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The authors proposed an evolutionary-optimization technique known as the Genetic Algorithm (GA) for the optimization and order reduction of high order systems (HOSs) in the time domain. As we know a lot of optimization techniques are available in the frequency domain but limited in the time domain. The proposed technique is applicable for time-domain systems. The reduced model (RM) obtained by the proposed technique can be replaced with the original HOS as it retains all the important time and frequency response specifications of the original HOS. The efficacy of the proposed method has been tested on few numerical examples from the literature. The important time and frequency response specifications of the proposed RM are compared with RM obtained by recent techniques using MATLAB/Simulink. The proposed algorithm is applicable for Single-input single-output (SISO) and multi-input multi-output (MIMO) linear, nonlinear, time-invariant, and time-variant systems.

A simplification method is suggested in this paper to simplify a large-scale dynamic system using logarithmic pole clustering and moments matching using Pade approximations. The denominator polynomial of the simplified model is computed by using logarithmic pole clustering while the numerator coefficients of the same model are determined by matching the time-moments of the original large-scale system. The viability of the proposed method has been tested on few large-scale systems taken from the literature.

The authors proposed a new mixed order reduction technique for large-scale linear dynamic systems (LSLDSs). The denominator of the original LSLDS is reduced by the proposed renovated pole clusterin...

A renovated pole clustering technique is proposed in this paper to reduce large scale linear dynamic systems into lower order linear dynamic systems. The denominator polynomial order is decreased by using renovated pole clustering technique and numerator coefficients are calculated by using improved pade approximations technique. The reduction algorithm is completely computational. The reduced system retained the stability characteristic of the original higher order system. The Comparison is performed by simulated graph and performance index like integral square error (ISE) which justify its excellence.

A renovated pole clustering technique is proposed in this paper to simplify large-scale linear dynamic systems into lower order. The denominator of the simplified system is obtained by using renovated pole clustering technique and numerator coefficients are computed by factor division algorithm. The proposed algorithm is computationally simple and capable to retain stability of the original high order system. The method is illustrated with the help few numerical examples and compared with the well-known order reduction methods existed in the literature. The proposed method is also applicable to linear multi- inputs and multi- outputs (MIMO) systems as well.

An order reduction method has been proposed for reducing the order of the large-scale dynamic systems where denominator polynomial determined through Eigen algorithm and numerator polynomial via factor division algorithm. In Eigen algorithm, the most dominant Eigen value of both original and reduced order systems remain same. The proposed mixed method confirm stability of the reduced model if the original system is stable and has been also compared in quality with other existing model order reduction methods.Keywords: Eigen algorithm; Order reduction; Factor division algorithm; Stability; Transfer function

A mixed method by using the modified pole clustering technique and simulated annealing is proposed to reduce higher-order mathematical model into a smaller one. The denominator and numerator polynomials are obtained by using a modified pole clustering technique and simulated annealing algorithm, respectively. The proposed-biased method generates k number of reduced models from higher-order systems. The compatibility of the method has been checked via time responses of the original higher-order system and the reduced-order system, respectively. Also, the proposed method has been compared with few known model-order reduction techniques through performance indices.

This paper presents a mixed method to reduce the order of the linear high order dynamic systems by combining improved modified pole clustering technique and improved Pade approximations. The denominator of the reduced order model is computed by improved modified pole clustering while the numerator coefficients are obtained by improved Pade approximations. The proposed method is competent in generating ‘k’ number of reduced order models from the original high order system. The superiority of the proposed method is concluded through numerical examples taken from literature and compared with existing well- known order reduction methods.

A system simplification method for large-scale dynamic system is proposed here. System simplification of the large-scale model is done via reducing the order of the denominator of the original system. The simplified model is obtained by using pole clustering and Cauer second form of Continued Fraction Expansion (CFE). The proposed method is easy to understand and capable to retain the stability of the original system. The suggested method is comparable to few well-known simplification algorithms and is validated with the help of an example.

Load frequency controller has been designed for reduced order model of single area and two-area reheat hydro-thermal power system through internal model control - proportional integral derivative (IMC-PID) control techniques. The controller design method is based on two degree of freedom (2DOF) internal model control which combines with model order reduction technique. Here, in spite of taking full order system model a reduced order model has been considered for 2DOF-IMC-PID design and the designed controller is directly applied to full order system model. The Logarithmic based model order reduction technique is proposed to reduce the single and two-area high order power systems for the application of controller design.The proposed IMC-PID design of reduced order model achieves good dynamic response and robustness against load disturbance with the original high order system.

A mixed method by combining a Eigen algorithm and Improved pade approximations is proposed for reducing the order of the large-scale multi-input multi-output (MIMO) systems. The most dominant Eigen value of both original and reduced order systems remain same in this method. The proposed method guarantees stability of the reduced model if the original high-order system is stable and is comparable in quality with the other well known existing order reduction methods. The viability of the proposed method is shown through numerical examples taken from the literature and compared with few well-known order reduction methods.

