FRIT of Internal Model Controllers for Poorly Damped Linear Time Invariant Systems: Kautz Expansion Approach

Hnin Si; Osamu Kaneko

doi:10.20965/jrm.2016.p0745

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JRM Vol.28 No.5 pp. 745-751

doi: 10.20965/jrm.2016.p0745

(2016)

Paper:

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FRIT of Internal Model Controllers for Poorly Damped Linear Time Invariant Systems: Kautz Expansion Approach

Hnin Si^* and Osamu Kaneko^**

^*Graduate School of Natural Science and Technology, Kanazawa University
Kakuma-machi, Kanazawa, Ishikawa 920-1192, Japan

^**Department of Mechanical Engineering and Intelligent Systems, The University of Electro-Communications
1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan

Received:

April 5, 2016

Accepted:

July 12, 2016

Published:

October 20, 2016

Keywords:

data-driven approach, fictitious reference iterative tuning (FRIT), internal model control (IMC), poorly damped systems, Kautz expansion

Abstract

This paper addresses the tuning of data-driven controllers for poorly damped linear time-invariant systems in the internal model control (IMC) architecture. In this study, fictitious reference iterative tuning (FRIT), which is one of the controller parameter tuning methods with the data obtained from a one-shot experiment, is used for tuning the controller. The Kautz expansion method in which the coefficients are tunable parameters is introduced to approximate the dynamics of linear time-invariant systems, which have poor damping characteristics. Such an approximated model with tunable parameters is implemented in the IMC architecture. A model and a controller can be realized simultaneously with a one-shot experiment by tuning the IMC with the parameterized Kautz expansion model and by using FRIT. The validity of the proposed method is examined with a numerical example.

Data-driven approach to internal model controller with tunable parameters

Cite this article as:

H. Si and O. Kaneko, “FRIT of Internal Model Controllers for Poorly Damped Linear Time Invariant Systems: Kautz Expansion Approach,” J. Robot. Mechatron., Vol.28 No.5, pp. 745-751, 2016.

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References

[1] H. T. Nguyen, O. Kaneko, and S. Yamamoto, “Fictitious Reference Iterative Tuning of Internal Model Controllers for Non-Minimum Phase Systems: A Laguerre Expansion Approach,” SICE J. of Control, Measurement and System Integration, Vol.6, No.1, pp. 38-44, 2012.
[2] B. Wahlberg, “System Identification using Laguerre Models,” IEEE Trans. on Automatic Control, Vol.36, No.5, pp. 551-562, 1991.
[3] S. Souma, O. Kaneko, and T. Fujii, “A new method of a controller parameter tuning based on input-output data: Fictitious reference iterative tuning,” Proc. of the 8th IFAC Workshop on Adaptation and Learning in Control and Signal Processing, pp. 789-794, 2004.
[4] O. Kaneko, “Data-Driven Controller Tuning: FRIT Approach,” Proc. of the 2nd IFAC Workshop on Adaptation and Learning in Control and Signal Processing, pp. 326-336, 2013.
[5] P. Lindskog and B. Wahlberg, “Application of Kautz Models in System Identifications,” Preprints of the 12th IFAC World Congress, pp. 309-312, 1993.
[6] B. Wahlberg, “System Identification using Kautz Models,” IEEE Trans. on Automatic Control, Vol.39, No.6, pp. 1276-1282, 1994.
[7] W. H. Kautz, “Transient Synthesis in the Time Domain,” IRE Trans.-Circuit Theory, Vol CT-1, pp. 29-39, 1954.
[8] B. Wahlberg and P. M. Makila, “On Approximation of Stable Linear Dynamical Systems using Laguerre and Kautz Functions,” Automatica, Vol.32, No.5, pp. 693-708, 1996.
[9] O. Kaneko, H. T. Nguyen, Y. Wadagaki, and S. Yamamoto, “Fictitious Reference Iterative Tuning for Non-Minimum Phase Systems in the IMC Architecture: Simultaneous Attainment of Controllers and Models,” SICE J. of Control, Measurement and System Integration, Vol.5, No.2, pp. 101-108, 2012.
[10] M. G. Safonov and T. C. Tsao, “The Unfalsified Control Concept and Learning,” IEEE Trans. on Automatic and Control, Vol.42, No.6, pp. 843-847, 1997.
[11] S. Hara and T. Sugie, “Inner-outer factorization for strictly proper functions with jω-axis zeros,” Systems and Control Letters, Vol.16, pp. 179-185, 1991.
[12] H. Okajima and T. Asai, “Tracking Performance Limitation for 1-DOF Control Systems Using a Set of Attainable Outputs,” SICE J. of Control, Measurement, and System Integration, Vol.8, No.5, pp. 348-353, 2015.
[13] A. C. den Brinker and H. J. W. Belt, “Using Kautz Model in Model Reduction,” Ch-13, pp. 185-196, Signal Analysis and Prediction, Springer Science+Business Media, 1998.
ISBN: 978-1-4612-7273-1
[14] S. da Silva, “Non-parametric identification of mechanical systems by Kautz filter with multiple poles,” Mechanical System and Signal Processing Vol.25, Issue 4, pp. 1103-1111, 2011.
[15] S. da Silva, V. Lope Junior, and M. J. Brennan, “Active Vibration Control using Kautz Filter,” Ch-4, pp. 87-104, doi: http://dx.doi.org/10.5772/50966, 2012.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] H. T. Nguyen, O. Kaneko, and S. Yamamoto, “Fictitious Reference Iterative Tuning of Internal Model Controllers for Non-Minimum Phase Systems: A Laguerre Expansion Approach,” SICE J. of Control, Measurement and System Integration, Vol.6, No.1, pp. 38-44, 2012.

