分数阶微积分在滑模控制中的应用研究  

Applicated research of fractional calculus in sliding mode control

作　　者：张鑫[1,2] 鲁文儒 缪仲翠 姜子运[1] 徐文波[1] ZHANG Xin;LU Wenru;MIAO Zhongcui;JIANG Ziyun;XU Wenbo(School of Automation and Electrical Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China;Gansu Provincial Engineering Research Center for Artificial Intelligence and Graphics and Image Processing,Lanzhou 730070,China)

机构地区：[1]兰州交通大学自动化与电气工程学院,甘肃兰州730070 [2]甘肃省人工智能与图形图像处理工程研究中心,甘肃兰州730070

出　　处：《传感器与微系统》2022年第2期46-49,57,共5页Transducer and Microsystem Technologies

基　　金：国家自然科学基金资助项目(61663022)。

摘　　要：针对滑模控制所存在的抖振问题以及趋近问题,将分数阶微积分理论与滑模控制策略的优点相互结合,提出一种有效的分数阶趋近律。在控制器的设计过程中,将分数阶微积分引入到滑模控制中提出分数阶趋近律,并运用Lyapunov理论进行证明,从而确保系统的稳定性。将提出的控制方法应用于二关节机械臂上,进行仿真验证。结果表明:所提出的分数阶趋近律相比传统指数趋近律可有效提高关节的跟踪速度与跟踪精度,很大程度上削弱系统抖振,并且使系统鲁棒性更强。Aiming at the chattering problem and approaching problem in sliding mode control, combining the advantages of fractional order calculus theory and sliding mode control strategy, an effective fractional order reaching law is proposed.In the design process of the controller, the fractional order calculus is introduced into the sliding mode control to propose the fractional order reaching law, and the Lyapunov theory is used to prove, so as to ensure the stability of the system.Finally, the proposed control method is applied to the two-joint mechanical arm for simulation verification.The results show that the proposed fractional reaching law can effectively improve the tracking speed and tracking accuracy of joints compared with the traditional exponential reaching law, greatly weaken the system chattering, and make the system more robust.

关 键 词：分数阶微积分 分数阶趋近律 指数趋近律 滑模控制 LYAPUNOV理论 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]