Fig. 1 Th priodic signal gnrator / 1 Tds T d 2 K q s T d 2 r 2 Fig. 2 Th block diagram of th sstm basd on 3 th plugin tp rptitiv cont

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1 ELECTRI C MACHINES AND CONTROL Vol. 17 No. 2 Fb : 针对直线电机驱动的凸轮加工随动系统实际加工应用中, 要求系统既要对周期性输入信号具有跟踪能力, 又要对周期性扰动具有抑制能力对这一问题, 根据基于内模原理的重复控制理论设计实用性强的插入型重复控制器, 来消除由周期性输入的基波和谐波所引起的误差, 以便减小系统周期性稳态跟踪误差为进一步改善控制器的性能, 有效地增加运行带宽, 设计改进的插入型重复控制器, 减小系统的跟踪误差, 使得系统的跟踪性能得到更好的改善最后, 对直线伺服电机驱动的凸轮加工中心进行了仿真研究, 结果表明所提出的控制方案提高了系统跟踪性能和鲁棒性能, 既有效地抑制系统周期性扰动的影响, 又对周期性输入信号实现准确跟踪 : 直线伺服系统 ; 周期信号 ; 重复控制器 ; 插入型重复控制器 ; 跟踪误差 TP 273 A X Modifid rptitiv control of priodic input linar srvo sstm ZHAO Ximi 1 2 SUN Xianfng 1 LIU Hao 2 LI Hongi 2 1. School of Elctrical Enginring Shnang Univrsit of Tchnolog Shnang 1187 China 2. Shnang Institut of Automation Chins Acadm of Scincs Shnang 1116 China Abstract For cam machining driv sstm drivn b th linar motor in man machining applications gnrall th sstm has tracking abilit of a priodic trajctor and rjction abilit of a priodic disturbanc. According to th priodic motion charactristic of th linar motor srvo sstm a practical plugin tp rptitiv controllr as dsignd according to th rptitiv control thor basd on innr modl principl. It liminatd th sstm rror causd b th priodic input fundamntal av and harmonic av to rduc th sstm priodic stadstat tracking rror. In ordr to furthr improv th prformanc of th controllr and ffctivl incras th oprating bandidth a modifid plugin tp rptitiv controllr as dsignd. It rducd th tracking rror of th sstm and mad th sstm tracking prformanc improvd. Finall th linar srvo motor drivn cam machining cntr as studid and th simulation rsults sho that th proposd control schm improvs th sstm tracking prformanc and robust prformanc and ffctivl inhibits sstm priodic prturbation ffcts and accuratl track th priodic input signal. K ords linar srvo sstm priodic signal rptitiv controllr plugin tp rptitiv controllr tracking rror : 国家自然科学基金 ( ) ; 国家自然青年科学基金 ( ) ; 沈阳市科技计划项目 ( F ) : 赵希梅 ( 1979 ), 女, 博士, 副教授, 硕士生导师, 研究方向为直线伺服数控技术机器人控制 ; : 赵希梅孙显峰 ( 1985 ), 男, 硕士研究生, 研究方向为直线伺服鲁棒控制 ; 刘浩 ( 198 ), 男, 博士, 副研究员, 研究方向为机器人学 ; 李洪谊 ( 1972 ), 男, 博士, 研究员, 博士生导师, 研究方向为机器人控制与机器人学

2 Fig. 1 Th priodic signal gnrator / 1 Tds T d 2 K q s T d 2 r 2 Fig. 2 Th block diagram of th sstm basd on 3 th plugin tp rptitiv controllr 2 K s S s = 1 / 1 G p s K q s K q = 1 H 6 1 G p s K q s T d s = R ω = K q jω S jω 2 1 G p ωr ω < 1 K q S < 1 T d > 1 K q s 5 T d S s 2 1 r T = 1 / 1 Tds G p s /1 G p s S T s = 1 jkω n k = ± 1 ± 2 S = M S S jω s =1 K q s S s ω n = 2π /T d 3 K q = 1 r std K q(s) std

