The Parametrization of All Robust Stabilizing Multi-Period Repetitive Controllers for Time-Delay Plants

• Published in: Theoretical and Applied Mechanics Japan Vol. 58; pp. 285 - 293
• Main Authors: HAGIWARA, Takaaki, YAMADA, Kou, NAKAZAWA, Nobuaki, MURAKAMI, Iwanori, ANDO, Yoshinori, LIU, Jia Wei, SAKANUSHI, Tatsuya
• Format: Journal Article
• Language: English
• Published: Tokyo National Committee for IUTAM 2010; Japan Science and Technology Agency
• ISSN: 1348-0693; 1349-4244
• DOI: 10.11345/nctam.58.285

In this paper, we investigate the parametrization of all robust stabilizing multi-period repetitive (MPR) controllers for single-input/single-output time-delay plants. The MPR controllers were proposed by Gotou et al., in order to improve the disturbance attenuation characteristic of the modified repetitive control systems. Yamada et al. proposed a design method of MPR controllers to attenuate wide-frequency disturbance based on the idea of changing time-delay. In addition, Yamada et al. obtained the parametrization of all stabilizing MPR controllers. However, the parametrization of all robust stabilizing MPR controllers for the time-delay plant with uncertainties has not been considered yet. In this paper, we propose the parametrization of all robust stabilizing MPR controllers for time-delay plants with uncertainties. The basic idea of the method is as follows. If the MPR control system is robustly stable for time-delay plant with uncertainties, then the MPR controller must satisfy the robust stability condition. This implies that if the MPR control system is robustly stable, then the MPR controller is included in the parametrization of all robust stabilizing controllers for the plant with uncertainties. Robust stabilizing controllers for the plant include a free parameter, which is designed to achieve desirable control characteristics. If the free parameter is chosen to give the control system robust servo characteristic for periodic reference input, then the controller operates as a robust stabilizing MPR controller. Conversely a MPR controller stabilizing the plant robustly, then the free-parameter is written by an appropriate form. Using this idea, we obtain the parametrization of all robust stabilizing MPR controllers.