Genetic Algorithm and Padé-Moment Matching for Model Order Reduction
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.
[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).
[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).
@article{"International Journal of Electrical, Electronic and Communication Sciences:71183", author = "Shilpi Lavania and Deepak Nagaria", title = "Genetic Algorithm and Padé-Moment Matching for Model Order Reduction", 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).", volume = "9", number = "6", pages = "632-5", }
