精密定位系统的摩擦力建模与补偿
|
摘要
为了提高由直线电机驱动的精密定位系统的定位精度,建立了优化Stribeck摩擦模型,对摩擦力这一影响定位精度的主要因素进行补偿。首先,对于传统的Stribeck摩擦模型进行优化,采用改进的最小二乘算法对模型参数进行辨识。然后,对所建立的摩擦模型补偿算法进行仿真并与扰动观测器的补偿算法进行比较,发现前者速度比后者速度在补偿后提高了4.33%,对摩擦力具有更好的补偿效果。最后,在大行程二维精密定位平台上进行验证,根据平台能够达到的最大速度定义0.005m/s为低速运动,0.05m/s为高速运动,在这两种速度下进行实验,并与基于库仑摩擦前馈补偿模型比较。实验结果表明:精密定位平台在速度为0.005m/s的低速运动时,优化模型的跟随误差减小了67.67%;在速度为0.05m/s的高速运动时,优化模型的跟随误差减小了51.63%,验证了优化Stribeck摩擦模型补偿算法的有效性。本文提出的优化Stribeck摩擦模型可用于提高由直线电机驱动的精密定位系统的定位精度。
To improve the positioning accuracy of a precise positioning system driven by a linear motor,the optimized Stribeck friction model was established that compensates for the main factors affecting the positioning accuracy of friction.First,the traditional Stribeck friction model was optimized.Second,the improved least square algorithm was used to identify the model parameters.Third,the friction model compensation algorithm was simulated and compared with the disturbance observer compensation algorithm.It is found that the speed of the former is 4.33% higher than that of the latter,and the friction compensation has a better compensation effect.Finally,the experiment was carried out on a two-dimensional precision positioning platform with large stroke according to the maximum speed of the platform;low and high speeds were defined as 0.005 and 0.05 m/s,respectively.Experiments were performed at these two speeds and compared with the Coulomb friction feed forward compensation model.The experimental results indicate that for the precision positioning platform at a low speed of 0.005 m/s,the proposed model tracking error is reduced by 67.67%;forahigh-speed movement of 0.05 m/s,the proposed model tracking error is reduced by 51.63%,which verifies the validity of the improved Stribeck friction model compensation algorithm.The improved Stribeck friction model proposed in this paper can be used to improve the positioning accuracy of a precision positioning system driven by a linear motor.
To improve the positioning accuracy of a precise positioning system driven by a linear motor,the optimized Stribeck friction model was established that compensates for the main factors affecting the positioning accuracy of friction.First,the traditional Stribeck friction model was optimized.Second,the improved least square algorithm was used to identify the model parameters.Third,the friction model compensation algorithm was simulated and compared with the disturbance observer compensation algorithm.It is found that the speed of the former is 4.33% higher than that of the latter,and the friction compensation has a better compensation effect.Finally,the experiment was carried out on a two-dimensional precision positioning platform with large stroke according to the maximum speed of the platform;low and high speeds were defined as 0.005 and 0.05 m/s,respectively.Experiments were performed at these two speeds and compared with the Coulomb friction feed forward compensation model.The experimental results indicate that for the precision positioning platform at a low speed of 0.005 m/s,the proposed model tracking error is reduced by 67.67%;forahigh-speed movement of 0.05 m/s,the proposed model tracking error is reduced by 51.63%,which verifies the validity of the improved Stribeck friction model compensation algorithm.The improved Stribeck friction model proposed in this paper can be used to improve the positioning accuracy of a precision positioning system driven by a linear motor.
引文
[1]AHN H S,CHEN Y Q.State-dependent friction force compensation using periodic adaptive learning control[J].Mechatronics,2009,19(6):896-904.
[2]ASTROM K J,CANUDAS-DE-WIT C.Revisiting the LuGre friction model stick-slip motion and rate dependence[J].IEEE Control Systems Magazine,2008,28(6):101-114.
[3]PENNESTRI E,ROSSI V,SALVINI P,et al..Review and comparison of dry friction force models[J].Nonlinear Dynamics,2015,83(4):1785-1801.
[4]王延忠,郭超,贾树王,等.基于Stribeck摩擦模型的盘式摩擦副稳定性分析[J].中国机械工程,2017,28(21):2521-2525.WANG Y ZH,GUO CH,JIA SH W,et al..Stability analysis of disc friction pairs based on Stribeck model[J].China Mechanical Engineering,2017,28(21):2521-2525.(in Chinese)
[5]CONG S,DENG K,SHANG W,et al..Isolation control for inertially stabilized platform based on nonlinear friction compensation[J].Nonlinear Dynamics,2015,84(3):1123-1133.
[6]陈浩,孟健,安琦.直线电机滑台摩擦特性和摩擦模型[J].华东理工大学学报:自然科学版,2017,43(4):571-577.CHEN H,MENG J,AN Q.Friction characterization and friction model of a linear-moter rollingguide stage[J].Journal of East China University of Science and Technology:Natural Science Edition,2017,43(4):571-577.(in Chinese)
[7]KATO H.Characteristic analysis on an extended dahl model for planar two-dimensional motion[J].Journal of the Japan Society for Precision Engineering,2017,83(6):607-612.
