,460 北京科技大学学报 第30卷 mal preview servo systems and optimal preview FF compensated 5.0 systems.Chin JAutom,1998.10(4):329 4.0 [2]KatayamaT,Ohki T.Inoue T,et al.Design of an optimal con- 一S=4输出y troller for a discrete time system subject to preview able demand. 3.0 一一S-8,输出y Int J Control.1985.3:677 一目标R() [3]Katayama T,Hirono T.Design of an optimal servomechanism 20 with preview action and its dual problem.Int JControl,1987.2: 407 1.0 [4]EgamiT,TsuchiyaT.Disturbance suppression control with pre 0 view action of linear DC brushless motor.IEEE Trans Ind Elee- 21 25 的 29 trom,1995,42(5):494 t/s [5]TsuchiyaT.Egami T.Digital Preview and Predictive Control. 图2两种情形闭环系统输出响应 Translated by Liao FC.Beijing:Beijing Science and Technology Fig.2 Closed-loop responses (preview steps:8 and 16) Press:1994 (土谷武士,江上正,最新自动控制技术一数字预见控制 0, t<20 廖福成,译.北京:北京科学技术出版社,1994) R(t)=0.5(t-20),20≤t<30 [6]Liao F C.Egami T,Tsuchiya T.A general frequency dependent 5, t≥30 digital optimal preview servo system.Appl Math Mech.1996.17 仍采样周期取为0.1s,针对预见步数为16(S=8) (4):319 和没有预见的情况,仿真结果如图3所示 [7]Choi C,Tsao T C.Hoo preview control for diserete time sys tems.J Dyn Syst Meas Control.2001.123(1):117 5.0 [8]Choi C.Kim JS,Lee G.Design of an Hoo-based preview con troller//Proceeding of European Control Conference.Brussels. 4.0 1997,1. 30 [9]Xia J.Multirate Digital Control Systems.Beijing:Science Press, 2003 2.0 (肖建.多采样率数字控制系统。北京:科学出版社,2003) 一S-0.输出y --S8.输出y [10]Zhong M Y.Ma C F,Liu Y X.Fast rate detection filter for 1.0 目标R() multirate sampled-date systems.Acta Autom Sin.2006.32 (3),433 20 25 30 35 [11]Polushin I G.Marquez H J.Multirate versions of sampled-date tis stabilization of nonlinear systems.Automatica.2004.40:1035 [12]Liao F C.Takaba K,Katayama T,et al.Design of an optimal 图3对斜坡信号的跟踪 preview servomechanism for discrete time systems in a multirate Fig.3 Tracking to the ramp signal setting Dyn Continuous Discrete Impulsive Syst B.2003.10. 6结论 727 [13]Liao F C.Liu HP.Design of an optimal preview controller for a kind 本文研究了带有状态时滞的多采样率离散时间 of discrete time systems.J Unin Sci Technol Beijing.2007.29(5): 线性系统的预见控制问题,首先利用离散时间系统 5M2 提升技术,把所研究的系统转化成一个形式上没有 (廖福成,刘贺平.多重采样离散时间系统的最优预见伺服控 制器设计,北京科技大学学报,2007,29(5):542) 时滞且是单一采样系统,其状态向量的维数比原系 [14]Xu Y J.Liao FC.Design of the optimum preview controller for 统要大一些;然后利用预见控制理论中常用的误差 a class of state-delay systems.J Univ Sci Technol Beijing, 系统方法,构造一个扩大误差系统,而且问题也转换 2006,28(4):403 为调节器设计问题;最后利用预见控制的相关理论 (徐玉洁,廖福成。一类状态时滞系统的最优预见控制器设 设计出了最优控制器.由预见控制理论知所得到的 计.北京科技大学学报,2006,28(4):403) 闭环系统包含一个积分器,从而系统的响应没有静 [15]Tangirala A K.Li D.Patwardhan R.et al.Issues in multirate process contro Proceeding of American Control Conference 态误差,通过数值仿真说明了控制器的有效性, San Diego.1999:2771 [16]Kailath T.Linear Systems.Englewood Cliffs:Prentice-Hall, 参考文献 1980 [1]Liao F C.TsuchiyaT.Egami T.et al.Unified approach to opti-图2 两种情形闭环系统输出响应 Fig.2 Closed-loop responses (preview steps:8and16) R( t)= 0 t<20 0∙5( t—20) 20≤t<30 5 t≥30 仍采样周期取为0∙1s针对预见步数为16( S=8) 和没有预见的情况仿真结果如图3所示. 