迭代学习控制在活塞异型加工中的应用研究
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摘要
活塞是发动机的核心部件,其外圆截面为非圆亦被称为异型截面。普通车削无法实现异型车削,专用伺服刀架可进行异型车削,但对于截面形状复杂的活塞,加工误差较大,无法满足设计精度要求。
在现有异型外圆加工设备的基础上,本文提出一种改进策略,旨在提高其加工复杂截面的精度。迭代学习控制是智能控制领域的一个重要分支,对于重复或类重复问题具有学习功能,其良好特性对于具有类重复性质的活塞异型截面加工,可有效提高伺服刀架跟踪精度,进而有效提高复杂截面的加工精度。
本文介绍了活塞异型外圆数控加工的基本原理,活塞截面数据特性和现有伺服刀架的基本控制方法。针对现有伺服刀架加工复杂活塞频响不足、精度较低的问题,提出了基于迭代学习控制的改进策略并给出了实现流程。介绍了迭代学习算法的基本原理,详细介绍了预期迭代学习控制及反馈前馈迭代学习控制算法,通过MATLAB数值仿真证明了迭代学习算法应用于活塞加工的可行性。对学习前活塞加工测量数据进行离线反馈前馈迭代学习控制,修正伺服刀架的控制输入数据并进行了再加工,对比了迭代学习控制前后的加工误差。在800r/min的转速下,利用迭代学习控制对复杂活塞外圆进行数控车削,最大误差由原来的0.0248mm大幅度减小到0.0086mm。实验结果表明,所应用的迭代学习控制算法能有效提高复杂截面活塞的加工精度,控制算法简单、实用,可行性强。
本文的工作对于提高复杂异型截面活塞的加工精度具有较高的理论价值与应用价值。
Piston is the one of the core part of the engine. The cross section of the piston is usually noncircular, which can’t be machined by the conventional lathe but can be realized by the special servo tool. However the tolerance of the machined part is often large if the cross section is very complicated.
A modified control strategy to improve the machining precision of complicated cross section is put forward in this dissertation based on the existing noncircular cylindrical piston numerical-control equipment. Iterative learning control, an important branch of intelligent control area, which has the learning ability for iterative problems or the analogy ones, is used to improve tracking precision for an iterative signal, as the process of the piston noncircular turning has the property of analogy iteration. As a result, the machining precision of the piston can be improved. The main contents are as follows:
Firstly, the basic noncircular section piston process principle was introduced, and the character of typical piston section data is analyzed. At the same time, the basic control method for the existing servo tool-post is also present. Secondly, aim at the limited frequency band of the servo tool-post and its low precision, an improved control strategy of iterative learning control with its realization flow is put forward. Thirdly, the basic iterative learning control principle is introduced, and the anticipatory iterative learning control and learning feed-back and feed-forward control are presented in detail. The MATLAB program numerical simulation shows the feasibility for the iterative learning control scheme to be used for the machining of piston. Fourthly, the process data is modified by the off-line learning feed-back and feed-forward control. Applying iterative learning control to complex section piston numerical control machining, maximum error could be decreased from 0.0248mm to 0.0086mm in the case of 800rmp. This result show that the machining precision was efficiently improved after the process data was modified by iterative learning control strategy.
Briefly, the research in the paper will help the precision improvement of complicated noncircular section piston machining.
在现有异型外圆加工设备的基础上,本文提出一种改进策略,旨在提高其加工复杂截面的精度。迭代学习控制是智能控制领域的一个重要分支,对于重复或类重复问题具有学习功能,其良好特性对于具有类重复性质的活塞异型截面加工,可有效提高伺服刀架跟踪精度,进而有效提高复杂截面的加工精度。
本文介绍了活塞异型外圆数控加工的基本原理,活塞截面数据特性和现有伺服刀架的基本控制方法。针对现有伺服刀架加工复杂活塞频响不足、精度较低的问题,提出了基于迭代学习控制的改进策略并给出了实现流程。介绍了迭代学习算法的基本原理,详细介绍了预期迭代学习控制及反馈前馈迭代学习控制算法,通过MATLAB数值仿真证明了迭代学习算法应用于活塞加工的可行性。对学习前活塞加工测量数据进行离线反馈前馈迭代学习控制,修正伺服刀架的控制输入数据并进行了再加工,对比了迭代学习控制前后的加工误差。在800r/min的转速下,利用迭代学习控制对复杂活塞外圆进行数控车削,最大误差由原来的0.0248mm大幅度减小到0.0086mm。实验结果表明,所应用的迭代学习控制算法能有效提高复杂截面活塞的加工精度,控制算法简单、实用,可行性强。
本文的工作对于提高复杂异型截面活塞的加工精度具有较高的理论价值与应用价值。
Piston is the one of the core part of the engine. The cross section of the piston is usually noncircular, which can’t be machined by the conventional lathe but can be realized by the special servo tool. However the tolerance of the machined part is often large if the cross section is very complicated.