[2] [2] B. Wahlberg, “System Identification using Laguerre Models,” IEEE Trans. on Automatic Control, Vol.36, No.5, pp. 551-562, 1991.

[3] [3] S. Souma, O. Kaneko, and T. Fujii, “A new method of a controller parameter tuning based on input-output data: Fictitious reference iterative tuning,” Proc. of the 8th IFAC Workshop on Adaptation and Learning in Control and Signal Processing, pp. 789-794, 2004.

[4] [4] O. Kaneko, “Data-Driven Controller Tuning: FRIT Approach,” Proc. of the 2nd IFAC Workshop on Adaptation and Learning in Control and Signal Processing, pp. 326-336, 2013.

[5] [5] P. Lindskog and B. Wahlberg, “Application of Kautz Models in System Identifications,” Preprints of the 12th IFAC World Congress, pp. 309-312, 1993.

[6] [6] B. Wahlberg, “System Identification using Kautz Models,” IEEE Trans. on Automatic Control, Vol.39, No.6, pp. 1276-1282, 1994.

[7] [7] W. H. Kautz, “Transient Synthesis in the Time Domain,” IRE Trans.-Circuit Theory, Vol CT-1, pp. 29-39, 1954.

[8] [8] B. Wahlberg and P. M. Makila, “On Approximation of Stable Linear Dynamical Systems using Laguerre and Kautz Functions,” Automatica, Vol.32, No.5, pp. 693-708, 1996.

[9] [9] O. Kaneko, H. T. Nguyen, Y. Wadagaki, and S. Yamamoto, “Fictitious Reference Iterative Tuning for Non-Minimum Phase Systems in the IMC Architecture: Simultaneous Attainment of Controllers and Models,” SICE J. of Control, Measurement and System Integration, Vol.5, No.2, pp. 101-108, 2012.

[10] [10] M. G. Safonov and T. C. Tsao, “The Unfalsified Control Concept and Learning,” IEEE Trans. on Automatic and Control, Vol.42, No.6, pp. 843-847, 1997.

[11] [11] S. Hara and T. Sugie, “Inner-outer factorization for strictly proper functions with jω-axis zeros,” Systems and Control Letters, Vol.16, pp. 179-185, 1991.

[12] [12] H. Okajima and T. Asai, “Tracking Performance Limitation for 1-DOF Control Systems Using a Set of Attainable Outputs,” SICE J. of Control, Measurement, and System Integration, Vol.8, No.5, pp. 348-353, 2015.

[13] [13] A. C. den Brinker and H. J. W. Belt, “Using Kautz Model in Model Reduction,” Ch-13, pp. 185-196, Signal Analysis and Prediction, Springer Science+Business Media, 1998.
ISBN: 978-1-4612-7273-1

[14] [14] S. da Silva, “Non-parametric identification of mechanical systems by Kautz filter with multiple poles,” Mechanical System and Signal Processing Vol.25, Issue 4, pp. 1103-1111, 2011.

[15] [15] S. da Silva, V. Lope Junior, and M. J. Brennan, “Active Vibration Control using Kautz Filter,” Ch-4, pp. 87-104, doi: http://dx.doi.org/10.5772/50966, 2012.

FRIT of Internal Model Controllers for Poorly Damped Linear Time Invariant Systems: Kautz Expansion Approach

Hnin Si* and Osamu Kaneko**

Hnin Si^* and Osamu Kaneko^**