基于改进干扰观测器的虚拟轴机床滑模控制研究
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摘要
圆弧齿轮加工用虚拟轴机床伺服系统存在的不确定性会影响系统的性能,从而降低圆弧齿轮的加工精度;同时,滑模控制中抖动现象会影响控制的精度和稳定性.为提高虚拟轴机床的加工精度和抑制滑模控制中的抖动现象,提出了基于改进观测器的滑模变结构控制算法来控制虚拟轴机床的伺服电机,算法中采用该干扰观测器对系统中的不确定性进行观测,利用饱和函数代替符号函数来抑制滑模控制中的抖动现象.推导了基于改进观测器的滑模变结构控制律,并证明了所设计控制器的稳定性;为验证算法的有效性,在MATLAB中进行了仿真,仿真结果表明:所提出的算法能够有效地观测系统中存在的不确定性因素,并抑制滑模控制中的抖动现象,系统具有较强的位置跟踪性能和抗干扰能力.
The uncertainties existed in the servo system of virtual axis machine tool that was used to process the circular arc gears will affect the performance of the system and reduce the machining accuracy of the circular arc gears,and the chattering phenomenon existed in the sliding mode control will influence the control accuracy and stability.In order to improve the machining accuracy of the virtual axis machine tool and reduce chattering phenomenon in the sliding mode control,an sliding model control scheme with improved disturbance observer was proposed to control the servo motor of the virtual axis machine tool.The disturbance observer was used to observe the uncertainties existed in the servo system of virtual axis machine tool in this algorithm and the symbolic function in the variable structure control was replaced by the saturation function to reduce the chattering phenomenon which was brought by the variable structure control system.The control law was deduced based on the improved observer of sliding mode variable structure,and the stability of the designed controller was proved.In order to verify the validity of the algorithm,the simulation was taken in MATLAB,the simulation results showed that the algorithm proposed could effectively observe the uncertainties in the system,and chattering phenomenon in the sliding model control was reduced,then the motor servo system had stronger position tracking performance and anti-interference ability.
The uncertainties existed in the servo system of virtual axis machine tool that was used to process the circular arc gears will affect the performance of the system and reduce the machining accuracy of the circular arc gears,and the chattering phenomenon existed in the sliding mode control will influence the control accuracy and stability.In order to improve the machining accuracy of the virtual axis machine tool and reduce chattering phenomenon in the sliding mode control,an sliding model control scheme with improved disturbance observer was proposed to control the servo motor of the virtual axis machine tool.The disturbance observer was used to observe the uncertainties existed in the servo system of virtual axis machine tool in this algorithm and the symbolic function in the variable structure control was replaced by the saturation function to reduce the chattering phenomenon which was brought by the variable structure control system.The control law was deduced based on the improved observer of sliding mode variable structure,and the stability of the designed controller was proved.In order to verify the validity of the algorithm,the simulation was taken in MATLAB,the simulation results showed that the algorithm proposed could effectively observe the uncertainties in the system,and chattering phenomenon in the sliding model control was reduced,then the motor servo system had stronger position tracking performance and anti-interference ability.
引文
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[13]王辉,万里瑞,王才东.基于智能滑模控制的永磁直线同步电机调速系统[J].电机与控制应用,2014,41(2):6-10,38.WANG Hui,WAN Li-rui,WANG Cai-dong.Research of speed regulating system based on intelligent SMC for permanent magnet linear synchronous motor[J].Electric Machines&Control Application,2014,41(2):6-10,38.
[2]宋爱平,易红,汤文成,等.渐开线弧齿圆柱齿轮及其啮合特性[J].中国机械工程,2006,17(18):1888-1892.SONG Ai-ping,YI Hong,TANG Wen-cheng,et al.Involute arc cylindrical gear and its mesh characteristics[J].China Mechanical Engineering,2006,17(18):1888-1892.