A modified control strategy to improve the machining precision of complicated cross section is put forward in this dissertation based on the existing noncircular cylindrical piston numerical-control equipment. Iterative learning control, an important branch of intelligent control area, which has the learning ability for iterative problems or the analogy ones, is used to improve tracking precision for an iterative signal, as the process of the piston noncircular turning has the property of analogy iteration. As a result, the machining precision of the piston can be improved. The main contents are as follows:
Firstly, the basic noncircular section piston process principle was introduced, and the character of typical piston section data is analyzed. At the same time, the basic control method for the existing servo tool-post is also present. Secondly, aim at the limited frequency band of the servo tool-post and its low precision, an improved control strategy of iterative learning control with its realization flow is put forward. Thirdly, the basic iterative learning control principle is introduced, and the anticipatory iterative learning control and learning feed-back and feed-forward control are presented in detail. The MATLAB program numerical simulation shows the feasibility for the iterative learning control scheme to be used for the machining of piston. Fourthly, the process data is modified by the off-line learning feed-back and feed-forward control. Applying iterative learning control to complex section piston numerical control machining, maximum error could be decreased from 0.0248mm to 0.0086mm in the case of 800rmp. This result show that the machining precision was efficiently improved after the process data was modified by iterative learning control strategy.
Briefly, the research in the paper will help the precision improvement of complicated noncircular section piston machining.
引文
[1] Stefan R,James F.C.Design and testing of a long-range,precision fast tool servo system for diamond turning[J].Precision Engineering 33 (2009),18~25.
[2] WU D,CHEN K,WANG X K.Tracking control and active disturbance rejection with application to noncircular machining[J].International Journal of Machine Tools & Manufacture,2007,(47):2207~2217.
[3] Adam A.C,Hiram A.F,Matthew T.B,etc.Workpiece dynamic analysis and prediction during chatter of turning process[J].Mechanical Systems and Signal Processing.2008(22):1481~1494.
[4]孙明轩,黄宝健.迭代学习控制[M].北京:国防工业出版社,1999.
[5]孙永强,冯之敬,赵广木.国内活塞异形外圆车削加工技术的现状[J].机械工程师,2002,3:7~9.
[6]朱更红,谌国权.活塞异型销孔的数控加工技术[J].内燃机配件,2002,3:27~28.
[7]李小弟.镗削活塞异型销孔[J].内燃机配件,2001.
[8]王先逵,刘金凌,张静荣,周惠兴.活塞数控车床刀具伺服系统的补偿控制[J].中国机械工程,1996年第6期.
[9] David M.Alter,Tsu-Chin Tsao.Optimal Feedfword Tracking Control of Linear Motor Machine Tool Drives[J].Proceeding of the 1995 American Control Conference,210-214.
[10] M . Tomizuka . Zeros Phase Error Tracking Algorithm for Digital Control[J].Journal of Dynamic Systems,Measurement and Control March 1987,Vol.109,65-68.
[11]谢胜利,田森平,谢振东.迭代学习控制的理论与应用[J].北京:科学出版社,2005.
[12]李新忠,简林柯,何诚.迭代学习控制的研究及应用[J].机床与液压,1997,6:3~5.
[13] Lee,T.H.,Tan,K.K.Lim.S.Y,& Dou,H.F.Iterative learning control of permanent magnet linear motor with relay automatic tuning[J].Mechatronics.2000,10,169~190.
[14] Choi,J.Y,& Do,H..M.A learning approach of wafer temperature control in a rapid thermal processing system[J].IEEE Transactions on Semiconductor Manufacturing,2001,14(1),1~10.
[15] Lee,K.S,Chin,S,& Lee,H.J.Model predictive control technique combinedwith iterative learning for batch processes[J].AIChE Journal,1999,45(10),2175~2187.
[16] Uchiyama M.Formulation of high-speed motion pattern of a mechanical arm by trial[J].Transactions of the Society of Instrumentation and Control Engineers,1978,14(6):706~712.