图3 对斜坡信号的跟踪 Fig.3 Tracking to the ramp signal 6 结论 本文研究了带有状态时滞的多采样率离散时间 线性系统的预见控制问题.首先利用离散时间系统 提升技术把所研究的系统转化成一个形式上没有 时滞且是单一采样系统其状态向量的维数比原系 统要大一些;然后利用预见控制理论中常用的误差 系统方法构造一个扩大误差系统而且问题也转换 为调节器设计问题;最后利用预见控制的相关理论 设计出了最优控制器.由预见控制理论知所得到的 闭环系统包含一个积分器从而系统的响应没有静 态误差.通过数值仿真说明了控制器的有效性. 参 考 文 献 [1] Liao F CTsuchiya TEgami Tet al.Unified approach to opt-i mal preview servo systems and optimal preview FF compensated systems.Chin J A utom199810(4):329 [2] Katayama TOhki TInoue Tet al.Design of an optimal controller for a discrete-time system subject to previewable demand. Int J Control19853:677 [3] Katayama THirono T.Design of an optimal servomechanism with preview action and its dual problem.Int J Control19872: 407 [4] Egami TTsuchiya T.Disturbance suppression control with preview action of linear DC brushless motor.IEEE T rans Ind Electron199542(5):494 [5] Tsuchiya TEgami T.Digital Preview and Predictive Control. Translated by Liao F C.Beijing:Beijing Science and Technology Press1994 (土谷武士江上正.最新自动控制技术———数字预见控制. 廖福成译.北京:北京科学技术出版社1994) [6] Liao F CEgami TTsuchiya T.A general frequency dependent digital optimal preview servo system.Appl Math Mech199617 (4):319 [7] Choi CTsao T C. H∞ preview control for discrete-time systems.J Dyn Syst Meas Control2001123(1):117 [8] Choi CKim J SLee G.Design of an H∞-based preview controller∥ Proceeding of European Control Conference.Brussels 1997:1. [9] Xiao J. Multirate Digital Control Systems.Beijing:Science Press 2003 (肖建.多采样率数字控制系统.北京:科学出版社2003) [10] Zhong M YMa C FLiu Y X.Fast rate detection filter for multirate sampled-date systems. Acta A utom Sin200632 (3):433 [11] Polushin I GMarquez H J.Multirate versions of sampled-date stabilization of nonlinear systems.A utomatica200440:1035 [12] Liao F CTakaba KKatayama Tet al.Design of an optimal preview servomechanism for discrete-time systems in a multirate setting.Dyn Continuous Discrete Impulsive Syst B200310: 727 [13] Liao F CLiu H P.Design of an optimal preview controller for a kind of discrete-time systems.J Univ Sci Technol Beijing200729(5): 542 (廖福成刘贺平.多重采样离散时间系统的最优预见伺服控 制器设计.北京科技大学学报200729(5):542) [14] Xu Y JLiao F C.Design of the optimum preview controller for a class of state-delay systems. J Univ Sci Technol Beijing 200628(4):403 (徐玉洁廖福成.一类状态时滞系统的最优预见控制器设 计.北京科技大学学报200628(4):403) [15] Tangirala A KLi DPatwardhan Ret al.Issues in multirate process control∥ Proceeding of A merican Control Conference. San Diego1999:2771 [16] Kailath T.Linear Systems.Englewood Cliffs:Prentice-Hall 1980 ·460· 北 京 科 技 大 学 学 报 第30卷