deteriorates sharply and reduces ride comfort. There is extensive existing research on vehicle active suspension control, trajectory tracking, and control methods. However, most of these studies focus on conventional operating conditions, while vehicle stability analysis under extreme operating conditions is much less studied. In order to improve the stability of the whole vehicle under extreme operating conditions, this paper investigates the stability of a vehicle under extreme operating conditions based on linear quadratic regulator (LQR) control. First, a seven degrees of freedom (7-DOF) dynamics model of the whole vehicle is established based on the use of electromagnetic active suspension, and then an LQR controller of the electromagnetic active suspension is designed. A joint simulation platform incorporating MATLAB and CarSim was built, and the CarSim model is verified by real vehicle tests. Finally, the stability of the vehicle under four different ultimate operating conditions was analyzed. The simulation results show that the root mean square (RMS) values of body droop acceleration and pitch angle acceleration are improved by 57.48% and 28.81%, respectively, under high-speed driving conditions on Class C roads. Under the double-shift condition with a low adhesion coefficient, the RMS values of body droop acceleration, pitch acceleration, and roll angle acceleration are improved by 58.25%, 55.41%, and 31.39%, respectively. These results indicate that electromagnetic active suspension can significantly improve vehicle stability and reduce driving risk under extreme working conditions when combined with an LQR controller.<\/jats:p>","DOI":"10.3390\/s22249791","type":"journal-article","created":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T03:21:52Z","timestamp":1670988112000},"page":"9791","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Vehicle Stability Analysis under Extreme Operating Conditions Based on LQR Control"],"prefix":"10.3390","volume":"22","author":[{"given":"Liping","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4390-0589","authenticated-orcid":false,"given":"Ran","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junshan","family":"Bao","sequence":"additional","affiliation":[{"name":"SIASUN Robot & Automation Co., Ltd., Shenyang 110169, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guang","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China"},{"name":"School of Mechanical Engineering, Shenyang Aerospace University, Shenyang 110136, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Feng","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fangchao","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junjie","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qi","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weikang","family":"Jiang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Nippon Institute of Technology, Saitama 345-8501, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoyou","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China"},{"name":"Department of Mechanical Engineering, Nippon Institute of Technology, Saitama 345-8501, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Aljarbouh, A., Fayaz, M., Qureshi, M.S., and Boujoudar, Y. 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