[17] Arimoto S,Kawamura S and Miyazaki F.Bettering operation of robots by learning[J].Journal of Robotic Systems,1984,1(2):123~140.
[18] Arimoto S,Kawamura S,Miyazaki F and Tamaki S.Learning control theory for dynamical systems[J].In:Proceedings of 24th IEEE Conference on Decision and Control,Ft. Lauderdale, FL,1985,3:1375~1380.
[19] Arimoto S,Kawamura S and Miyazaki F.Bettering operation of dynamic system by learning : A new control theory for servomechanism and mechatronics sys[A].In: Proceedings of 23th IEEE Conference on Decision and Control,,Las Vegas,1984,NV,1064~1069.
[20]谢振东,刘永清,分布参数系统目标跟踪的二阶P型学习算法[J].暨南大学学报,1998,19(1):60~64.
[21]田森平,谢胜利,傅予力.连续非线性系统的迭代学习控制算法[J].中山大学学报,2000,39(6):313~317.
[22]谢胜利,谢振东,田森平.非线性系统的迭代学习控制及其算法实现[J].控制理论与应用,2002,19(2):167~173.
[23] Tayebi A,and Zaremba MB.Iterative learning control for non-linear systems described by a blended multiple model representation[J].International Journal of control,200,75(16):1376~1384.
[24]谢振东,谢胜利,韦岗.非线性学习控制理论及其在机器人系统上的应用[A].中国控制会议文集,北京:国防大学出版社,1998,957~961.
[25] Tian Senping,Xie shengli.A nonlinear Algorithm of Iterative Learning Control Based on Vector Plots Analysis[A].Proceedings of the Second International Symposium on Intelligent and Complex Systems,Wuhan,china,October 2001:17~20.
[26]田森平,谢胜利,傅予力.一种新的迭代学习控制快速算法[J].华南理工大学学报,2002,30(5):37~40.
[27] Qu Z.An iterative learning algorithm for boundary control of a stretched moving string[J].Automatica,2002,38(5):821~827.
[28] Xie Shengli and Tian Senping.A Fast Algorithm of Iterative Learning ControlBased on the Geometric Analysis[J].Proceedings of the 2002 International Conference on Control and Automation approaches.Automatica,2002,38(11):563~594.
[29]谢胜利,田森平,谢振东.基于几何分析的迭代学习控制快速算法[J].控制理论与应用,2003,20(3):419~422.
[30] Xu JX,Tan Y.Robust optimal design and convergence properties analysis of iterative learning control approaches[J].Automatica,2002,38(11):1867-1880.
[31]谢振东.非线性迭代学习控制理论及其在机器人控制上的应用[D].华南理工大学博士学位论文,2000.
[32]孙志毅,丁伟东,吴聚华.D型闭环迭代学习控制的2-D模型及收敛分析[J].太原重型机械学院学报,2002,23(3):191~194.
[33]田森平.迭代学习控制快速算法及计算机仿真[J].华南理工大学博士后研究报告,2001.
[34]于少娟,齐向东,吴聚华.迭代学习控制理论及应用[M].北京:机械工业出版社,2005.07.
[35] Kawamura S,Miyazaki F and Arimoto S.Realization of robot motion based on a learning method[J].IEEE Transactions on System,Man ,and Cybernetics,1988,18(1):126~134.
[36] Naniwa T and Arimoto S.Learning control for robot tasks under geometric endpoint constrains[J].IEEE Transactions on Robotics and Automation,1995,11(3):432~342.
[37] Arimoto S.Learning control theory for robotic motion[J].International Journal of Adaptive Control and signal Processing.1990,4(6):543~564.
[38] Heinzinger G,Fenwick D,Paden B and Miyazaki F.Stability of learning control with disturbances and uncertain Initial conditions[J].IEEE Transactions on Automatic Control,1992,37(1):49~59.
[39] Lee HS and Bien Z.Study on robustness of iterative learning control with non-zero initial error[J].International Journal of Control,1996,64(3):345~359.
[40]刘志学,吴丽娟.模糊迭代学习在单关节机器人运动控制中的应用[J].辽宁科技大学学报,2009,08(4):378~382.
[41]张茜,黄越洋.基于滑膜变结构的迭代学习控制器算法[J].科学技术与工程,2009,9(11):3093~3095.
[42]李昆仑,胡小明.一种改进型BP算法在自适应控制系统中应用的研究[J].自动化仪表2001,12(12):15~18.
[43]杨国华.神经网络离散建模算法在迭代学习控制中的应用[J].科技通报,2003,11(6):470~472.