[8]于伟,马佳光,李锦英,等.基于LuGre模型实现精密伺服转台摩擦参数辨识及补偿[J].光学精密工程,2011,19(11):2736-2743.YU W,MA J G,LI J Y,et al..Friction parameter identification and friction compensation for precision servo turning table[J].Opt.Precision Eng.,2011,19(11):2736-2743.(in Chinese)
[9]晋超琼,张葆,李贤涛,等.基于LuGre模型的航空光电稳定平台的摩擦力矩补偿[J].科学技术与工程,2016,16(30):103-107.JIN CH Q,ZHANG B,LI X T,et al..Friction compensation of aerial photoelectrical stabilized platform based on the LuGre model[J].Science Technology and Engineering,2016,16(30):103-107.(in Chinese)
[10]郭鹏飞,邓永停,王帅,等.基于摩擦模型的反演滑模控制在大型望远镜上的应用[J].光学精密工程,2017,25(10):2620-2626.GUO P F,DENG Y T,WANG SH,et al..Backstepping sliding mode control of large telescope based on friction model[J].Opt.Precision Eng.,2017,25(10):2620-2626.(in Chinese)
[11]YEH S S,SU H C.Development of friction identification methods for feed drives of CNC machine tools[J].The International Journal of Advanced Manufacturing Technology,2010,52(1):263-278.
[12]姜振海,徐思晨,谷东伟,等.基于区间分析理论的摩擦补偿研究[J].光学精密工程,2017,25(6):1519-1525.JIANG ZH H,XU S CH,GU D W,et al..Research on friction compensation based on interval analysis[J].Opt.Precision Eng.,2017,25(6):1519-1525.(in Chinese)
[13]曾德林,肖凯,林竹翀,等.航空遥感惯性稳定平台LuGre摩擦参数的分步辨识[J].光学精密工程,2016,24(5):1148-1158.ZENG D L,XIAO K,LIN ZH CH,et al..Substep identification of LuGre friction parameters of inertially stabilized platform for airborne remote sensing[J].Opt.Precision Eng.,2016,24(5):1148-1158.(in Chinese)
[2]ASTROM K J,CANUDAS-DE-WIT C.Revisiting the LuGre friction model stick-slip motion and rate dependence[J].IEEE Control Systems Magazine,2008,28(6):101-114.
[3]PENNESTRI E,ROSSI V,SALVINI P,et al..Review and comparison of dry friction force models[J].Nonlinear Dynamics,2015,83(4):1785-1801.
[4]王延忠,郭超,贾树王,等.基于Stribeck摩擦模型的盘式摩擦副稳定性分析[J].中国机械工程,2017,28(21):2521-2525.WANG Y ZH,GUO CH,JIA SH W,et al..Stability analysis of disc friction pairs based on Stribeck model[J].China Mechanical Engineering,2017,28(21):2521-2525.(in Chinese)
[5]CONG S,DENG K,SHANG W,et al..Isolation control for inertially stabilized platform based on nonlinear friction compensation[J].Nonlinear Dynamics,2015,84(3):1123-1133.
[6]陈浩,孟健,安琦.直线电机滑台摩擦特性和摩擦模型[J].华东理工大学学报:自然科学版,2017,43(4):571-577.CHEN H,MENG J,AN Q.Friction characterization and friction model of a linear-moter rollingguide stage[J].Journal of East China University of Science and Technology:Natural Science Edition,2017,43(4):571-577.(in Chinese)
[7]KATO H.Characteristic analysis on an extended dahl model for planar two-dimensional motion[J].Journal of the Japan Society for Precision Engineering,2017,83(6):607-612.
[8]于伟,马佳光,李锦英,等.基于LuGre模型实现精密伺服转台摩擦参数辨识及补偿[J].光学精密工程,2011,19(11):2736-2743.YU W,MA J G,LI J Y,et al..Friction parameter identification and friction compensation for precision servo turning table[J].Opt.Precision Eng.,2011,19(11):2736-2743.(in Chinese)
[9]晋超琼,张葆,李贤涛,等.基于LuGre模型的航空光电稳定平台的摩擦力矩补偿[J].科学技术与工程,2016,16(30):103-107.JIN CH Q,ZHANG B,LI X T,et al..Friction compensation of aerial photoelectrical stabilized platform based on the LuGre model[J].Science Technology and Engineering,2016,16(30):103-107.(in Chinese)
[10]郭鹏飞,邓永停,王帅,等.基于摩擦模型的反演滑模控制在大型望远镜上的应用[J].光学精密工程,2017,25(10):2620-2626.GUO P F,DENG Y T,WANG SH,et al..Backstepping sliding mode control of large telescope based on friction model[J].Opt.Precision Eng.,2017,25(10):2620-2626.(in Chinese)
[11]YEH S S,SU H C.Development of friction identification methods for feed drives of CNC machine tools[J].The International Journal of Advanced Manufacturing Technology,2010,52(1):263-278.
[12]姜振海,徐思晨,谷东伟,等.基于区间分析理论的摩擦补偿研究[J].光学精密工程,2017,25(6):1519-1525.JIANG ZH H,XU S CH,GU D W,et al..Research on friction compensation based on interval analysis[J].Opt.Precision Eng.,2017,25(6):1519-1525.(in Chinese)
[13]曾德林,肖凯,林竹翀,等.航空遥感惯性稳定平台LuGre摩擦参数的分步辨识[J].光学精密工程,2016,24(5):1148-1158.ZENG D L,XIAO K,LIN ZH CH,et al..Substep identification of LuGre friction parameters of inertially stabilized platform for airborne remote sensing[J].Opt.Precision Eng.,2016,24(5):1148-1158.(in Chinese)