A Study on a Novel Robust Repetitive Control Method

这是确认由作者提供的恢复控制是对trajectory的extremely效果control to the periodic input. It remains, however，an unsettled question how guarantee the stability of the控制方法因为控制器有一个dea* element Accordingly，we have discussed the unsettled question in detail to overcome it question成功发现其开发novel repetitive control method which is able to changethe stability domain in a complex plane without any additional outside the controller.For the usual恢复控制方法，这之前已经forced that a vector locus of a controlled system must be kept within a stability domaincontroller which is a circle with a radius of 1 so that the repetitive control system isstable. is an unsettled problem for the control method. the novel repetitive controller wasdeveloped that had forward transfer function e^<-jwL>/K instead of e^<-jwL> which was used for ausual repetitive controller and positive feedback with gain K.自频率传输函数of the new controller becomes 1/ k.e ^<-jwL>/(1-e^<-jwL>)，控制系统不只是extremely effective because of the infinity gain against periodicinput or disturbance as usual，but the system is always able to be kept stable因为控制领域的稳定性method is the domain within a circle with radius of K, center of (K)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 be to be stable domain by rearrangement the elements in the proposedrepetitive controller. The proposed repetitive control method was confirmed by simulations ofseveral examples.This research partially supported by the Ministry of Education, Science，Sports and Culture, Grant-in-Aid for Scientific Research (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.