[44]逄振旭,李从心.迭代学习PID控制器在液压系统中的应用[J].机械工程学报,2001,37(4):103~1051.
[45] Geng Z,Carroll R,Janmshidi M,et al.An adaptive learning control approach with application to water tankl evel control[J].Contr.Theory Advanced Tech.1992,8(3):577~592.
[46] Pandit M and Buchheit K H.Optimizing Iterative learning control of cyclic production process with application to extruders[J].IEEE Trars.Contr.Tech.,1999,7(3):382~390.
[47]曹阳,沈毅力,李天石.加速闭环P型迭代学习在电液伺服协调加载系统中的应用[J].机床与液压,2000(5):38~39.
[48] WU Huaiyu,ZHOU Zhaoying ang Xiong Shanshu,D-Type Iterative learning control with Application to FNS limb motion control system[J].Control theory and Applications,2001,13(3):410~413.
[49]姚仲舒,杨成梧.迭代学习控制烟叶发酵系统中的应用[J].自动化仪表,2002(12):41~43.
[50] SHAO Cheng,GAO Fu Rong,YANG Yi.Robust Stability of Optimal Iterative learning Control and Applica2tion to Injection Molding Machine[J] . Acta Automatica Sinica,2003,29(1):73~79.
[51] Qian W,Panda S K.Xu J-X.Speed ripp le minimization in PM synchronous motors using iterative learning control[J].IEEE Trans,on Energy Conversion,2005,20(1):53~61.
[52]吴晓峰.坐标测量机迭代学习控制研究[J].自动化学报,1994,20(5):637~639.
[53]陈志华.非圆截面零件车削控制研究[D].国防科学技术大学博士学位论文,2000,5.
[54]陈志华,崔红娟.活塞外圆智能加工系统[J].机械科学与技术,1998.5.
[55]程超.伺服刀架频率特性分析与测试[D].国防科学技术大学硕士论文.2009.
[56]刘政华,何将三,龙佑喜,张耀辉,廖平著.机械电子学[M].长沙:国防科技大学出版社,1999,10.
[57] Wang D W.On D-type and P-type ILC designs and anticipatory approach [J].Int.J.Contr,2000,73(10):890~901.
[58] Sun M X,Wang D W.Anticipatory iterative learning control for nonlinear systems with arbitrary relative degree[J].IEEE Trans.Auot.Contr,2001,46(5):783~788.
[59] Sun M X,Wang D W.Higher relative degree nonlinear systems with ILC using lower-order differentiations [J].Asian journal of Control (Special Issue:Iterative Learning Control),2002,4(1):38~48.
[60]皮道映,孙优贤.非线性时变系统开闭环P型迭代学习控制的收敛性[J].自动化学报,1999,25(3):351~354.
[61]于乃润,万百五.工业过程稳态优化中的迭代学习控制[J].控制理论与应用,1996,12(13):717~722.
[62] Wang D W,Ye Y Q.Design and experiments of anticipatory learning control:frequency domain approach[J].IEEE/ASME Transactions on mechatronics,2004,1(11):1~6.
[63] P.Scholten.Iterative Learning Control A Design for a Linear Motor Motion System[J].M.Sc.Thesis,2000.
[2] WU D,CHEN K,WANG X K.Tracking control and active disturbance rejection with application to noncircular machining[J].International Journal of Machine Tools & Manufacture,2007,(47):2207~2217.
[3] Adam A.C,Hiram A.F,Matthew T.B,etc.Workpiece dynamic analysis and prediction during chatter of turning process[J].Mechanical Systems and Signal Processing.2008(22):1481~1494.
[4]孙明轩,黄宝健.迭代学习控制[M].北京:国防工业出版社,1999.
[5]孙永强,冯之敬,赵广木.国内活塞异形外圆车削加工技术的现状[J].机械工程师,2002,3:7~9.
[6]朱更红,谌国权.活塞异型销孔的数控加工技术[J].内燃机配件,2002,3:27~28.
[7]李小弟.镗削活塞异型销孔[J].内燃机配件,2001.
[8]王先逵,刘金凌,张静荣,周惠兴.活塞数控车床刀具伺服系统的补偿控制[J].中国机械工程,1996年第6期.
[9] David M.Alter,Tsu-Chin Tsao.Optimal Feedfword Tracking Control of Linear Motor Machine Tool Drives[J].Proceeding of the 1995 American Control Conference,210-214.