[3]宋爱平,吴伟伟,高尚,等.弧齿圆柱齿轮理想几何参数及其加工方法[J].上海交通大学学报,2010,44(12):1735-1740.SONG Ai-ping,WU Wei-wei,GAO Shang,et al.The ideal geometry parameters of arch cylindrical gear and its process method[J].Journal of Shanghai Jiaotong University,2010,44(12):1735-1740.
[4]宋爱平.弧齿圆柱齿轮及其加工方法和加工装置.ZL200410041297.2[P].2005-02-23.SONG Ai-ping.Arc tooth cylindrical gears and its machining method and devices[J].ZL200410041297.2[P].2005-02-23.
[5]王少江,侯力,董璐,等.面向制造的弧齿圆柱齿轮建模及强度分析[J].四川大学学报(工程科学版),2012,44(2):210-215.WANG Shao-jiang,HOU Li,DONG Lu,et al.Modeling and strength analysis of cylindrical gears with curvilinear shape teeth for manufacture[J].Journal of Sichuan University(Engineering Science Edition),2012,44(2):210-215.
[6]肖华军,侯力,董璐,等.旋转刀盘母面成形的弧齿线圆柱齿轮数学建模[J].四川大学学报(工程科学版),2013,45(3):171-175.XIAO Hua-jun,HOU Li,DONG Lu,et al.Mathematical modeling of rotary cutter arc tooth line of cylindrical gear shaped by origin face of rotary cutter[J].Journal of Sichuan University(Engineering Science Edition),2013,45(3):171-175.
[7]张立杰,李永泉,黄真.一种新型运动副及其在并联机床上的应用[J].机械工程学报,2005,41(12):216-221.ZHANG Li-jie,LI Yong-quan,HUANG Zhen.Novel compound-sphere-joint and its application in parallel machine tool[J].Journal of Mechanical Engineering,2005,41(12):216-221.
[8]韩庆涛,郭庆鼎,谢冬梅.直线伺服6杆虚拟轴机床轨迹跟踪控制的研究[J].沈阳工业大学学报,2002,24(6):485-489.HAN Qing-tao,GUO Qing-ding,XIE Dong-mei.Trajectory tracking control for 6-DOF virtual axis machine tool driven by permanent magnetic synchronous linear motor[J].Journal of Shenyang University of Technology,2002,24(6):485-489.
[9]陆华才,徐月同,杨伟民,等.永磁直线同步电机进给系统模糊PID控制[J].电工技术学报,2007,22(4):59-63.LU Hua-cai,XU Yue-tong,YANG Wei-min,et al.Fuzzy pid controller design for a permanent magnet linear synchronous motor feeding system[J].Transactions of China Electrotechnical Society,2007,22(4):59-63.
[10]张宏伟,余发山,卜旭辉,等.基于鲁棒迭代学习的永磁直线电机控制[J].电机与控制学报,2012,16(6):81-86.ZHANG Hong-wei,YU Fa-shan,BU Xu-hui,et al.Robust iterative learning control for permanent magnet linear motor[J].Electric Machines and Control,2012,16(6):81-86.
[11]蔡满军,赵成圆.永磁直线同步电机的自适应迭代学习控制[J].微特电机,2014,42(6):48-51.CAI Man-jun,ZHAO Cheng-yuan.Adaptive and iterative learning control of pmlsm[J].Small&Special Electrical Machines,2014,42(6):48-51.
[12]刘军,韩明文,俞金寿.基于滑模变结构的永磁同步直线电机控制系统研究[J].控制工程,2012,19(6):1093-1096.LIU Jun,HAN Ming-wen,YU Jin-shou.Research on permanent magnet linear synchronous motor based on sliding mode control[J].Control Engineering of China,2012,19(6):1093-1096.
[13]王辉,万里瑞,王才东.基于智能滑模控制的永磁直线同步电机调速系统[J].电机与控制应用,2014,41(2):6-10,38.WANG Hui,WAN Li-rui,WANG Cai-dong.Research of speed regulating system based on intelligent SMC for permanent magnet linear synchronous motor[J].Electric Machines&Control Application,2014,41(2):6-10,38.