Controller Gain Design of 2-D Linear Systems Based on the Existing 1-D Analytical Solution

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Abstract. A controller gain design problem of two-dimensional (2-D) linear systems is proposed in this paper. For one-dimensional (1-D) systems, the necessary and sufficient conditions have been established for the problem, and an analytical solution for the feedback gain is given by [1]. Based on the existing 1-D analytical solution, a 2-D state feedback controller gain can be designed to achieve the desired poles. Finally, two numerical examples are shown to exhibit the validity of the proposed approach.

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55-59

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April 2013

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© 2013 Trans Tech Publications Ltd. All Rights Reserved

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[1] K. Ogata, Discrete-Time Control Systems, Englewood Cliffs, N.J.: Prentice Hall, Inc., (1995).

Google Scholar

[2] G. C. Goodwin, S. F. Graebe, and M. E. Salgado, Control System Design. Upper Saddle River, New Jersey: Prentice-Hall, Inc., (2001).

Google Scholar

[3] W. J. Palm, Modeling, Analysis and Control of Dynamic Systems. New York: John Wiley & Sons, Inc., (2003).

Google Scholar

[4] M. Gopal, Digital Control and State Variable Methods. McGraw-Hill Book Company, (2003).

Google Scholar

[5] P. N. Paraskevopoulos, K. I. Diamantaras, Algorithm for characteristic polynomial assignment of two-dimensional discrete systems, IEE Proceedings Pt.D. 137 (1990) March.

DOI: 10.1049/ip-d.1990.0011

Google Scholar

[6] M. Sebek, On 2-D pole placement, IEEE Trans. on Automatic Control. 30 (1985) 819-822.

DOI: 10.1109/tac.1985.1104065

Google Scholar

[7] J. Shimonishi, N.K. Sinha and T. Hinamoto, Eigenvalue assignment of linear multivariable two-dimensional systems using two-dimensional dynamical compensators, Int. J. Systems Sci. 20 (1989) 779-792.

DOI: 10.1080/00207728908910169

Google Scholar

[8] W. J. Liu, Factorization of two-dimensional MIMO systems into a cascade of one-dimensional systems via observer-based feedback, CACS Automatic Control Conference, Taipei, Taiwan, (2006).

Google Scholar

[9] W. J. Liu, Design of a 2-D proportional-integral-derivative controller for multi-input multi-output systems, Proceedings of 2007 CACS International Automatic Control Conference, Taiwan, Nov., (2007).

Google Scholar

[10] W. J. Liu, Plant input-output feedback control design for a class of two-dimensional systems in Roesser Model, 2012 International Conference on Gerontic Technology and Service Management , Nantou, Taiwan, pp.1369-1375, (2012).

Google Scholar

[11] R. P. Roesser, A discrete state-space model for linear image processing, IEEE Trans. Automatic Control. 20 (1975) 1-10.

DOI: 10.1109/tac.1975.1100844

Google Scholar