IJBTT

Applying Model Order Reduction Algorithm for Control Design of the Digital Filter

Applying Model Order Reduction Algorithm for Control Design of the Digital Filter
	© 2022 by IJETT Journal
	Volume-70 Issue-11
	Year of Publication : 2022
	Author : Bui Huy Hai
	DOI : 10.14445/22315381/IJETT-V70I11P231

How to Cite?

Bui Huy Hai, "Applying Model Order Reduction Algorithm for Control Design of the Digital Filter," International Journal of Engineering Trends and Technology, vol. 70, no. 11, pp. 288-294, 2022. Crossref, https://doi.org/10.14445/22315381/IJETT-V70I11P231

Abstract
Digital filters are increasingly used in the field of digital signal processing. Designing a digital filter is to determine the transfer function of a digital filter that meets the specified requirements. However, the design of digital filters often leads to high-order digital filters. The article has applied model reduction methods to reduce the high-order digital filter. Through comparison, evaluation of low-order filters according to different order reduction algorithms shows that low-order filters can completely replace high-order digital filters. Using a low-order digital filter will help reduce the calculation time, and increase the response speed of the filter, but still ensure the quality of the filter.

Keywords
Digital filter, Model order reduction, IIR digital filter.

Reference
[1] Komarasamy, Dr Ramesh and A. Nirmalkumar, “Design of Digital IIR Filters with the Advantages of Model Order Reduction Technique”. International Journal of Electronic Engineering Research, vol. 1, no. 2, pp. 89–100, 2009.
[2] Ngoc Kien Vu, Hong Quang Nguyen, “Balancing Control of Two-Wheel Bicycle Problems”, Mathematical Problems In Engineering, pp. 1-12, 2020. Crossref, https://doi.org/10.1155/2020/6724382
[3] Ngoc Kien Vu and Hong Quang Nguyen, "Design Low-Order Robust Controller for Self-Balancing Two-Wheel Vehicle", Mathematical Problems in Engineering, pp. 22, 2021. Crossref, https://doi.org//10.1155/2021/6693807
[4] Vu Ngoc Kien, Nguyen Hien Trung and Nguyen Hong Quang, “Design Low Order Robust Controller for the Generator’s Rotor Angle Stabilization PSS System”, Emerging Science Journal, vol. 5, no. 5, pp. 598-618, 2021. Crossref, https://doi.org/0.28991/esj-2021-01299
[5] Vu Ngoc Kien, Nguyen Hong Quang and Ngo Kien Trung, “Application of Model Reduction for Robust Control of Self-Balancing Two-Wheeled Bicycle,” TELKOMNIKA Telecommunication, Computing, Electronics and Control, vol. 19, no. 1, pp. 252-264, 2021. https://doi.org/10.12928/telkomnika.v19i1.16298
[6] B. Moore, “Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction," IEEE Transactions on Automatic Control, vol. 26, no. 1, pp. 17–32, 1981, Crossref, https://doi.org/10.1109/Tac.1981.1102568
[7] Vu Ngoc Kien and Nguyen Hong Quang, “Model Reduction of Unstable Systems Based on Balanced Truncation Algorithm,” International Journal of Electrical and Computer Engineering, vol. 11, no. 3, pp. 2045-2053, 2021. Crossref, https://doi.org//10.11591/ijece.v11i3.pp2045-2053
[8] I. Perenbo and L.M. Silverman, “Model Reduction Via Balanced State Space Representation”, IEEE Transactions on Automatic Control, vol. 27, no. 2, pp. 328-387, 1982. Crossref, https://doi.org/10.1109/TAC.1982.1102945
[9] 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. Crossref, https://doi.org/10.1080/00207178408933239
[10] D. Enns, “Model Reduction with Balanced Realizations: An Error Bound and A Frequency Weighted Generalization,” The 23rd IEEE Conference on Decision and Control, 1984. Crossref, https://doi.org/10.1109/CDC.1984.272286
[11] U.B. Desai and D. Pal, “A Transformation Approach to Stochastic Model Reduction,” IEEE Transactions on Automatic Control, vol. 29, no. 12, pp. 1097–1100, 1984. Crossref, https://doi.org/10.1109/TAC.1984.1103438
