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浙江大学学报(工学版)  2021, Vol. 55 Issue (6): 1150-1158    DOI: 10.3785/j.issn.1008-973X.2021.06.016
能源工程、机械工程     
基于观测器摩擦补偿的机电系统高精度控制
李曦(),胡健*(),姚建勇,魏科鹏,王鹏飞,邢浩晨
南京理工大学 机械工程学院,江苏 南京 210094
High precision control of electromechanical system based on observer friction compensation
Xi LI(),Jian HU*(),Jian-yong YAO,Ke-peng WEI,Peng-fei WANG,Hao-chen XING
School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
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摘要:

针对机电作动系统在低速阶段摩擦非线性明显且同时存在其他干扰,易导致系统跟踪精度、稳定性下降这一问题,设计基于非线性观测器摩擦补偿的自适应鲁棒控制器. 针对摩擦非线性,利用LuGre摩擦模型描述系统的摩擦现象,提出非线性观测器对模型的内部摩擦状态进行观测. 针对系统摩擦系数、转动惯量及其他不确定性参数,设计参数自适应律进行估计. 利用前馈补偿的方法,对摩擦非线性和参数不确定性进行补偿,设计鲁棒项克服系统的其他扰动. 利用Lyapunov稳定性定理证明了提出的控制器在存在扰动的情况下可以实现系统的有界稳定性. 实验结果表明,提出的控制器具有较高的控制精度与较强的鲁棒性,跟踪精度较传统的PID控制器提高了一个数量级.

关键词: 机电作动系统LuGre摩擦模型非线性观测器自适应鲁棒控制有界稳定性    
Abstract:

An adaptive robust controller based on nonlinear observer friction compensation was designed aiming at the problem of obvious friction nonlinearity and other interferences in the electromechanical actuation system at low speed, which may easily lead to the decrease of system tracking accuracy and stability. The LuGre friction model was used to describe the friction phenomenon of the system for the nonlinearity of friction, and a nonlinear observer was proposed to observe the internal friction state of the model. The parameter adaptive law was designed for uncertain parameters such as system friction coefficient and rotational inertia. The friction nonlinearity and parameter uncertainty were compensated by feed-forward compensation, and robust terms were designed to overcome other disturbances in the system. Lyapunov stability theory was used to prove that the proposed controller can achieve the bounded stability of the system in the presence of disturbances. The experimental results show that the proposed controller has higher control accuracy and stronger robustness, which is an order of magnitude higher than the tracking accuracy of traditional PID controller.

Key words: electromechanical actuation system    LuGre friction model    nonlinear observer    adaptive robust control    bounded stability
收稿日期: 2020-07-05 出版日期: 2021-07-30
CLC:  TP 273  
基金资助: 国家自然科学基金资助项目(51975294);高性能复杂制造国家重点实验室开放课题基金资助项目(Kfkt2019–11);中央高校基本科研业务费专项资金资助项目(30920010009)
通讯作者: 胡健     E-mail: lixi_l@126.com;hujiannjust@163.com
作者简介: 李曦(1996—),女,硕士生,从事机电伺服控制的研究. orcid.org/0000-0002-1463-6363. E-mail: lixi_l@126.com
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李曦
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王鹏飞
邢浩晨

引用本文:

李曦,胡健,姚建勇,魏科鹏,王鹏飞,邢浩晨. 基于观测器摩擦补偿的机电系统高精度控制[J]. 浙江大学学报(工学版), 2021, 55(6): 1150-1158.

Xi LI,Jian HU,Jian-yong YAO,Ke-peng WEI,Peng-fei WANG,Hao-chen XING. High precision control of electromechanical system based on observer friction compensation. Journal of ZheJiang University (Engineering Science), 2021, 55(6): 1150-1158.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2021.06.016        https://www.zjujournals.com/eng/CN/Y2021/V55/I6/1150

图 1  控制器设计思路
图 2  给定位置输入及各控制器跟踪误差
指标 Me μ σ
PID 0.0031 0.0034 0.0071
ARC 0.0025 0.0016 5.2158×10?4
NOARC 6.0003×10?4 2.4833×10?4 5.1198×10?4
表 1  阶跃工况下的性能指标
图 3  摩擦状态观测曲线和观测误差曲线
图 4  摩擦力观测曲线和观测误差曲线
图 5  参数估计曲线
图 6  给定位置输入及各控制器跟踪误差
指标 M μ σ
PID 0.153 6 8.868 6×10?3 0.077 2
ARC 0.043 8 8.618 1×10?4 0.025 6
NOARC 0.010 1 1.638 5×10?4 0.006 9
表 2  低速低频工况下的性能指标
图 7  摩擦状态观测曲线和观测误差曲线
图 8  摩擦力观测曲线和观测误差曲线
图 9  参数估计曲线
图 10  机电伺服系统的实验平台总装图
图 11  机电伺服实验平台的控制系统
元器件名称 规格
执行电机 kollmorgen伺服电机D063M-13-1310
旋转编码器 海德汉高安全性位置测量系统
扭矩传感器 CD1140系列扭矩传感器
联轴器 JB/ZQ4376-86 YL1型凸缘刚性联轴器
惯量盘 0.3 kg·m2
表 3  机电伺服系统实验平台的元器件表
参数 参数值
电机连续电流有效值 4.187 A
电机直轴峰值电流有效值 1 A
电机峰值电流有效值 14.5 A
电机惯量 86.5 kg·cm2
电机转矩系数有效值 4.406 N·m/A
电机最大速度 500 r/min
电机最大电压有效值 240 V
电机额定感应电压有效值 230 V
表 4  电机参数
图 12  给定阶跃位置输入及各控制器跟踪误差
图 13  给定正弦位置输入及各控制器跟踪误差
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