第5期 廖福成等：多重采样离散时间系统的最优预见伺服控制器设计 .547. with preview action and its dual problem.Int J Control,1987 6 结论 (2):407 本文研究了多重采样离散时间线性系统的预见 [5]Katayama T,Yamamoto H.Ogawa M.et al.A design of digital tracking controller in the presence of load change(in Japanese). 控制问题，并结合单一采样系统LQ预见控制方法 Trans Inst Syst Control Inform Eng.1992(3)111 和离散提升技术解决了这一问题，研究表明，这种 [6]土谷武士，江上正·最新自动控制技术一数字预见控制，廖 最优预见控制器的目标值信号预见和干扰信号预见 福成，译.北京：北京科学技术出版社，1994 补偿的系数矩阵是时变的和周期的，同时证明了在 [7]Liao F.Egami T.Tsuchiya T.A general frequency dependent 基本假设下这种最优控制器的存在性， digital optimal preview servo system.Appl Math Mech.1996.4 (17):319 参考文献 [8]Choi C,Tsao T C.Hoo preview control for discrete time sys- tems.J Dyn Syst Meas Control.2001.123(1):117 [1]Tomizuka M.Optimal continuous finite preview problem.IEEE [9]Liao F,Takaba K.Katayama T.et al.Design of an optimal pre- Trans Autom Control.1975.20(3):326 view servomechanism for discrete time systems in a multirate set- [2]Liao F.Tsuchiya T.EgamiT.et al.Unified approach to optimal ting Dyn Continuous Discrete Impulsive Syst Ser B.2003.10: preview servo systems and optimal preview FF compensated sys- 727 tems.Chin J Autom.1998.10(4):329 [10]Tangirala A K,Li D,Patwardhan R,et al.Issues in multirate [3]Katayama T,OhkiT,Inoue T,et al.Design of an optimal con- process control/Proe.of American Control Conf.San Diego. troller for a discretetime system subject to previewable demand. 1999,2771 Int J Control.1985(3):677 [11]Kailath T.Linear Systems.Englewood Cliffs:Prentice-Hall, [4]Katayama T,Hirono T.Design of an optimal servomechanism 1980 Design of an optimal preview controller for a kind of discrete time systems LIAO Fucheng),LIU Heping2) 1)Applied Science School.University of Science and Technology Beijing.Beijing 100083.China 2)Information Engineering School.University of Seience and Technology Beijing.Beijing 100083.China ABSTRACI A kind of linear discrete time system with multirate control setting was studied and a controller design method was presented for the system.By using discrete time lifting technique the multirate discrete time system was reduced to a single rate system.And then a discrete integrator was introduced by applying state vec- tors augmentation.Based on the standard linear quadratic optimal preview control theory,the desired preview controller was obtained. KEY WORDS preview control:sampling control;discrete-time lifting technique;algebraic Riccati equation; servomechanism6 结论 本文研究了多重采样离散时间线性系统的预见 控制问题‚并结合单一采样系统 LQ 预见控制方法 和离散提升技术解决了这一问题．研究表明‚这种 最优预见控制器的目标值信号预见和干扰信号预见 补偿的系数矩阵是时变的和周期的．同时证明了在 基本假设下这种最优控制器的存在性． 参 考 文 献 ［1］ Tomizuka M．Optimal continuous finite preview problem．IEEE Trans Autom Control‚1975‚20（3）：326 ［2］ Liao F‚Tsuchiya T‚Egami T‚et al．Unified approach to optimal preview servo systems and optimal preview FF compensated sys￾tems．Chin J Autom‚1998‚10（4）：329 ［3］ Katayama T‚Ohki T‚Inoue T‚et al．Design of an optimal con￾troller for a discrete-time system subject to previewable demand． Int J Control‚1985（3）：677 ［4］ Katayama T‚Hirono T．Design of an optimal servomechanism with preview action and its dual problem．Int J Control‚1987 （2）：407 ［5］ Katayama T‚Yamamoto H‚Ogawa M‚et al．A design of digital tracking controller in the presence of load change（in Japanese）． Trans Inst Syst Control Inform Eng‚1992（3）111 ［6］ 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 ［7］ Liao F‚Egami T‚Tsuchiya T．A general frequency dependent digital optimal preview servo system．Appl Math Mech‚1996‚4 （17）：319 ［8］ Choi C‚Tsao T C． H∞ preview control for discrete-time sys￾tems．J Dyn Syst Meas Control‚2001‚123（1）：117 ［9］ Liao F‚Takaba K‚Katayama T‚et al．Design of an optimal pre￾view servomechanism for discrete-time systems in a multirate set￾ting．Dyn Continuous Discrete Impulsive Syst Ser B‚2003‚10： 727 ［10］ Tangirala A K‚Li D‚Patwardhan R‚et al．Issues in multirate process control∥Proc．of American Control Conf．San Diego‚ 1999：2771 ［11］ Kailath T．Linear Systems．Englewood Cliffs：Prentice-Hall‚ 1980 Design of an optimal preview controller for a kind of discrete-time systems LIAO Fucheng 1‚2）‚LIU Heping 2） 1） Applied Science School‚University of Science and Technology Beijing‚Beijing100083‚China 2） Information Engineering School‚University of Science and Technology Beijing‚Beijing100083‚China ABSTRACT A kind of linear discrete-time system with multirate control setting was studied and a controller design method was presented for the system．By using discrete-time lifting technique the multirate discrete-time system was reduced to a single-rate system．And then a discrete integrator was introduced by applying state vec￾tors augmentation．Based on the standard linear quadratic optimal preview control theory‚the desired preview controller was obtained． KEY WORDS preview control；sampling control；discrete-time lifting technique；algebraic Riccati equation； servomechanism 第5期 廖福成等： 多重采样离散时间系统的最优预见伺服控制器设计 ·547·