3-D Visualization and Optimization for SISO Linear Systems Using Parametrization of Two-Stage Compensator Design
In this paper, we consider the two-stage compensator
designs of SISO plants. As an investigation of the characteristics of
the two-stage compensator designs, which is not well investigated
yet, of SISO plants, we implement three dimensional visualization
systems of output signals and optimization system for SISO plants by
the parametrization of stabilizing controllers based on the two-stage
compensator design. The system runs on Mathematica by using
“Three Dimensional Surface Plots,” so that the visualization can
be interactively manipulated by users. In this paper, we use the
discrete-time LTI system model. Even so, our approach is the
factorization approach, so that the result can be applied to many
linear models.
[1] C. A. Desoer, R. W. Liu, J. Murray, and R. Saeks, “Feedback system
design: The fractional representation approach to analysis and synthesis,”
IEEE Trans. Automat.Contr., vol. AC-25, pp. 399-412, 1980.
[2] M. Vidyasagar, H. Schneider, and B. A. Francis, “Algebraic
and topological aspects of feedback stabilization,” IEEE
Trans. Automat. Contr., vol. AC-27, pp. 880-894, 1982.
[3] K.Mori, “Parametrization of all strictly causal stabilizing controllers,”
IEEE Trans. Automat. Contr., vol. AC-54, pp.2211-2215, 2009.
[4] M. Vidyasagar, Control System Synthesis: A Factorization Approach,
Cambridge, MA:MIT Press, 1985.
[5] K. Mori, “Multi-stage compensator design -a factorization approach-,” in
Proceedings of The 8th Asian Control Conference(ASCC 2011), 2011,
1012-1017.
[6] V. R .Sule, “Feedback stabilization over commutative rings: The matrix
case,” SIAM J. Control and Optim., vol. 32, no. 6, pp. 1675-1695, 1944.
[7] K. Mori and K. Abe, “Feedback stabilization over commutative rings:
Further study of coordinate-free approach, ” SIAM J. Control and Optim.,
vol. 39, no. 6, pp. 1952-1973, 2001.
[8] S. Shankar and V. R.Sule, “Algebraic geometric aspects of feedback
stabilization,” SIAM J. Control and Optim., vol. 30, no. 1, pp. 11-30,
1992.
[9] P. Wellin, Programming with Mathematica:An Introduction, Cambridge
University Press, 2013.
[10] ThreeDimensionalSurfacePlots: URL: http://reference.wolfram.com/
mathematica/tutorial/ThreeDimensionalSurfacePlots.en.html
[11] S. Wolfram, “The Mathematica Book Forth
Edition,”Wolfram Research, Inc.
[12] F. A. Aliev and V. B. Schneider, “Comments on Optimizing
Simultaneously Over the Numerator and Denominator Polynomials in the
Youla-Kucera Parameterization” IEEE Trans. Automat. Contr., vol. 52,
no. 4 pp. 763, 2007.
[13] D. C. Youla, H. A. Jabr. and J. J. Bongiorno, “Modern Wiener-Hopf
design of optimal controllers Part II: The multivariable case,” IEEE
Trans. Automat. Contr., vol. AC-21, no. 3 pp. 319-338, Jun. 1976.
[14] V. Kuˇcela, “Stability of discrete linear control systems,” Preprintsc 6th
IFAC World Congr., Boston, MA, 1975.
[15] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery,
“Numerical Recipes Third Edition: Golden Section Search in One
Dimension,” Cambridge university, pp. 492-495, 2007.
[16] K. Hashimoto and K. Mori, “Visualization Input-Output Relation with
Parametrization of Two Stage Compensator Design”, The Society of
Instrument and Control Engineers Tohoku Chapter., Japan, Fukushima,
no. 284-7, Nov. 2013.
[17] K. Hashimoto and K. Mori, “Visualization of The Input-Output Relation
of Multi-Input Multi-Output System Using Parametrization of Two-Stage
Compensator Design”, Tohoku-Section Joint Convention of Institutes of
Electrical and information Engineers, Japan, Yamagata, no. 2F01, Aug.
2013.
[18] K. Hashimoto and K. Mori, “Visualization Of The Input-output Relation
Of Single-input Single-output System And Multi-input Multi-output
System Using Parametrization Of Two-stage Compensator Design”, 34th
International Association of Science and Technology for Development
Conference on Modelling, Identification and Control MIC 2015, Austria,
Innsbruck, no. 826-032, Feb. 2015.
[1] C. A. Desoer, R. W. Liu, J. Murray, and R. Saeks, “Feedback system
design: The fractional representation approach to analysis and synthesis,”
IEEE Trans. Automat.Contr., vol. AC-25, pp. 399-412, 1980.