[10] M . Tomizuka . Zeros Phase Error Tracking Algorithm for Digital Control[J].Journal of Dynamic Systems,Measurement and Control March 1987,Vol.109,65-68.
[11]谢胜利,田森平,谢振东.迭代学习控制的理论与应用[J].北京:科学出版社,2005.
[12]李新忠,简林柯,何诚.迭代学习控制的研究及应用[J].机床与液压,1997,6:3~5.
[13] Lee,T.H.,Tan,K.K.Lim.S.Y,& Dou,H.F.Iterative learning control of permanent magnet linear motor with relay automatic tuning[J].Mechatronics.2000,10,169~190.
[14] Choi,J.Y,& Do,H..M.A learning approach of wafer temperature control in a rapid thermal processing system[J].IEEE Transactions on Semiconductor Manufacturing,2001,14(1),1~10.
[15] Lee,K.S,Chin,S,& Lee,H.J.Model predictive control technique combinedwith iterative learning for batch processes[J].AIChE Journal,1999,45(10),2175~2187.
[16] Uchiyama M.Formulation of high-speed motion pattern of a mechanical arm by trial[J].Transactions of the Society of Instrumentation and Control Engineers,1978,14(6):706~712.
[17] Arimoto S,Kawamura S and Miyazaki F.Bettering operation of robots by learning[J].Journal of Robotic Systems,1984,1(2):123~140.
[18] Arimoto S,Kawamura S,Miyazaki F and Tamaki S.Learning control theory for dynamical systems[J].In:Proceedings of 24th IEEE Conference on Decision and Control,Ft. Lauderdale, FL,1985,3:1375~1380.
[19] Arimoto S,Kawamura S and Miyazaki F.Bettering operation of dynamic system by learning : A new control theory for servomechanism and mechatronics sys[A].In: Proceedings of 23th IEEE Conference on Decision and Control,,Las Vegas,1984,NV,1064~1069.
[20]谢振东,刘永清,分布参数系统目标跟踪的二阶P型学习算法[J].暨南大学学报,1998,19(1):60~64.
[21]田森平,谢胜利,傅予力.连续非线性系统的迭代学习控制算法[J].中山大学学报,2000,39(6):313~317.
[22]谢胜利,谢振东,田森平.非线性系统的迭代学习控制及其算法实现[J].控制理论与应用,2002,19(2):167~173.
[23] Tayebi A,and Zaremba MB.Iterative learning control for non-linear systems described by a blended multiple model representation[J].International Journal of control,200,75(16):1376~1384.
[24]谢振东,谢胜利,韦岗.非线性学习控制理论及其在机器人系统上的应用[A].中国控制会议文集,北京:国防大学出版社,1998,957~961.
[25] Tian Senping,Xie shengli.A nonlinear Algorithm of Iterative Learning Control Based on Vector Plots Analysis[A].Proceedings of the Second International Symposium on Intelligent and Complex Systems,Wuhan,china,October 2001:17~20.
[26]田森平,谢胜利,傅予力.一种新的迭代学习控制快速算法[J].华南理工大学学报,2002,30(5):37~40.
[27] Qu Z.An iterative learning algorithm for boundary control of a stretched moving string[J].Automatica,2002,38(5):821~827.
[28] Xie Shengli and Tian Senping.A Fast Algorithm of Iterative Learning ControlBased on the Geometric Analysis[J].Proceedings of the 2002 International Conference on Control and Automation approaches.Automatica,2002,38(11):563~594.
[29]谢胜利,田森平,谢振东.基于几何分析的迭代学习控制快速算法[J].控制理论与应用,2003,20(3):419~422.
[30] Xu JX,Tan Y.Robust optimal design and convergence properties analysis of iterative learning control approaches[J].Automatica,2002,38(11):1867-1880.
[31]谢振东.非线性迭代学习控制理论及其在机器人控制上的应用[D].华南理工大学博士学位论文,2000.
[32]孙志毅,丁伟东,吴聚华.D型闭环迭代学习控制的2-D模型及收敛分析[J].太原重型机械学院学报,2002,23(3):191~194.
[33]田森平.迭代学习控制快速算法及计算机仿真[J].华南理工大学博士后研究报告,2001.
[34]于少娟,齐向东,吴聚华.迭代学习控制理论及应用[M].北京:机械工业出版社,2005.07.
[35] Kawamura S,Miyazaki F and Arimoto S.Realization of robot motion based on a learning method[J].IEEE Transactions on System,Man ,and Cybernetics,1988,18(1):126~134.
