Abstract
The paper proposes a new mixed method for reducing the order of interval systems i.e., systems having uncertain but bounded parameters. The denominator of the reduced order model is obtained by α table and numerator is derived by applying factor division and Cauer second form. A numerical example has been discussed to illustrate the procedures. The errors between the original higher order and reduced order models have also been highlighted to support the effectiveness of the proposed methods.
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References
Aoki M (1968) Control of large-scale dynamic systems by aggregation. IEEE Trans Autom Control 13:246–253
Shamash Y (1974) Stable reduced order models using pade type approximation. IEEE Trans Autom Control 19:615–616
Hutton MF, Friedland B (1975) Routh approximation for reducing order of linear time invariant system. IEEE Trans Autom Control 20:329–337
Krishnamurthy V, Seshadri V (1978) Model reduction using routh stability criterion. IEEE Trans Autom Control 23:729–730
Sinha NK, Kuszta B (1983) Modelling and identification of dynamic systems. New York Van Nostrand Reinhold, Chapter 8, pp 133–163
Glover K (1984) All optimal hankel-norm approximations of linear multivariable systems and their error bounds. Int J Control 39(6):1115–1193
Shamash Y (1975) Model reduction using routh stability criterion and the pade approximation. Int J Control 21:475–484
Parmar G (2007) A mixed method for large-scale systems modelling using eigen spectrum analysis and cauer second form. IETE J Res 53(2):93
Bai-Wu W (1981) Linear model reduction is using mihailov criterion and pade approximation technique. Int J Control 33(6):1073
Kharitonov VL (1978) Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differentsialnye Uravneniya 14:2086–2088
Bhattacharyya SP (1987) Robust stabilization against structured perturbations (lecture notes in control and information sciences). Springer, New York
Bandyopadhyay B, Ismail O, Gorez R (1994) Routh pade approximation for interval systems. IEEE Trans Autom Control 39:2454–2456
Bandyopadhyay B (1997) γ-δ Routh approximations for interval systems. IEEE Trans Autom Control 42:1127–1130
Sastry GVK, Raja Rao GR, Rao PM (2000) Large scale interval system modelling using routh approximants. Electron Lett 36(8):768
Dolgin Y, Zeheb E (2003) On routh pade model reduction of interval systems. IEEE Trans Autom Control 48(9):1610–1612
Dolgin Y (2005) Author’s reply. IEEE Trans Autom Control 50(2):274–275
Hwang C, Yang S-F (1999) Comments on the computation of interval routh approximants. IEEE Trans Autom Control 44(9):1782–1787
Choo Younseok (2007) A note on discrete interval system reduction via retention of dominant poles. Int J Control Autom Syst 5(2):208–211
Saraswathi G (2007) A mixed method for order reduction of interval systems. Int Conf Intell Adv Syst pp 1042–1046
Ismail O, Bandyopadhyay B (1995) Model order reduction of linear interval systems using pade approximation. IEEE Int Symp Circ Syst
Singh VP, Chandra D (2010) Routh approximation based model reduction using series expansion of interval systems. IEEE Int Conf Power Control Embed Syst (ICPCES) 1:1–4
Singh VP, Chandra D (2011) Model reduction of discrete interval system using dominant poles retention and direct series expansion method. In: Proceedings of the IEEE 5th International power engineering and optimization conference (PEOCO), vol 1. pp 27–30
Kranthi Kumar D, Nagar SK, Tiwari JP (2011) Model order reduction of interval systems using modified routh approximation and factor division method. In: Proceedings of 35th national system conference (NSC), IIT Bhubaneswar, India
Hansen E (1965) Interval arithmetic in matrix computations. Part I Siam J Numer Anal pp 308–320
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Kranthi Kumar, D., Nagar, S.K., Tiwari, J.P. (2013). Order Reduction of Interval Systems Using Alpha and Factor Division Method. In: Malathi, R., Krishnan, J. (eds) Recent Advancements in System Modelling Applications. Lecture Notes in Electrical Engineering, vol 188. Springer, India. https://doi.org/10.1007/978-81-322-1035-1_22
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DOI: https://doi.org/10.1007/978-81-322-1035-1_22
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