Genetic Algorithm and Padé-Moment Matching for Model Order Reduction
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33122
Genetic Algorithm and Padé-Moment Matching for Model Order Reduction

Authors: Shilpi Lavania, Deepak Nagaria

Abstract:

A mixed method for model order reduction is presented in this paper. The denominator polynomial is derived by matching both Markov parameters and time moments, whereas numerator polynomial derivation and error minimization is done using Genetic Algorithm. The efficiency of the proposed method can be investigated in terms of closeness of the response of reduced order model with respect to that of higher order original model and a comparison of the integral square error as well.

Keywords: Model Order Reduction (MOR), control theory, Markov parameters, time moments, genetic algorithm, Single Input Single Output (SISO).

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1109495

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3538

References:


[1] L.T.Piliage and R.A.Rohrer, “Asymptotic Waveform Evaluation For Timing Analysis”, IEEE Transactions on Computer-Aided Design, vol. 9, no. 4, pp. 352–366 (1990).
[2] P. Feldmann and R. W. Freund, “Efficient Linear Circuit Analysis By Pade Approximation Via The Lanczos Process”, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems , vol. 14, no. 5, pp. 639–649 (1995).
[3] R. W. Freund, “Reduced-Order Modeling Techniques Based On Krylov Subspaces And Their Use In Circuit Simulation, Numerical Analysis”, Manuscript No. 98-3-02, Bell Laboratories, Murray Hill, New Jersey, Available online http://www.cm.bell-labs.com/cs/doc/98, February (1998).
[4] Y.Chen, “Model Order Reduction for Nonlinear Systems”, M.S. Thesis, Massachusetts Institute of Technology, September (1999).
[5] E. Gildin, R .H. Bishop, A.C. Antoulas and D.Sorensen, “An Educational Perspective to Model and Controller Reduction of Dynamical Systems” , Proceedings 46th IEEE Conference on Decision and Control New Orleans, LA, USA, Dec. 12-14 (2007).
[6] M.Aoki, “Control of large-scale dynamic systems by aggregation”, IEEE Transaction on Automation Control, vol. AC-13, no. 3, pp. 246-253 (1968).
[7] P.V.Kokotovic, R.E.O’Malley and Sannuti, “Singular Perturbations and Order Reduction in Control Theory-An Overview”, Automatica, vol.12, pp. 123-132 (1976).
[8] E.J.Davison, “A Method For Simplifying Linear Dynamic Systems”, IEEE Transactions on Automatic Control, vol.AC-11, no. 1, pp. 93-101, January (1972).
[9] S.A.Marshall, “An Approximation Method for Reducing the Order of a Large System”, Control Engg., vol.10, pp. 642-648 (1996).
[10] J.H.Anderson, “Geometrical Approach to Reduction of Dynamical System”, Proc.Inst.of Electrical Engineering, vol.114, pp.1014-1018 (1967).
[11] N.K.Sinha and W.Pille, “A New Method for Reduction of Dynamic System”, Int.J.Control, vol.14, pp.111-118 (1971).
[12] C.F Chen, and L.S.Shieh, “An Algebraic Method for Control System Design”, Int.J.Control, vol.11, pp. 717-739 (1970).
[13] H.Pade, “Sur La Representation Approaches Dune Function Pardes Fractions Rationales, Annales Scientifiques De’l Ecole Normale Supieure”, Ser 3 (Suppl) 9, pp. 1-93 (1892).
[14] V.Krishnamurthy and V.Seshadri, “A Simple And Direct Method Of Reducing The Order Of Linear Time Invariant Systems By Routh Approximation In The Frequency Domain”, IEEE Transactions on Automatic Control, vol. AC-21, no. 5, pp. 797-799 (1976).
[15] V.Krishnamurthy and V.Seshadri, “Model Reduction Using Routh Stability Criterion”, IEEE Tracsaction on Automatic Control, vol.AC- 23, Issue 4, pp. 729-731 (1978).
[16] Y.Shamash, “Stable Reduced Order Models Using Padé Type Approximation”, IEEE Transactions on Automatic Control, vol. AC-19, pp. 615-616 (1974).
[17] D.Nagaria, G.N.Pillaiand H.O.Gupta, “A Particle Swarm Optimization Approach for Controller Design in WECS equipped with DFIG”, Journal of Electrical Systems, vol.6, no.2, pp. 2-17 (2010).
[18] V.Singh,D.Chandra, and H.Kar, “Improved Routh–Padé Approximants: a computer –aided approach”, IEEE Transactions on Automatic Control, vol. 49, no.2, pp. 292-296 (2004).
[19] A.Pati,A.Kumar and D.Chandra, “Suboptimal Control Using Model Order Reduction”, Chinese Journal of Engineering, vol.2014, article ID 797581, pp. 1-5 (2014).
[20] S.C.Chuang, “Homographic transformation for the simplification of discrete-time transfer functions by Pad´e approximation,” International Journal of Control, vol. 22, no. 5, pp. 721–728(1975).
[21] O.M.K. Alsmadi and Z.S.A. Hammour, “A Robust Computational Technique for Model Order Reduction of Two-Scale Discrete Systems via Genetic Algorithms”, Computational Intelligence and Neuroscience, vol. 2015, article ID 615079, pp. 1-10 (2015).
[22] S.Panda, J.S.Yadav N.P.Patidar and C.Ardil, “Evolutionary Techniques for Model Order Reduction of Large Scale Linear Syatems”, International Journal of Electrical, Computer, Electronics and Communication Engineering, vol.6, issue no.9 (2012).
[23] S.Panda and N.P.Padhy, “Optimal Location and Controller Design of STATCOM UsingPartical Swarm Optimization”, Journal of the Frankin Institute, vol. 345, pp.166-181 (2008).
[24] N.Singh, “Reduced Order Modelling and Controller Design”, Ph.D. Thesis, IIT Roorkee (2007).
[25] M.S.Mahmoud and M.G.Singh, “Large Scale System Modeling”, Pergamon Press International Series on System and Control, vol.3, Ist Edition (1981).
[26] S.Panda, S.K.Tomar, R.Prasad and C.Ardil, “Reduction of Linear Time- Invariant Systems Using Routh-Approximation and PSO”, International Journal of Electrical, Robotics, Electronics and Communications Engineering (World Academy Science, Engineering and Technology), vol.3, no.9 (2009).