A Design Method for Simple Repetitive Controllers for Time-Delay Plants
Article Sidebar
Main Article Content
Abstract
The modified repetitive control system is a type of servomechanism for the periodic reference input. That is, the modi¯ed repetitive control system follows the periodic reference input with small steady state error, even if a periodic disturbance or uncertainty exists in the plant. Using previously proposed modified repetitive controllers, even if the plants does not includes time-delay, the transfer function from the periodic reference input to the output and that from the disturbance to the output have an infinite number of poles. When the transfer function from the periodic reference input to the output and that from the disturbance to the output have an infinite number of poles, it is dificult to specify the input output characteristic and the disturbance attenuation characteristic. From the practical point of view, it is desirable that the input-output characteristic and the disturbance attenuation characteristic are easily specified. In order to specify the input-output characteristic and the disturbance attenuation characteristic easily, the transfer function from the periodic reference input to the output and that from the disturbance to the output are desirable to have a finite number of poles. Yamada et al. proposed the concept of simple repetitive control systems such that the controller works as a modified repetitive controller and the transfer function from the periodic reference input to the output and that from the disturbance to the output have a finite number of poles. In addition, Yamada et al. clarified the parametrization of all stabilizing simple repetitive controllers. However the method by Yamada et al. cannot be applied for time-delay plants. The purpose of this paper is to propose the parametrization of all stabilizing simple repetitive controllers for time-delay plants.
Article Details
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.
- Creative Commons Copyright License
The journal allows readers to download and share all published articles as long as they properly cite such articles; however, they cannot change them or use them commercially. This is classified as CC BY-NC-ND for the creative commons license.
- Retention of Copyright and Publishing Rights
The journal allows the authors of the published articles to hold copyrights and publishing rights without restrictions.
References
[2] T. Inoue, S. Iwai and M. Nakano, "High Accuracy Control of Play-Back Servo System", The Trans. of The Institute of Electrical Engineers of Japan, Vol.C101, No.4, pp.89-96, 1981.
[3] S. Hara, T. Omata, and M. Nakano, "Stability Condition and Synthesis Methods for Repetitive Control System", Trans. of the Society of Instrument and Control Engineers, Vol.22, No.1, pp.36-42, 1986.
[4] S. Hara and Y. Yamamoto, "Stability of Multi variable Repetitive Control Systems - Stability Condition and Class of Stabilizing Controllers", Trans. of the Society of Instrument and Control Engineers, Vol.22, No.12, pp.1256-1261, 1986.
[5] Y. Yamamoto and S. Hara, "The Internal Model Principle and Stabilizability of Repetitive Control System", Trans. of the Society of Instrument and Control Engineers, Vol.22, No.8, pp.830-834, 1987.
[6] S. Hara, Y. Yamamoto, T. Omata and M. Nakano, "Repetitive Control System: A New Type Servo System for Periodic Exogenous Signals", IEEE Trans. on Automatic Control, Vol.AC-33, No.7, pp.659-668, 1988.
[7] T. Nakano, T. Inoue, Y. Yamamoto and Hara, S., "Repetitive Control," SICE Publications, 1989.
[8] S. Hara, P. Trannitad and Y. Chen, "Robust stabilization for repetitive control systems," Proceedings of the 1st Asian Control Conference, pp.541-544, 1994.
[9] G. Weiss, "Repetitive Control Systems: Old and New Ideas," Systems and Control in the Twenty First Century, pp.389-404, 1997.
[10] T. Omata, S. Hara and M. Nakano, "Nonlinear Repetitive Control with Application to Trajectory Control of Manipulators", J. of Robotic Systems, Vol.4, No.5, pp.631-652, 1987.
[11] K.Watanabe and M. Yamatari, "Stabilization of Repetitive Control System-Spectral Decomposition Approach", Trans. of the Society of Instrument and Control Engineers, Vol.22, No.5, pp. 535-541, 1986.
[12] M. Ikeda and M. Takano, "Repetitive Control for Systems with Nonzero Relative Degree", Proc. 29th CDC, pp. 1667-1672, 1990.
[13] H. Katoh and Y. Funahashi, "A Design Method of Repetitive Controlles", Trans. of the Society of Instrument and Control Engineers, Vol.32, No.12, pp.1601-1605, 1996.
[14] Y. Yamamoto and S. Hara, "Internal and external stability and robust stability condition for a class of infinite-dimensional systems," Automatica, Vol.28, pp.81-93, 1992.
[15] Y. Yamamoto, "Learning control and related problems in infinite-dimensional systems", Essays on control: Perspectives in the theory and its applications , pp.191-222, 1993.
[16] M. Vidyasagar, "Control System Synthesis - A factorization approach -", MIT Press, 1985.
[17] K. Yamada, H. Takenaga, Y. Saitou, K. Satoh, "Proposal for simple repetitive controllers," Proceedings of the 2007 Electrical Engineering/Electronics, Computer, Telecommunication, and Information Technology (ECTI) International Conference, Vol.I, pp.225-228, 2007.
[18] K. Yamada, H. Takenaga, Y. Saitou and K. Satoh, "Proposal for simple repetitive controllers," ECTI Transactions on Electrical Eng., Electronics, and Communications, Vol.6, No.1, pp.64-72, 2008.