The Parameterization of all Stabilizing Modified Repetitive Controllers for Multiple-Input/Multiple-Output Plants with the Specified Input-Output Frequency Characteristic

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In this paper, we examine the parameterization of all stabilizing modified repetitive controllers for multiple-input/multiple-output plants with the specified input-output frequency characteristic. The parameterization of all stabilizing modified repetitive controllers for non-minimum phase systems was solved by Yamada et al. However, when we design a stabilizing modified repetitive controller using the parameterization by Yamada et al., the input-output frequency characteristic of the control system cannot be settled so easily. The input-output frequency characteristic of the control systems is required to be easily settled. This problem is solved by obtaining the parameterization of all stabilizing modified repetitive controllers with the specified input-output frequency characteristic. However, no paper has proposed the parameterization of all stabilizing modified repetitive controllers for multiple-input/multiple-output plants with the specified input-output frequency characteristic. In this paper, we propose the parameterization of all stabilizing modified repetitive controllers for multiple-input/multiple-output plants with the specified input-output frequency characteristic.

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273-281

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October 2010

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[1] T. Inoue, M. Nakano, T. Kubo and S. Matsumoto: High Accuracy Control Magnet Power Supply of Proton Synchrotron in Recurrent Operation The Trans. of The Institute of Electrical Engineers of Japan Vol. 100 (1980), pp.234-240.

Google Scholar

[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. 101-4 (1981), pp.89-96.

Google Scholar

[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. 22-1 (1986), pp.36-42.

DOI: 10.9746/sicetr1965.22.36

Google Scholar

[4] 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. 23-8 (1987), pp.830-834.

Google Scholar

[5] 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. 22-12 (1986), pp.1256-1261.

DOI: 10.9746/sicetr1965.22.1256

Google Scholar

[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-33-7 (1988), pp.659-668.

DOI: 10.1109/9.1274

Google Scholar

[7] T. Omata, S. Hara and M. Nakano: Nonlinear Repetitive Control with Application to Trajectory Control of Manipulators J. of Robotic Systems Vol. 4-5 (1987), pp.631-652.

DOI: 10.1002/rob.4620040505

Google Scholar

[8] K. Watanabe and M. Yamatari: Stabilization of Repetitive Control System-Spectral Decomposition Approach Trans. of the Society of Instrument and Control Engineers Vol. 22-5 (1986), pp.535-541.

DOI: 10.9746/sicetr1965.22.535

Google Scholar

[9] M. Ikeda and M. Takano: Repetitive Control for Systems with Nonzero Relative Degree Trans. of the Society of Instrument and Control Engineers Vol. 24-6 (1988), pp.575-582.

DOI: 10.9746/sicetr1965.24.575

Google Scholar

[10] M. Gotou, S. Matsubayashi, F. Miyazaki, S. Kawamura and S. Arimoto: A Robust System with an Iterative Learning Compensator and a Proposal of Multi-Period Learning Compensator J. of The Society of Instrument and Control Engineers Vol. 5 (1987).

Google Scholar

[11] H. Katoh and Y. Funahashi: A Design Method of Repetitive Controllers Trans. of the Society of Instrument and Control Engineers Vol. 32-12 (1996), pp.1601-1605.

DOI: 10.9746/sicetr1965.32.1601

Google Scholar

[12] 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 (1976), pp.3-13.

DOI: 10.1109/tac.1976.1101139

Google Scholar

[13] 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 (1994), pp.433-434.

DOI: 10.1109/9.272352

Google Scholar

[14] C.A. Dedoer, R.W. Liu, J. Murray and R. Saeks: Feedback system design: The fractional representation approach to analysis and synthesis IEEE Trans. on Automatic Control Vol. AC-25 (1980), pp.399-412.

DOI: 10.1109/tac.1980.1102374

Google Scholar

[15] V. Kucera: Discrete linear system, The polynomial eqnarray approach Wiley (1979).

Google Scholar

[16] 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).

DOI: 10.3182/20020721-6-es-1901.00115

Google Scholar

[17] 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 (2002).

DOI: 10.3182/20020721-6-es-1901.00115

Google Scholar

[18] K. Yamada and T. Okuyama: Characterization of all causal internally stabilizing repetitive controllers for minimum phase systems Theoretical and Applied Mechanics Vol. 50 (2001), pp.193-200.

Google Scholar

[19] K. Yamada, K. Satoh and T. Arakawa: The parametrization of all stabilizing modified repetitive controllers The International Conference on Cybernetics and Information Technologies, System and Applications Vol. Ⅱ (2004), pp.358-363.

Google Scholar

[20] K. Yamada, K. Satoh and M. Kowada: A design method of modified repetitive controllers with the specified input-output characteristics Journal of the Japan Society of Applied Electromagnetics and Mechanics Vol. 15-2(2007), pp.170-176.

Google Scholar

[21] M. Vidyasagar: Control System Synthesis - A factorization approach MIT Press (1985).

Google Scholar