Comparison of Singular Perturbations Approximation Method and Meta-Heuristic-Based Techniques for Order Reduction of Linear Discrete Systems
Applied and Computational Mathematics
Volume 6, Issue 4-1, July 2017, Pages: 48-54
Received: Aug. 16, 2016; Accepted: Sep. 12, 2016; Published: Dec. 8, 2016
Views 4418      Downloads 163
Anouar Bouazza, Department of Electrical Engineering, National Engineering School of Monastir, Sousse, Tunisia
Article Tools
Follow on us
This paper presents a survey of Singular Perturbations Approximation (SPA) method and meta-heuristic techniques for order reduction of linear systems in discrete case. A comparison of intelligent techniques to determine the reduced order model of higher order linear systems is presented. Two approaches are considered: Particle Swarm Optimization (PSO) and Shuffled Frog Leaping Algorithm (SFLA). These methods are employed to reduce the higher order model and based on the minimization of the Mean Square Error (MSE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Each method is illustrated through numerical examples.
Order Reduction Techniques, Singular Perturbations Approximations Method, Meta-Heuristics Methods, Particle Swarm Optimization, Shuffled Frog Leaping Algorithm
To cite this article
Anouar Bouazza, Comparison of Singular Perturbations Approximation Method and Meta-Heuristic-Based Techniques for Order Reduction of Linear Discrete Systems, Applied and Computational Mathematics. Special Issue: Some Novel Algorithms for Global Optimization and Relevant Subjects. Vol. 6, No. 4-1, 2017, pp. 48-54. doi: 10.11648/j.acm.s.2017060401.14
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A. Bouazza, A. Sakly, and M. Benrejeb, “Order Reduction of Complex Systems described by TSK Fuzzy Models based on Singular Perturbations Method,” International Journal of Systems Science, vol. 44. no. 3, pp. 442–449, March 2013.
A. Bouazza, A. Sakly, and M. Benrejeb, “On order reduction of discrete complex systems described by TSK fuzzy models,” the 9th International conference on Sciences and Techniques of Automatic control & computer engineering, Sousse, Tunisia, 2008.
A. Bouazza, A. Sakly, and F. M'sahli, “Comparison of Different Meta-heuristic-based Techniques for Order Reduction of Linear Systems,” the 13th International conference on Sciences and Techniques of Automatic control & computer engineering, Monastir, Tunisia, 2012.
V. Singh, D. Chandra, and H. KarI, “Improved Routh-Pade Approximants: A Computer-Aided Approach,” IEEE Trans. Auto. Control, vol. 49. no. 2, pp. 292-296, 2004.
M. Frangos and I. M. Jaimoukha, “Rational interpolation: Modified rational Arnoldi algorithm and Arnoldi-like equations,” 46th IEEE Conference on Decision and Control, New Orleans LA, USA, 2007.
S. Devi and R. Prasad, “Reduction of Discrete time systems by Routh approximation,” National System Conference, pp. 30-33, IIT Kharagpur, 2003.
L. Coluccio, A. Eisinberg, and G. Fedele, “A Prony-like polynomial-based approach to model order reduction, 15th Mediterranean conference on control & automation, 2007.
J. Lubuma and K. Patidar, “Towards the implementation of the singular function method for singular perturbation problems,” Applied mathematics and computation, 2009.
C. B. Vishwakarma and R. Prasad, “Clustering Method for Reducing Order of Linear System using Pade Approximation,” IETE Journal of Research, vol. 54, Issue 5, pp. 326-330, 2008.
C. S. Hsieh and C. Hwang, “Model reduction of linear discrete-time systems using bilinear Schwarz approximation”. J. Systems Sci, no. 1, pp. 33-49, 1990.
G. Parmar, S. Mukherjee, and R. Prasad, “System reduction using factor division algorithm and eigen spectrum analysis,” Applied Mathematical Modelling, pp. 2542-2552, 2007.
G. Saraswathi, G. A. Gopala Rao, and Amarnath, “A Mixed method for order reduction of interval systems having complex eigenvalue,” International Journal of Engineering and Technology, vol. 2, no. 4, pp. 201-206, 2008.
