|
|
Research on 2-order Time-delay Systems Based on Iterative Learning Control |
ZHAN Yu-zhi1,LIANG Cheng-bin2,ZHANG Qing-fang1 |
1. Electrical Engineering College, Guizhou University, Guiyang, Guizhou 550025, China
2. College of Electrical and Information Engineering, Hunan University, Changsha, Hunan 410082, China |
|
|
Abstract For the process of systems characterized by 2-order delay differential equation, using the exact solution expressed by the delayed matrix sine and cosine an iterative learning control algorithm is designed to control the output of systems tracking to the desired output. A sufficient condition for output of delay systems converge to a given desired output with the increase number of iterations is given. And through iteration, the optimal control input can be obtained. The experimental results of the numerical simulation show that the designed iterative algorithm can make the output of the system converge to the desired output with the increase of the number of iterations, and the validity of the proposed method is verified.
|
|
|
|
|
|
[1]秦元勋, 刘永清, 王联, 等. 带有时滞的动力系统的运动稳定性[M]. 2版. 北京:科学出版社, 2017.
[2]刘彬, 姜甲浩, 刘飞, 等. 基于轧件水平振动的轧机辊系振动补偿模型[J]. 计量学报, 2018, 39(1): 56-60.
Liu B,Jiang J H, Liu F, et al. Compensative Vibration Model of Roll System Based on Horizontal Vibration of Rolled Piece[J]. Acta Metrologica Sinica, 2018, 39(1): 56-60.
[3]刘彬, 姜佳磊, 潘贵翔, 等. 基于吸振器控制的两自由度轧机辊系特性研究[J]. 计量学报, 2019, 40(5): 868-874.
Liu B, Jiang J L, Pan G X, et al. Research on Roller Characteristics of Two Degree of Freedom Rolling Mill Based on Vibration Absorber Control[J].Acta Metrologica Sinica, 2019, 40(5): 868-874.
[4]项国波. 时滞系统优化控制[M]. 北京: 中国电力出版社, 2009.
[5]梁坤, 张爱敏, 高小珣. 时间频率传递GPS接收机内延迟差分校准技术研究[J]. 计量学报, 2012, 33(1): 77-80.
Liang K, Zhang A M, Gao X X. Study on the Differential Calibration Techniques for the Internal Time Delays of the GPS Receivers for Time and Frequency Transfer[J]. Acta Metrologica Sinica. 2012, 33(1): 77-80.
[6]Omalley R E. Singular Perturbation Methods for Ordinary Differential Equations[M]. New York: Springer, 1991.
[7]Uchiyama M. Formation of High Speed Motion Pattern of Mechanical Arm by Trial[J]. Transactions of the Society of Instrument & Control Engineers, 1978, 14(6): 706-712.
[8]Arimoto S. Bettering Operation of Robots by Learning[J]. Journal of Robotic Systems, 1984, 1(2): 123-140.
[9]郝晓弘, 周勃. 非线性系统的改进型迭代学习控制算法研究[J]. 机械设计与制造, 2018, (6): 29-32.
Hao X H, Zhou B, Improved Iterative Learning Control Algorithm for Nonlinear Systems[J]. Machinery Design & Manufacture, 2018, (6): 29-32.
[10]陶洪峰, 沈建强, 杨慧中. 一类不确定性离散非线性重复过程的迭代学习容错控制[J]. 信息与控制, 2019, 48(1): 88-96.
Tao H F, Shen J Q, Yang H Z. Iterative Learning Fault-tolerant Control for a Class of Uncertain Nonlinear Discrete Repetitive Processes[J]. Information and Control. 2019, 48(1): 88-96.
[11]惠宇, 池荣虎. 基于迭代扩张状态观测器的数据驱动最优迭代学习控制[J]. 控制理论与应用, 2018, 35(11): 1672-1679.
Hui Y, Chi R H. Iterative Extended State Observer Based Data Driven Optimal Iterative Learning Control[J]. Control Theory & Applications, 2018, 35(11): 1672-1679.
[12]何凯, 林成涛, 李亮, 等. 电控机械式变速箱换档过程迭代学习控制[J]. 机械工程学报, 2019, 55(04): 84-90.
He K, Lin C T, Li L, et al. Iterative Learning Control for Gear Shifting Process in Electrical Mechanical Transmission [J]. Journal of Mechanical Engineering, 2019, 55(4): 84-90.
[13]Khusainov D Y, Diblík J, Ru°icˇková M, et al. Representation of a solution of the Cauchy problem for an oscillating system with pure delay[J]. Nonlinear Oscillations, 2008, 11(2): 276-285.
[14]Liang C, Wei W, Wang J. Stability of delay differential equations via delayed matrix sine and cosine of polynomial degrees[J]. Advances in Difference Equations, 2017, 131: 1-17. |
|
|
|