A Study on a Novel Robust Repetitive Control Method

这证实了作者提出的重复控制对周期输入的轨迹控制具有极大的影响。它仍然是，如何，一个未确定的问题如何保证控制方法的稳定性，因为控制器确实是一个最好的元素，我们在细节上讨论了未确定的问题，以弥补它的问题，并成功地找到了它的解决方案来开发一种新颖的重复控制方法，它可以在控制器之外的任何额外平面中改变稳定域。对于通常的重复控制方法，它被强迫，因为控制系统的矢量位置必须保持在控制器的稳定域中，它是一个半径为1的圆圈，所以重复控制系统是稳定的。这对控制方法来说是一个不确定的问题。一种新型重复性控制器是开发的，它具有正向转移功能e^<-jwL>/K在e^<-jwL>中使用的，是一种普通重复性控制器，并带有积极反馈的K。自从新控制器的频率转移函数成为1/K ·e^<-jwL>/（1-e ^<-jwL>），控制系统并不只是在正常情况下有效地导致无限增益的周期性输入或干扰，但系统也总是可以保持稳定，因为控制方法的稳定域是在K的半径范围内的域，中心为（K，）O）在复杂平面上。因此，稳定域是可变的，而且在极端情况下，复杂平面中的整个正确区域都是可以成为稳定域的。在Furthmore中，整个复合域可以通过重新排列建议的重复控制器中的元素来成为稳定域。拟议的重复控制方法是通过几个示例的模拟证实的，本研究部分由教育、科学、体育和文化部支持，科学研究补助金（C）， 14550452， 2002.4-2004.3。

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.