[36] Naniwa T and Arimoto S.Learning control for robot tasks under geometric endpoint constrains[J].IEEE Transactions on Robotics and Automation,1995,11(3):432~342.
[37] Arimoto S.Learning control theory for robotic motion[J].International Journal of Adaptive Control and signal Processing.1990,4(6):543~564.
[38] Heinzinger G,Fenwick D,Paden B and Miyazaki F.Stability of learning control with disturbances and uncertain Initial conditions[J].IEEE Transactions on Automatic Control,1992,37(1):49~59.
[39] Lee HS and Bien Z.Study on robustness of iterative learning control with non-zero initial error[J].International Journal of Control,1996,64(3):345~359.
[40]刘志学,吴丽娟.模糊迭代学习在单关节机器人运动控制中的应用[J].辽宁科技大学学报,2009,08(4):378~382.
[41]张茜,黄越洋.基于滑膜变结构的迭代学习控制器算法[J].科学技术与工程,2009,9(11):3093~3095.
[42]李昆仑,胡小明.一种改进型BP算法在自适应控制系统中应用的研究[J].自动化仪表2001,12(12):15~18.
[43]杨国华.神经网络离散建模算法在迭代学习控制中的应用[J].科技通报,2003,11(6):470~472.
[44]逄振旭,李从心.迭代学习PID控制器在液压系统中的应用[J].机械工程学报,2001,37(4):103~1051.
[45] Geng Z,Carroll R,Janmshidi M,et al.An adaptive learning control approach with application to water tankl evel control[J].Contr.Theory Advanced Tech.1992,8(3):577~592.
[46] Pandit M and Buchheit K H.Optimizing Iterative learning control of cyclic production process with application to extruders[J].IEEE Trars.Contr.Tech.,1999,7(3):382~390.
[47]曹阳,沈毅力,李天石.加速闭环P型迭代学习在电液伺服协调加载系统中的应用[J].机床与液压,2000(5):38~39.
[48] WU Huaiyu,ZHOU Zhaoying ang Xiong Shanshu,D-Type Iterative learning control with Application to FNS limb motion control system[J].Control theory and Applications,2001,13(3):410~413.
[49]姚仲舒,杨成梧.迭代学习控制烟叶发酵系统中的应用[J].自动化仪表,2002(12):41~43.
[50] SHAO Cheng,GAO Fu Rong,YANG Yi.Robust Stability of Optimal Iterative learning Control and Applica2tion to Injection Molding Machine[J] . Acta Automatica Sinica,2003,29(1):73~79.
[51] Qian W,Panda S K.Xu J-X.Speed ripp le minimization in PM synchronous motors using iterative learning control[J].IEEE Trans,on Energy Conversion,2005,20(1):53~61.
[52]吴晓峰.坐标测量机迭代学习控制研究[J].自动化学报,1994,20(5):637~639.
[53]陈志华.非圆截面零件车削控制研究[D].国防科学技术大学博士学位论文,2000,5.
[54]陈志华,崔红娟.活塞外圆智能加工系统[J].机械科学与技术,1998.5.
[55]程超.伺服刀架频率特性分析与测试[D].国防科学技术大学硕士论文.2009.
[56]刘政华,何将三,龙佑喜,张耀辉,廖平著.机械电子学[M].长沙:国防科技大学出版社,1999,10.
[57] Wang D W.On D-type and P-type ILC designs and anticipatory approach [J].Int.J.Contr,2000,73(10):890~901.
[58] Sun M X,Wang D W.Anticipatory iterative learning control for nonlinear systems with arbitrary relative degree[J].IEEE Trans.Auot.Contr,2001,46(5):783~788.
[59] Sun M X,Wang D W.Higher relative degree nonlinear systems with ILC using lower-order differentiations [J].Asian journal of Control (Special Issue:Iterative Learning Control),2002,4(1):38~48.
[60]皮道映,孙优贤.非线性时变系统开闭环P型迭代学习控制的收敛性[J].自动化学报,1999,25(3):351~354.
[61]于乃润,万百五.工业过程稳态优化中的迭代学习控制[J].控制理论与应用,1996,12(13):717~722.
[62] Wang D W,Ye Y Q.Design and experiments of anticipatory learning control:frequency domain approach[J].IEEE/ASME Transactions on mechatronics,2004,1(11):1~6.
[63] P.Scholten.Iterative Learning Control A Design for a Linear Motor Motion System[J].M.Sc.Thesis,2000.