R. Prasad, A. K. Mittal, and S. P. Sharma, “A mixed method for the reduction of multi-variable systems,” Journal of the Institution of Engineers, vol. 85, pp. 177-18, 2005.
O. M. K. Alsmadi and M. O. Abdalla, “Order Model Reduction for Two-Time-Scale Systems Based on Neural Network Estimation,” 15th Mediterranean conference on Control & automation, 2007.
R. Sampaio and C. Soize, “Remarks on the efficiency of POD and KL methods for model reduction in nonlinear dynamics of continuous systems,” International Journal for Numerical Methods in Engineering, 2006.
J. S. Yadav, N. P. Patidar, J. Singhai, S. Panda, and C. Ardil, “A Combined Conventional and Differential Evolution Method for Model Order Reduction,” International Journal of Computational Intelligence, vol. 5, no. 2, pp. 111-118, 2009.
F. H. Bellamine and A. Elkamel, “Model order reduction using neural network principal component analysis and generalized dimensional analysis,” International Journal for Computer-Aided Engineering and Software, 2008.
J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” IEEE International Conference on Neural Networks, Piscataway, pp. 1942-1948, 1995.
Satakshi, S. Mukherjee, and R. C. Mittal, “Order reduction of linear discrete systems using a genetic algorithm,” Applied Mathematical modeling, Vol. 28, Issue 11, pp. 983-1005, November 2004.
N. H. Chahkandi, R. Jahani, and G. R. Sarlak, G, “Applying Shuffled Frog Leaping Algorithm for Economic Load Dispatch of Power System,” American Journal of Scientific Research, Issue 20 pp. 82-89, 2011.
D. Soudani, “Sur la détermination explicite de solutions à des problèmes d’analyse et de synthèse de systèmes singulièrement perturbés, Application à un générateur de vapeur d’un navire,” Thèse de doctorat, ENIT Tunisia, 1997.
M. N. Abdelkrim, “Sur la modélisation et la synthèse des systèmes singulièrement perturbés. Application aux processus dynamiques,” Thèse de doctorat, ENIT, Tunisia, 1985.
G. Dauphin-Tanguy, P. Borne, and A. Fossard, “Analyse et synthèse des systèmes à plusieurs échelles de temps,” Journal d’étude, pp. 169-196, 1985.
Z. S. Abo-Hammour, O. M. K. Alsmadi, and A. M. AlSmadi, “Frequency-based model order reduction via genetic algorithm approach,” Systems, Signal Processing and their Applications (WOSSPA), 7th International Workshop on, IEEE Xplore, pp. 91-94, 2011.
S. Panda, S. K. Tomar, R. Prasad, and C. Ardil, “ Model Reduction of Linear Systems by Conventional and Evolutionary Techniques,” International Journal of Computational and Mathematical Sciences, vol. 3, no. 1, pp. 28-34, 2009.
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 Applied Science, Engineering and Technology, vol. 5, no. 1, pp. 22-28, 2009.
S. Panda, N. P. Padhy, and R. N. Patel, “Power System Stability Improvement by PSO Optimized SSSC-based Damping Controller,” Electric Power Components & Systems, Taylor and Francis, vol. 36, no. 5, pp. 468-490, 2008.
S. Panda, N. P. Padhy, and R. N. Patel, “Robust Coordinated Design of PSS and TCSC using PSO Technique for Power System Stability Enhancement,” Journal of Electrical Systems, vol. 3, no. 2, pp. 109-123, 2007.
G. Pamar and S. Mukherjee, “Reduced order modeling of linear dynamic systems using Particle Swarm optimized eigen spectrum analysis,” International journal of Computational and Mathematical Sciences, pp. 45-52, 2007.
M. Eusuff and K. E. Lansey, K. E, “Optimization of Water Distribution Network Design Using the Shuffled Frog Leaping Algorithm,” J Water Resour Plan Manage, no. 3, pp. 10-25, 2003.
M. Tavakolan, A. Baabak, and N. Chiara, “Applying the Shuffled Frog-Leaping Algorithm to improve scheduling of construction projects with activity splitting allowed,” Management and Innovation for a Sustainable Built Environment, pp. 20-23, 2011.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186