3 K q S < 1 K q jω s = 1 /M s 3 M s 1 S (j 棕 ) 2 7 1/M s K q(j 棕 ) τ q l kω n δ kω n u kω n X jkω n 1 kω n < 棕 s F ( 1 S 频率 ) u kω n = cos 1 jkω n 2 /2 [ 1 2R S jkω n S jkω n ] 3 K q s S s 槡 Im S Fig. 3 Frqunc rspons of K q s and S s tan 1 jkω n 1 R S jkω n 8 G q s ω s M S S s l kω n = u kω n 9 K q s K q s τ q max l kω n δ kω n min u kω n kω n < k k 2 s S^ r jkω n S jkω n X jkω n 2 s = S s X s 4 1 K q s st d X s = 1 S s K q s 5 st d X s kω n s 3 1 K q S kω n K q S 1 1 R S jkω n cosδ kω n Im S jkω n sinδ kω n 1 2 K q jkω n 1 S jkω n 2 X jkω n 1 S^ r jkω n S jkω n δ ω = arg K q jω 2 1 K q s K q s K q s τ q s K q s = ζ q = 槡 ω 2 q 2ζ qs 1 ( ) ω 2 s 2ζ 2 qω 2 2 s < ω4 s M 2 s 1 M 2 s 1 ω 2 s 2ζ 2 qω 2 s 槡 M 2 s 1 7 τ q 2 S jkω n kω n < 2 4 K q s K q S < 1 k > 2 k 2 S K q k 1 2 S K q k k k 2 τ q ζ q τ q ζ q = 槡 2 /2 K q 1 3 K q s 2

4 2 115 DSP 5 1 ms 4 τ b s T d τ b τ q s K b s K b s = τ b s τ b 子 bs r 4 Fig. 4 K q(s) std K b(s) Th block diagram of th sstm basd on th modifid plug in tp rptitiv controllr G p K q K b G p G p 1 T d s = 1 R^ ω = K q jω S^ jω 11 S^ jω = 1 K b jω G p jω 1 G p jω 12 T^ s = K b s G p s 1 G p s 13 K s G s G s = G V s /s K b s = τ b s T^ s = T s K =. 8 S^ γ = S s X^ s 14 X^ s = 1 K q s st d 15 1 S^ s st d X^ s S s K q s = K b s K q S^ K q S < 1 16 S^ jkω γ n S jkω n kω n < (Td 子 b 子 q)s 2 q r 5 Fig. 5 棕 2 灼 qs 棕 q 1 Th block diagram of th quivalnt modifid rptitiv control sstm G v s = 7. 32s 2. 4 K G P s = 4 Hz = 2π /T d = 2π /. 25 ω s = 22 Hz M s = K q s K b s ω 2 q. 138s 2ζ qs 1 = 21 Hz ζ q = 槡 2 2 K b s =. 1s

5 p/mm 6 Fig. 6 p/mm 输入指令跟踪误差输出响应 t/s Th sstm tracking rspons and rror curvs basd on th plugin tp rptitiv controllr for th ccloidal command 输入指令跟踪误差输出响应 t/s 5 CHEN C L CHIU G T C. Spatiall priodic disturbanc rjction 7 ith spatiall sampld robust rptitiv control J. ASME Journal of Dnamic Sstms Masurmnt and Control Fig. 7 Th sstm tracking rspons and rror curvs 11. basd on th improvd plugin tp rptitiv 6 CHEN S L HSIEH T H. Rptitiv control dsign and implmntation for linar motor machin tool J. Intrnational Journal of controllr for th ccloidal command Machin Tools and Manufactur TSAI M C YAO W S. Dsign of a plugin tp rptitiv controllr for priodic inputs J. IEEE Transactions on Control Sstms Tchnolog TAN K K LEE T H. Prcision motion control ith disturbanc obsrvr for puls idthmodulatddrivn prmanntmagnt linar motors J. IEEE Transactions on Magntics ANDREW W O MATTHEW A F. Dsigning robust rptitiv controllrs J. ASME Journal of Dnamic Sstms Masurmnt and Control YAO W S TSAI M C. Analsis and stimation of tracking rrors of plugin tp rptitiv control sstms J. IEEE Transactions on Automatic Control ( 编辑 : 刘素菊 )

64 4 ρ θ R X x X Y ε' XY X Y 曲率圆 XY 期望轨迹 Y (X o,y o) XY 切线 XY 着 R 2 Korn 兹 Crosscoupld O CNC 2 Fig. 2 Contour rror of arbitrar contour trajctor

64 4 ρ θ R X x X Y ε' XY X Y 曲率圆 XY 期望轨迹 Y (X o,y o) XY 切线 XY 着 R 2 Korn 兹 Crosscoupld O CNC 2 Fig. 2 Contour rror of arbitrar contour trajctor 4 9 2 9 ELECTRI C MACHINES AND CONTROL Vol. 4 No. 9 Sp. 2 XY 78 XY H ZPETC H ZPETC XY H TP 273 A 7 449X 2 9 63 6 Contour rror analsis and normal crosscoupld control for dirct driv XY tabl WANG LimiWU ZhitaoSUN