基于扰动补偿的磁悬浮转台分数阶滑模控制  

Fractional-Order Sliding Mode Control for Maglev Rotary Table Based on Disturbance Compensation

作　　者：许贤泽[1] 宋明星 龚勇兴 徐逢秋[1] 王递进 隋博文 郭清泉 XU Xianze;SONG Mingxing;GONG Yongxing;XU Fengqiu;WANG Dijin;SUI Bowen;GUO Qingquan(Electronic Information School,Wuhan University,Wuhan 430072,China;Huawei Technologies Co.,Ltd.,Shanghai 200120,China;Yunnan Hailite Electric Automation Co.,Ltd.,Kunming 650000,China)

机构地区：[1]武汉大学电子信息学院,湖北武汉430072 [2]华为技术有限公司,上海200120 [3]云南海力特电气自动化有限公司,云南昆明650000

出　　处：《西南交通大学学报》2024年第4期766-775,共10页Journal of Southwest Jiaotong University

基　　金：国家自然科学基金(52275569);扬州市重点研发项目(YZ2022013);云南省专家工作站项目(202205AF150061);湖北省技术创新计划重点研发专项(2023BAB050);武汉东湖新技术开发区“揭榜挂帅”项目(2022KJB129);中国科协青年人才托举工程(2022QNRC001)。

摘　　要：针对存在非线性、耦合性和不确定性的磁悬浮转台的高精度运动控制问题,提出一种基于非线性干扰观测器的分数阶滑模控制方法以提高跟踪精度.首先,基于系统电磁力模型和动态解耦方法,构建六自由度磁悬浮转台系统动力学模型;其次,设计非线性干扰观测器,对包含系统误差、六自由度间耦合项和外界干扰的集总扰动进行估计,证明了估计误差有界且可调节到任意小;然后,在离散域提出了一种分数阶滑模面,采用分数幂函数替代传统符号函数来抑制抖振,引入分数阶微积分来减小跟踪误差;最后,设计有限时间收敛的分数阶滑模控制策略,并利用李雅普诺夫稳定性理论证明闭环系统稳定性.实验结果表明:与整数阶滑模控制方法相比,采用所提方法,2个水平自由度和绕竖直方向旋转自由度对三角波的跟踪误差均方根分别减小了12.8%、16.8%和23.7%,最大跟踪误差分别减小9.26%、13.00%和33.20%;跟踪圆形轨迹时,2个水平自由度的跟踪误差均方值分别减小6.39%和12.40%,最大跟踪误差分别减小9.90%和12.10%.In view of the high-precision motion control problem of the maglev rotary table with nonlinearity,coupling,and uncertainty,a fractional-order sliding mode control method based on a nonlinear disturbance observer was proposed to improve the tracking accuracy.Firstly,based on the electromagnetic force model of the system and the dynamic decoupling method,the dynamical model of the six-degree-of-freedom maglev rotary table system was constructed.Secondly,a nonlinear disturbance observer was designed to estimate the lumped disturbance including system error,coupling term between six degrees of freedom,and external interference.It was proved that the estimation error was bounded and could be made arbitrarily small.Then,a fractional-order sliding surface was proposed in the discrete domain,where the fractional power function was used instead of the traditional symbolic function to suppress jitter,and the fractional calculus was introduced to reduce the tracking error.Finally,a fractional-order sliding mode control strategy with finite time convergence was designed,and the stability of the closed-loop system was proved by Lyapunov stability theory.The experimental results reveal thatcompared to the integer-order sliding mode control method,the proposed method reduces the root mean square of tracking error for triangular waves by 12.8%,16.8%,and 23.7%for the two horizontal degrees of freedom and the rotational degree about the vertical axis,respectively,while the maximum tracking errors are reduced by 9.26%,13.00%,and 33.20%respectively.When tracking a circular trajectory,the mean square values of tracking errors for two horizontal degrees of freedom are decreased by 6.39%and 12.40%,and the maximum tracking errors are reduced by 9.90%and 12.10%,respectively.

关 键 词：磁悬浮转台 分数阶微积分 滑模控制 非线性干扰观测器 轨迹跟踪 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]