Journals A-Z
All Subjects
Free Journals
sciepub.com
Journal of Automation and Control
ISSN (Print): 2372-3033 ISSN (Online): 2372-3041 Website: https://www.sciepub.com/journal/automation Editor-in-chief: Santosh Nanda
Open Access
Journal Browser
Go
Issue 1, Volume 4
Article Metrics
  • 44133
    Views
  • 42630
    Saves
  • 2
    Citations
  • 6
    Likes
Export Article
Journal of Automation and Control. 2016, 4(1), 1-9
DOI: 10.12691/automation-4-1-1
Open AccessArticle

Model Order Reduction Using Routh Approximation and Cuckoo Search Algorithm

D. K. Sambariya1, and Omveer Sharma1

1Department of Electrical Engineering, Rajasthan Technical University, Kota, India

Pub. Date: April 29, 2016
View Full Text Full Text PDF (340 KB) Full Text ePUB(474 KB)

Cite this paper:
D. K. Sambariya and Omveer Sharma. Model Order Reduction Using Routh Approximation and Cuckoo Search Algorithm. Journal of Automation and Control. 2016; 4(1):1-9. doi: 10.12691/automation-4-1-1

Abstract

In this paper, a large order system is reduced by using the Cuckoo Search Algorithm (CSA) to a reduced order approximate model. The denominator coefficients of a desired reduced order system are determined by Routh approximation method while the numerator coefficients are determined using CSA based on integral square error minimization as an objective function pertaining to a unit step as input. The efficacy of the proposed method is tested with three SISO test systems to get a corresponding reduced order system and extended to a MIMO system. The results are satisfactory in terms of minimum error with the proposed method as compared to Routh Pade approximation and weighted sum multi-objective harmony search based reduced models.

Keywords:
ISE minimization approach large scale systems Model order reduction Optimization using Cuckoo search algorithm Routh approximation

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Figures

Figure of 13

References:

[1]  H. N. Soloklo and M. M. Farsangi, “Multiobjective weighted sum approach model reduction by Routh-Pade approximation using harmony search,” Turk J Elec Eng & Comp Sci, vol. 21, pp. 2283 - 2293, 30.10.2013 2013.
 
[2]  V. Singh, D. Chandra, and H. Kar, “Optimal Routh approximants through integral squared error minimisation: computer-aided approach,” IEE Proceedings - Control Theory and Applications, vol. 151, pp. 53-58, 2004.
 
[3]  V. Singh, “Obtaining Routh-Pade approximants using the Luus-Jaakola algorithm,” IEE Proceedings - Control Theory and Applications, vol. 152, pp. 129-132, 2005.
 
[4]  V. Singh, D. Chandra, and H. Kar, “Improved Routh-Pade approximants: a computer-aided approach,” IEEE Transactions on Automatic Control, vol. 49, pp. 292-296, 2004.
 
[5]  N. K. Sinha and G. J. Lastman, “Reduced Order Models for Complex Systems-A Critical Survey,” IETE Technical Review, vol. 7, pp. 33-40, 1990/01/01 1990.
 
[6]  I. El-nahas, N. K. Sinha, and R. T. H. Alden, “Pade and Routh approximation in the time domain,” in Decision and Control, 1983. The 22nd IEEE Conference on, 1983, pp. 243-246.
 
[7]  C.-q. Gu and J. Yang, “Stable Routh-Padé-type approximation in model reduction of interval systems,” Journal of Shanghai University (English Edition), vol. 14, pp. 369-373, 2010/10/01 2010.
 
[8]  B.-W. Wan, “Linear model reduction using Mihailov criterion and Padé approximation technique,” International Journal of Control, vol. 33, pp. 1073-1089, 1981/06/01 1981.
 
[9]  D. K. Sambariya and R. Prasad, “Routh Approximation based Stable Reduced Model of Single Machine Infinite Bus System with Power System Stabilizer,” in DRDO-CSIR Sponsered: IX Control Instrumentation System Conference (CISCON - 2012), Department of Instrumentation and Control Engineering, Manipal Institute of Technology (A Constitute Institute of Manipal University), Manipal-576104; ISBN 978-93-82338-26-0 | © 2012 Bonfring; CIS-162; , 2012, pp. 85-93.
 
[10]  T. C. Chen, C. Y. Chang, and K. W. Han, “Model reduction using the stability-equation method and the continued-fraction method,” International Journal of Control, vol. 32, pp. 81-94, 1980/07/01 1980.
 
[11]  S. R. Desai and R. Prasad, “A new approach to order reduction using stability equation and big bang big crunch optimization,” Systems Science & Control Engineering, vol. 1, pp. 20-27, 2013/12/01 2013.
 
