Abstract
In recent years, model order reduction (MOR) has been interested in more and more scientists. A lot of MOR algorithms have been introduced by many different approaches, among which preserving the dominant poles of the original system and Hankel singular values of the original system in order reduction system are appropriate approaches with many advantages. The article introduces a new MOR algorithm applied for stable and unstable linear systems, based on the idea of preserving the dominant poles of the original system during the order reduction. The algorithm will switch matrix-A of the original high-order system into the upper triangular matrix, then arrange the poles under the measure of dominance- H, H2, and mixed points on the main diagonal of upper triangular matrix-A, in order to attain a small error order reduction and preserve dominant poles simultaneously. The effectiveness of the new algorithm is illustrated through the order reduction of the high-order controller. Simulation results have proven the correctness of the algorithm.
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References
A. C. Antoulas, Approximation of Large-scale Dynamical Systems, SIAM, Philadelphia, 2005.
C. Boess, N. K. Nichols and G. Bunse, “Model reduction for discrete unstable control systems using a balanced truncation approach,” https://www.reading.ac.uk/web/FILES/maths/Preprint_10_06_Nichols.pdfdate11/06/2019.
N. H. Cong, V. N. Kien, D. H. Du, and B. T. Thanh, “Researching model order reduction based on Schur analysis,” Proc. of IEEE Conference on Cybernetics and Intelligent Systems (CIS), pp. 60–65, 2013.
D. Casagrande, W. Krajewski, and U. Viaro, “On the asymptotic accuracy of reduced-order models,” International Journal of Control, Automation and Systems, October 2017, vol. 15, no. 5, pp. 2436–2442, 2017.
E. Malekshahi and S. -M. -A. Mohammadi, “The model order reduction using LS, RLS and MV estimation methods,” International Journal of Control, Automation and Systems, vol. 12, no. 3, pp. 572–581, 2014.
Fatmawati, R. Saragih, R. T. Bambang, and Y. Soeharyadi, “Balanced truncation for unstable infinite dimensional systems via reciprocal transformation,” International Journal of Control, Automation, and Systems, vol. 9, no. 2, pp. 249–257, 2011.
K. Glover, “All optimal Hankel-norm approximations of linear multivariable systems and their L∞-error bounds,” International Journal of Control, vol. 39, no. 6, pp. 1115–1193, 1984.
G. Golub and C. V. Loan, Matrix Computations, The Johns Hopkins Press Ltd, London, 1996.
H. B. Minh and K. Takaba, “Model reduction in Schur basic with pole retention and H∞-norm error bound,” Proc. of InternationalWorkshop on Modeling, Systems, and Conrol, 2011.
E. A. Jonckheere and L. M. Silverman, “A New Set of Invariants for Linear System-Application to Reduced Order Compensator Design,” IEEE Transactions on Automatic Control, vol. 28, no. 10, pp. 953–964, 1983.
D. McFarlane and K. Glover, “A loop shaping design procedure using H synthesis,” IEEE Trans. Automat. Contr., vol 37, no 6, pp. 759–769, 1992.
B. C. Moore, “Principal component analysis in linear systems: Controllability, observability, and model reduction,” IEEE Trans. Auto. Contr., vol. 26, pp. 17–32, 1981.
N. H. Trung, Application of RH∞ Optimal Theory to Improve Quality of Power System Stabilizer, Ph.D. Thesis, Thai Nguyen University of Technology, Thai Nguyen University, 2012.
J. Rommes, Methods for Eigenvalue Problems with Applications in Model Order Reduction, Ph.D. Thesis, Utrecht University, 2007.
A. Varga, “Coprime factors model reduction based on accuracy enhancing techniques,” Systems Analysis Modeling and Simulation, vol. 11, pp. 303–311, 1993.
K. Zhou, G. Salomon, and E. Wu, “Balanced realization and model reduction method for unstable systems,” International Journal of Robust and Nonlinear Control, vol. 9, no. 3, pp. 183–198, 1999.
A. Zilouchian, “Balanced structures and model reduction of unstable systems,” Proc. of IEEE SOUTHEASTCON’ 91, Williamsburg, VA, USA, vol. 2, pp. 1198–1201, 1991
N. H Cong, V. N. Kien, and D. T. Hai, “Model reduction based on triangle realization with pole retention,” Applied Mathematical Sciences, vol. 9, 2015, no. 44, pp. 2187–2196, 2015.
M. G. Safonov, R. Y. Chiang, and D. J. N. Limebeer, “Optimal Hankel model reduction for nonminimal systems,” IEEE Trans. on Automat. Contr., vol. 35, no. 4, pp. 496–502, 1990.
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This research was funded by Thai Nguyen University of Technology, No. 666, 3/2 street, Thai Nguyen, Viet Nam.
Ngoc Kien Vu was born in 1983. He received his Master’s degree in automatic control in 2011 and his Ph.D. degree in automatic control in 2015 from Thai Nguyen university of technology. From 2006 to now, he was a lecturer at Thai Nguyen University of technology. His main researches are model order reduced algorithm, automatic.
Hong Quang Nguyen received his Master’s degree in control engineering and automation from Hanoi University of Science and Technology (HUST), Viet Nam, 2012 and a Ph.D. degree from Thai Nguyen University of Technology (TNUT), Vietnam, 2019. He is currently a lecturer at the Faculty of Mechanical, Electrical, and Electronic Technology, Thai Nguyen University of Technology (TNUT). His research interests include electrical drive systems, control systems and its applications, adaptive dynamic programming control, robust nonlinear model predictive control, motion control, and mechatronics.
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Vu, N.K., Nguyen, H.Q. Model Order Reduction Algorithm Based on Preserving Dominant Poles. Int. J. Control Autom. Syst. 19, 2047–2058 (2021). https://doi.org/10.1007/s12555-019-0990-8
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DOI: https://doi.org/10.1007/s12555-019-0990-8