[12] M. Green, “A Relative Error Bound for Balanced Stochastic Truncation,” IEEE Transactions on Automatic Control, vol. 33, no. 10, pp. 961 – 965, 1998. Crossref, https://doi.org/10.1109/9.7255
[13] W. Gawronski and J.N. Juang, “Model Reduction In Limited Time and Frequency Intervals,” International Journal of Systems Science, vol. 21, no. 2, pp. 349-376, 1990. Crossref, https://doi.org//10.1080/00207729008910366
[14] A. C. Antoulas, D. C. Sorensen and S. Gugercin, “A Survey of Model Reduction Methods for Large-Scale Systems”, Structured Matrices In Mathematics, Computer Science, and Engineering, vol. 280, 2001. Crossref, https://doi.org/10.1090/conm/280
[15] M. G. Safonov and R. Y. Chiang, "A Schur Method for Balanced-Truncation Model Reduction," In IEEE Transactions on Automatic Control, vol. 34, no. 7, pp. 729-733, 1989, Crossref, https://doi.org/10.1109/9.29399.
[16] N.K. Vu, H.Q. Nguyen, K.T. Ngo and P. N. Dao, “Study on Model Reduction Algorithm Based on Schur Analysis,” Advances in Intelligent Systems and Computing, vol. 1254, 2021. Crossref, https://doi.org/10.1007/978-981-15-7527-3_18
[17] 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. Crossref, https://doi.org/10.1109/TAC.1983.1103159
[18] K. Zhou, G. Salomon and E. Wu, “Balanced Realization and Model Reduction for Unstable Systems,” International Journal of Robust and Nonlinear Control, vol. 9, no. 3, pp. 183-198. Crossref, https://doi.org//10.1002/(SICI)1099-1239(199903)9:3<183::AID-RNC399>3.0.CO;2-E
[19] A. Zilouchian, “Balanced Structures and Model Reduction of Unstable Systems,” IEEE Proceedings of the SOUTHEASTCON ’91, 1991. Crossref, https://doi.org/10.1109/SECON.1991.147956
[20] C. Boess, N. Nichols and A. Bunse-Gerstner, “Model Reduction for Discrete Unstable Control Systems Using a Balanced Truncation Approach,” Preprint MPS, University of Reading, 2010.
[21] Ngoc Kien Vu, Hong Quang Nguyen, “Reduced Order of the Unstable System Using Balanced Truncation Algorithm Based on Continuous-Discrete Mapping and Its Application to Control,” Journal of Mechanical Engineering Research and Developments, vol. 43 no.6, pp. 299-307, 2020
[22] Kien Vu Ngoc and Quang Nguyen Hong, “Combined Balanced Truncation Algorithm and Linear Differential Mapping for Controller Order Reduction Problem,” Journal of Mechanical Engineering Research and Developments, vol. 43, no. 4, pp. 310-319, 2020.
[23] Ngoc Kien Vu and Hong Quang Nguyen, “Model Order Reduction Algorithm Based on Preserving Dominant Poles,” International Journal of Control, Automation, and Systems, vol. 19, pp. 2047-2058, 2021, Crossref, https://doi.org/10.1007/S12555-019-0990-8
[24] Vu Ngoc Kien and Nguyen Hong Quang, “Model Reduction in Schur Basic with Pole Retention and H2 Norm Error Bound,” Journal of Mechanical Engineering Research and Developments, vol. 44, no. 1, pp. 279-293, 2021.
[25] Er. Nitin Yadav and Er. Dharmendra Singh, "Model Order Reduction Using Routh Approximation Method, Factor Division Method and Genetic Algorithm," SSRG International Journal of Electrical and Electronics Engineering, vol. 5, no. 9, pp. 9-15, 2018. Crossref, https://doi.org/10.14445/23488379/IJEEE-V5I9P102
[26] N. K. Sinha, I. El-Nahas and R. T. H. Alden, “Routh Approximation of Multivariable Systems,” Problems of Control and Information Theory, vol. 11, no. 3, pp. 420-425, 1982.
[27] S. Panda, J. S. Yadav, N. P. Patidar and C. Ardil, “Evolutionary Techniques for Model Order Reduction of Large Scale Linear Systems”, International Journal of Electrical and Computer Engineering, vol. 6, No. 9, 2012.
[28] V. R. Dehkordi and A. G. Aghdam, "A Computationally Efficient Algorithm for Order-Reduction of IIR Filters Using Control Techniques," Proceedings of 2005 IEEE Conference on Control Applications, pp. 898-903, 2005. Crossref, https://doi.org/10.1109/CCA.2005.1507243
[29] N. G. Nath and N. N. San, “An Approach to Linear Model Reduction,” Control Cybersecurity, vol. 20 , no. 2, pp. 69-89, 1991.