[12]  A. Sikander and R. Prasad, “A Novel Order Reduction Method Using Cuckoo Search Algorithm,” IETE Journal of Research, vol. 61, pp. 83-90, 2015/03/04 2015.
 
[13]  D. K. Sambariya and R. Prasad, “Routh Stability Array Method based reduced model of Single Machine Infinite Bus with Power System Stabilizer,” in International Conference on Emerging Trends in Electrical, Communication and Information Technologies (ICECIT-2012), ISBN-9789351070504, at Srinivasa Ramanujan Institute of Technology, Rotarypuram (V), B K Samudram (M), Anantapur (Dist). - 515701, Andhrapradesh, India., 2012, pp. 27-34.
 
[14]  R. K. Appiah, “Linear model reduction using Hurwitz polynomial approximation,” International Journal of Control, vol. 28, pp. 477-488, 1978/09/01 1978.
 
[15]  Y. Shamash, “Model reduction using the Routh stability criterion and the Padé approximation technique,” International Journal of Control, vol. 21, pp. 475-484, 1975/03/01 1975.
 
[16]  D. K. Sambariya and G. Arvind, “High Order Diminution of LTI System Using Stability Equation Method,” British Journal of Mathematics & Computer Science, vol. 13, pp. 1-15, December 29, 2015 2016.
 
[17]  D. K. Sambariya and H. Manohar, “Model order reduction by differentiation equation method using with Routh array Method,” in 10th International Conference on Intelligent Systems and Control (ISCO 2016), Karpagam College of Engineering, Coimbatore, Tamilnadu, India, 2016, pp. 341-346.
 
[18]  D. K. Sambariya and H. Manohar, “Preservation of Stability for Reduced Order Model of Large Scale Systems Using Differentiation Method,” British Journal of Mathematics & Computer Science, vol. 13, pp. 1-17, 2016.
 
[19]  H. Manohar and D. K. Sambariya, “Model order reduction of MIMO system using differentiation method,” in 10th International Conference on Intelligent Systems and Control (ISCO 2016), Karpagam College of Engineering, Coimbatore, Tamilnadu, India, 2016, pp. 347-351.
 
[20]  G. Parmar, R. Prasad, and S. Mukherjee, “Order Reduction of Linear Dynamic Systems using Stability Equation Method and GA,” International Journal of Computer, Information, and Systems Science, and Engineering, vol. 1, pp. 1, 26-32 2007.
 
[21]  U. Salma and K. Vaisakh, “Reduced Order Modeling of Linear MIMO Systems Using Soft Computing Techniques,” in Swarm, Evolutionary, and Memetic Computing. vol. 7077, B. Panigrahi, P. Suganthan, S. Das, and S. Satapathy, Eds., ed: Springer Berlin Heidelberg, 2011, pp. 278-286.
 
[22]  I. Saaki, P. C. Babu, C. K. Rao, and D. S. Prasad, “Integral square error minimization technique for linear multi input and multi output systems,” in Power and Energy Systems (ICPS), 2011 International Conference on, 2011, pp. 1-5.
 
[23]  F. Wu and J. J. Jaramillo, “Computationally Efficient Algorithm For Frequency-Weighted Optimal H∞ Model Reduction,” Asian Journal of Control, vol. 5, pp. 341-349, 2003.
 
[24]  J. Shen and J. Lam, “H∞ Model Reduction for Positive Fractional Order Systems,” Asian Journal of Control, vol. 16, pp. 441-450, March 2014 2014.
 
[25]  Y. Ebihara, Y. Hirai, and T. Hagiwara, “On ℋ∞ model reduction for discrete-time linear time-invariant systems using linear matrix inequalities,” Asian Journal of Control, vol. 10, pp. 291-300, 2008.
 
[26]  A. Ghafoor, V. Sreera, and R. Treasure, “Frequency weighted model reduction technique retaining Hankel singular values,” Asian Journal of Control, vol. 9, pp. 50-56, 2007.
 
[27]  L. Cao and H. M. Schwartz, “Reduced-order models for feedback stabilization of linear systems with a singular perturbation model,” Asian Journal of Control, vol. 7, pp. 326-336, 2005.
 
[28]  D. K. Sambariya and R. Prasad, “Stable reduced model of a single machine infinite bus power system with power system stabilizer,” in International Conference on Advances in Technology and Engineering (ICATE-2013) 2013, pp. 1-10.
 
