Proposal for Simple Repetitive Controllers
Article Sidebar
Main Article Content
Abstract
The modified repetitive control system is a type of servomechanism for periodic reference input. Even if the plant does not include a time delay, the transfer functions from both the reference input and the disturbance of the output of the modi¯ed repetitive control system generally have an in¯nite number of poles, and for this reason it is di±cult to settle the input-output and the disturbance attenuation characteristics of a modi¯ed repetitive control system. From a practical point of view, the input{output and the disturbance attenuation characteristics of a control system need to be settled easily, and thus, it is desirable that the transfer functions from both the reference input and the disturbance to the output have a finite number of poles. In order to easily specify the input-output and the disturbance attenuation characteristics, we propose the concept of a simple repetitive control system in which the controller works as a stabilizing modi¯ed repetitive controller and the transfer functions to the output from both the reference input and the disturbance have a ¯nite number of poles. In addition, the parametrization of all stabilizing simple repetitive controllers is clarified. A simple design procedure for a stabilizing simple repetitive controller is presented.
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 Multivariable 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 S. Hara, "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 in¯nite-dimensional systems", Essays on control: Perspectives in the theory and its applications, pp.191-222, 1993.
[16] K. Yamada and T. Okuyama, "A parametrization of all stabilizing repetitive controllers for linear minimum phase systems", Trans. of the Society of Instrument and Control Engineers, Vol.38, No.4, pp.328-334, 2000.
[17] K. Yamada, K. Satoh and T. Okuyama, "The parameterization of all stabilizing repetitive controllers for a certain class of non-minimum phase systems", Preprints of the 15th IFAC World Congress CD-ROM, 2002.
[18] K. Yamada, K. Satoh, N. Iida and T. Okuyama, "Control structure of all stabilizing repetitive controllers for the non-minimum phase systems", Proceedings of the 4th Asian Control Conference,
pp.753-758, 2002.
[19] D. C. Youla, H. Jabr and J. J. Bongiorno, "Modern Wiener-Hopf design of optimal controllers. Part I", IEEE Trans. on Automatic Control, Vol.AC-21, pp.3-13, 1976.
[20] V. Kucera, "Discrete linear system, The polynomial eqnarray approach", Wiley, 1979.
[21] J. J. Glaria and G. C. Goodwin, "A parameterization for the class of all stabilizing controllers for linear minimum phase system", IEEE Trans. on Automatic Control, Vol.AC-39, No.2, pp.433-434, 1994.
[22] M. Vidyasagar, "Control System Synthesis-A factorization approach", MIT Press, 1985.