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A Study on a Novel Robust Repetitive Control Method

一种新型鲁棒重复控制方法的研究

基本信息

批准号：
14550452
负责人：
NAKANO Michio
金额：
$ 2.11万
依托单位：
TAKUSHOKU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2003
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14550452/
关键词：
Repetitive Control Periodic Input Elimination of Periodic Disturbance Learning Control Repetitive Controller Positive Feedback Infinity Gain Stability Circle ポジティブフィーバック無限大ゲイン

项目摘要

It is confirmed that the repetitive control proposed by author is extremely effective for trajectory control to the periodic input. It remains, however, an unsettled question how guarantee the stability of the control method, because that controller has a dea* element Accordingly, we have discussed the unsettled question in detail to overcome it question, and successfully found its solut developing novel repetitive control method which is able to change the stability domain in a complex plane without any additional outside the controller.For the usual repetitive control method, it has been forced that a vector locus of a controlled system must be kept within a stability domain of the controller which is a circle with a radius of 1 so that the repetitive control system is stable. That is an unsettled problem for the control method. The novel repetitive controller was developed that had forward transfer function e^<-jwL>/K instead of e^<-jwL> which was used for a usual repetitive controller and positive feedback with gain K. Since the frequency transfer function of the new controller becomes 1/K ・e^<-jwL>/(1-e^<-jwL>), the control system is not only extremely effective because of the infinity gain against periodic input or disturbance as usual, but also the system is always able to be kept stable because the stability domain of the control method is the domain within a circle with radius of K, center of (K, O) on complex plane. Therefore, the stability domain is changeable and, in an extreme case, the whole right area in a complex plane was able to be stable domain. Furthermore, whole complex domain can be able to be stable domain by rearrangement the elements in the proposed repetitive controller. The proposed repetitive control method was confirmed by simulations of several examples.This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 14550452, 2002.4-2004.3.

验证了作者提出的重复控制对于周期输入的轨迹控制是非常有效的。然而，如何保证控制方法的稳定性仍然是一个悬而未决的问题，因为控制器有相应的dea*单元，我们详细讨论了这一悬而未决的问题，并成功地找到了它的解决方案，开发了一种新的重复控制方法，该方法可以在复杂平面上改变稳定域，而不需要控制器外的任何附加。对于通常的重复控制方法，被控系统的矢量轨迹必须保持在控制器的稳定域内，该稳定域是半径为1的圆，这样重复控制系统才稳定。这是控制方法尚未解决的问题。新型重复控制器具有前向传递函数e^<-jwL>/K，而不是用于通常的重复控制器的e^<-jwL>和增益为K的正反馈。由于新控制器的频率传递函数变为1/K·e^<-jwL>/(1-e^<-jwL>)，控制系统不仅非常有效，因为对周期输入或干扰的无限增益。而且由于控制方法的稳定域是复平面上半径为K，圆心为（K， O）的圆内的域，所以系统始终能够保持稳定。因此，稳定域是可变的，在极端情况下，复平面的整个右区域都可以是稳定域。此外，通过对重复控制器中的元素进行重排，可以使整个复杂域成为稳定域。通过几个算例的仿真验证了所提出的重复控制方法。本研究得到国家教育、科学、体育和文化部科学研究资助项目(C), 14550452, 2002.4-2004.3的部分资助。