[29]  D. K. Sambariya and R. Prasad, “Stable Reduction Methods of Linear Dynamic Systems in Frequency Domain,” 17th National Power Systems Conference (NPSC-2012) at Indian Institute of Technology (BHU), Vranasi, pp. 549-558, December 12-14, 2012 2012.
 
[30]  D. K. Sambariya and R. Prasad, “Stability Equation method based Stable Reduced Model of Single Machine Infinite Bus System with Power System Stabilizer,” International Journal of Electronic and Electrical Engineering, vol. 5, pp. 101-106, September 29-30, 2012 2012.
 
[31]  D. K. Sambariya and H. Manohar, “Model order reduction by integral squared error minimization using bat algorithm,” in Proceedings of 2015 RAECS UIET Panjab University Chandigarh 21 − 22nd December 2015, Chandigarh, India, 2015, pp. 1-7.
 
[32]  S. Walton, O. Hassan, K. Morgan, and M. R. Brown, “Modified cuckoo search: A new gradient free optimisation algorithm,” Chaos, Solitons & Fractals, vol. 44, pp. 710-718, 2011.
 
[33]  X.-S. Yang and S. Deb, “Multiobjective cuckoo search for design optimization,” Computers & Operations Research, vol. 40, pp. 1616-1624, 2013.
 
[34]  E. Valian, S. Tavakoli, S. Mohanna, and A. Haghi, “Improved cuckoo search for reliability optimization problems,” Computers & Industrial Engineering, vol. 64, pp. 459-468, 2013.
 
[35]  Y. Xin-She and S. Deb, “Cuckoo Search via Levy flights,” in World Congress on Nature & Biologically Inspired Computing, 2009. NaBIC 2009., 2009, pp. 210-214.
 
[36]  I. Pavlyukevich, “Levy Flights, Non-local Search and Simulated Annealing,” J Comput Phys, vol. 226, pp. 1830-1844, 26 Jan 2007 2007.
 
[37]  X.-S. Yang and S. Deb, “Engineering Optimisation by Cuckoo Search,” International Journal of Mathematical Modelling and Numerical Optimisation, vol. 1, pp. 330-343, 23 Dec 2010 2010.
 
[38]  P. Civicioglu and E. Besdok, “A conceptual comparison of the Cuckoo-search, particle swarm optimization, differential evolution and artificial bee colony algorithms,” Artif. Intell. Rev., vol. 39, pp. 315-346, 2013.
 
[39]  A. Gandomi, X.-S. Yang, and A. Alavi, “Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems,” Engineering with Computers, vol. 29, pp. 17-35, 2013/01/01 2013.
 
[40]  S. Mukherjee and R. N. Mishra, “Order reduction of linear systems using an error minimization technique,” Journal of the Franklin Institute, vol. 323, pp. 23-32, 1987.
 
[41]  S. R. Desai and R. Prasad, “A novel order diminution of LTI systems using Big Bang Big Crunch optimization and Routh Approximation,” Applied Mathematical Modelling, vol. 37, pp. 8016-8028, 2013.
 
[42]  B. Philip and J. Pal, “An evolutionary computation based approach for reduced order modelling of linear systems,” in Computational Intelligence and Computing Research (ICCIC), 2010 IEEE International Conference on, 2010, pp. 1-8.
 
[43]  D. K. Sambariya and R. Prasad, “Optimal Tuning of Fuzzy Logic Power System Stabilizer Using Harmony Search Algorithm,” International Journal of Fuzzy Systems, vol. 17, pp. 457-470, September 2015 2015.
 
[44]  D. K. Sambariya and R. Prasad, “Robust tuning of power system stabilizer for small signal stability enhancement using metaheuristic bat algorithm,” International Journal of Electrical Power & Energy Systems, vol. 61, pp. 229-238, 2014.
 
[45]  D. K. Sambariya and R. Prasad, “Design of Robust PID Power System Stabilizer for Multimachine Power System Using HS Algorithm,” American Journal of Electrical and Electronic Engineering, vol. 3, pp. 75-82, July 16, 2015 2015.
 
[46]  V. P. Singh and D. Chandra, “Routh-approximation based model reduction using series expansion of interval systems,” in Power, Control and Embedded Systems (ICPCES), 2010 International Conference on, 2010, pp. 1-4.
 
[47]  R. Salim and M. Bettayeb, “H2 and H∞ optimal model reduction using genetic algorithms,” Journal of the Franklin Institute, vol. 348, pp. 1177-1191, 2011.
 
[48]  C. B. Vishwakarma and R. Prasad, “MIMO System Reduction Using Modified Pole Clustering and Genetic Algorithm,” Modelling and Simulation in Engineering, vol. 2009, 2009.
 
Manuscript template