{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T09:26:06Z","timestamp":1769160366939,"version":"3.49.0"},"reference-count":69,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T00:00:00Z","timestamp":1662595200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Joint Development Research Institute of Intelligent Motion Control Technology of the Liaoning Provincial Department of Education and the National Key R &amp; D Program of China","award":["2017YFB1300700"],"award-info":[{"award-number":["2017YFB1300700"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>As a complex nonlinear system, the first-order incremental relationship between the state variables of the beam and ball system (BABS) is asymmetric in the definition domain of the variables, and the characteristics of the system do not satisfy the superposition theorem. Studying the balance control of the BABS can help to better grasp the relevant characteristics of the nonlinear system. In this paper, the deep reinforcement learning method is used to study the BABS based on a visual sensor. First, the detail-reward function is designed by observing the control details of the system, and the rationality of the function is proved based on Q-function; secondly, considering and comparing the applicability of image processing methods in ball coordinate location, an intelligent location algorithm is proposed, and the location effects between the algorithms are compared and analyzed; then, combining the nonlinear theory and LQR theory, a reinforcement learning policy model is proposed to linearize near the equilibrium point, which significantly improves the control effect. Finally, experiments are designed to verify the effectiveness of the above methods in the control system. The experimental results show that the design scheme can be effectively applied to the control system of the BABS. It is verified that the introduction of detail-reward mechanism into a deep reinforcement learning algorithm can significantly reduce the complexity of the nonlinear control system and iterative algorithm, and effectively solve nonlinear control problems.<\/jats:p>","DOI":"10.3390\/sym14091883","type":"journal-article","created":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T09:51:09Z","timestamp":1662630669000},"page":"1883","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Research on Solving Nonlinear Problem of Ball and Beam System by Introducing Detail-Reward Function"],"prefix":"10.3390","volume":"14","author":[{"given":"Shixuan","family":"Yao","sequence":"first","affiliation":[{"name":"School of Software Engineering, Dalian University of Foreign Languages, Dalian 116044, China"}]},{"given":"Xiaochen","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Dalian Jiaotong University, Dalian 116028, China"}]},{"given":"Yinghui","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Dalian Jiaotong University, Dalian 116028, China"}]},{"given":"Ze","family":"Cui","sequence":"additional","affiliation":[{"name":"School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"144","DOI":"10.3166\/ejc.9.144-158","article-title":"Future directions in control, dynamics, and systems: Overview, grand challenges, and new courses","volume":"9","author":"Murray","year":"2003","journal-title":"Eur. 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