[2] M. Vidyasagar, H. Schneider, and B. A. Francis, “Algebraic
and topological aspects of feedback stabilization,” IEEE
Trans. Automat. Contr., vol. AC-27, pp. 880-894, 1982.
[3] K.Mori, “Parametrization of all strictly causal stabilizing controllers,”
IEEE Trans. Automat. Contr., vol. AC-54, pp.2211-2215, 2009.
[4] M. Vidyasagar, Control System Synthesis: A Factorization Approach,
Cambridge, MA:MIT Press, 1985.
[5] K. Mori, “Multi-stage compensator design -a factorization approach-,” in
Proceedings of The 8th Asian Control Conference(ASCC 2011), 2011,
1012-1017.
[6] V. R .Sule, “Feedback stabilization over commutative rings: The matrix
case,” SIAM J. Control and Optim., vol. 32, no. 6, pp. 1675-1695, 1944.
[7] K. Mori and K. Abe, “Feedback stabilization over commutative rings:
Further study of coordinate-free approach, ” SIAM J. Control and Optim.,
vol. 39, no. 6, pp. 1952-1973, 2001.
[8] S. Shankar and V. R.Sule, “Algebraic geometric aspects of feedback
stabilization,” SIAM J. Control and Optim., vol. 30, no. 1, pp. 11-30,
1992.
[9] P. Wellin, Programming with Mathematica:An Introduction, Cambridge
University Press, 2013.
[10] ThreeDimensionalSurfacePlots: URL: http://reference.wolfram.com/
mathematica/tutorial/ThreeDimensionalSurfacePlots.en.html
[11] S. Wolfram, “The Mathematica Book Forth
Edition,”Wolfram Research, Inc.
[12] F. A. Aliev and V. B. Schneider, “Comments on Optimizing
Simultaneously Over the Numerator and Denominator Polynomials in the
Youla-Kucera Parameterization” IEEE Trans. Automat. Contr., vol. 52,
no. 4 pp. 763, 2007.
[13] D. C. Youla, H. A. Jabr. and J. J. Bongiorno, “Modern Wiener-Hopf
design of optimal controllers Part II: The multivariable case,” IEEE
Trans. Automat. Contr., vol. AC-21, no. 3 pp. 319-338, Jun. 1976.
[14] V. Kuˇcela, “Stability of discrete linear control systems,” Preprintsc 6th
IFAC World Congr., Boston, MA, 1975.
[15] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery,
“Numerical Recipes Third Edition: Golden Section Search in One
Dimension,” Cambridge university, pp. 492-495, 2007.
[16] K. Hashimoto and K. Mori, “Visualization Input-Output Relation with
Parametrization of Two Stage Compensator Design”, The Society of
Instrument and Control Engineers Tohoku Chapter., Japan, Fukushima,
no. 284-7, Nov. 2013.
[17] K. Hashimoto and K. Mori, “Visualization of The Input-Output Relation
of Multi-Input Multi-Output System Using Parametrization of Two-Stage
Compensator Design”, Tohoku-Section Joint Convention of Institutes of
Electrical and information Engineers, Japan, Yamagata, no. 2F01, Aug.
2013.
[18] K. Hashimoto and K. Mori, “Visualization Of The Input-output Relation
Of Single-input Single-output System And Multi-input Multi-output
System Using Parametrization Of Two-stage Compensator Design”, 34th
International Association of Science and Technology for Development
Conference on Modelling, Identification and Control MIC 2015, Austria,
Innsbruck, no. 826-032, Feb. 2015.
@article{"International Journal of Electrical, Electronic and Communication Sciences:73168", author = "Kazuyoshi Mori and Keisuke Hashimoto", title = "3-D Visualization and Optimization for SISO Linear Systems Using Parametrization of Two-Stage Compensator Design", abstract = "In this paper, we consider the two-stage compensator
designs of SISO plants. As an investigation of the characteristics of
the two-stage compensator designs, which is not well investigated
yet, of SISO plants, we implement three dimensional visualization
systems of output signals and optimization system for SISO plants by
the parametrization of stabilizing controllers based on the two-stage
compensator design. The system runs on Mathematica by using
“Three Dimensional Surface Plots,” so that the visualization can
be interactively manipulated by users. In this paper, we use the
discrete-time LTI system model. Even so, our approach is the
factorization approach, so that the result can be applied to many
linear models.", keywords = "Linear systems, visualization, optimization, two-Stage
compensator design, Mathematica.", volume = "10", number = "6", pages = "734-6", }