The study deals with the morphological and thermal analysis of binary rubber blends of acrylonitrile-co-butadiene rubber (NBR) with another polymer. Either ethylene propylene diene terpolymer (EPDM), ethylene vinyl acetate (EVA), chlorosulphonated polyethylene (CSM), or polyvinyl chloride (PVC) has been selected for the second phase. Depending on the relative polarity and interaction parameter of the components, the binary blends showed development of a bi-phasic morphology through scanning electron microscopy (SEM). Use of different types of thermal analysis techniques revealed that these blends are generally incompatible excepting one of NBR and PVC. Derivative differential scanning calorimetry (DDSC), in place of conventional DSC, has been used to characterize the compatibility behavior of the blends. NBR–PVC shows appearance of only one glass transition temperature (Tg) averaging the individual Tg’s of the blend components. The partially missible blend of NBR and CSM shows a broadening of Tg interval between the phase components, while the immiscible blends of either NBR–EPDM or NBR–EVA do not show any change in Tg values corresponding to the individual rubbers of their blend. The experimental Tg values were also compared with those calculated theoretically by Fox equation and observed to match closely with each other. Studies have also been made to evaluate the thermal stability of these blends by thermo-gravimetric analysis (TG) and evaluation of activation energy of respective decomposition processes by Flynn and Wall method. Thermo-mechanical analysis (TMA) was found to be effective for comparison of creep recovery and dimensional stability of the blends both at sub-ambient as well as at elevated temperatures.

To reduce the order of the large-scale dynamic systems, a method has been proposed by merging improved modified pole clustering and Genetic Algorithm. Reduced order denominator and numerator polynomial is obtained via improved modified pole clustering technique and Genetic Algorithm respectively. The method produces ‘k’ number of reduced order systems for kth — order reduction. A numerical example has been taken from the literature to show the viability of the proposed mixed method and also compared with existing order reduction methods.

A mixed method by combining modified pole clustering technique and modified cauer continued fraction is proposed for reducing the order of the large-scale dynamic systems. The denominator polynomial of the reduced order model is obtained by using modified pole clustering technique while the coefficients of the numerator are obtained by modified cauer continued fraction. This method generated 'k' number of reduced order models for kth order reduction. The superiority of the proposed method has been elaborated through numerical example taken from the literature and compared with few existing order reduction methods., {"references":["V. Singh, D. Chandra and H. Kar, \"Improved Routh Pade approximants:\nA Computer aided approach\", IEEE Trans. Autom. Control, 49(2), 2004,\npp.292-296.","S.Mukherjee and R.N. Mishra, \"Reduced order modeling of linear\nmultivariable systems using an error minimization technique\", Journal\nof Franklin Inst., 325 (2), 1988., pp.235-245.","Sastry G.V.K.R Raja Rao G. and Mallikarjuna Rao P., \"Large scale\ninterval system modeling using Routh approximants\", Electronic Letters,\n36(8), 2000, pp.768-769.","R. Prasad, \"Pade type model order reduction for multivariable systems\nusing Routh approximation\", Computers and Electrical Engineering, 26,\n2000, pp.445-459.","G. Parmar, S. Mukherjee and R. Prasad, \" division algorithm and eigen\nspectrum analysis\", Applied Mathematical Modelling, Elsevier, 31, 2007,\npp.2542-2552.","C.B. Vishwakarma and R. Prasad, \"Clustering method for reducing\norder of linear system using Pade approximation\" IETE Journal of\nResearch, Vol.54, No. 5, Oct. 2008, pp. 323-327.","C.B. Vishwakarma and R. Prasad, \"Order reduction using the\nadvantages of differentiation method and factor division\", Indian\nJournal of Engineering & Materials Sciences, Niscair, New Delhi, Vol.\n15, No. 6, December 2008, pp. 447-451.","A.K. Sinha, J. Pal, Simulation based reduced order modeling using a\nclustering technique, Computer and Electrical Engg., 16(3), 1990,\npp.159-169.","CB Vishwakarma, \"Order reduction using Modified pole clustering and\npade approximans\", world academy of science, engineering and\nTechnology 80 2011.\n[10] Chen, C. F., and Shieh, L. S 'A novel approach to linear model\nsimplification', Intt. J. Control, 1968,8, pp. 561-570.\n[11] Chaung, S. G. 'Application of continued fraction methods for modeling\ntransfer function to give more accurate initial transient response',\nElectron . Lett., 1970,6, pp. 861-863\n[12] R. Parthasarathy and S. John, \"Cauer continued fraction method for\nmodel reduction,\" Electron. Lett., vol. 17, 1981, pp. 792-793. [13] R. Parthasarathy and S. John, \"State space models using modified Cauer\ncontinued fraction\", Proceedings IEEE (lett.), Vol. 70, No. 3, 1982, pp.\n300-301.\n[14] R. Parthasarathy and S. John, \"System reduction by Routh\napproximation and modified Cauer continued fraction\", Electronic\nLetters, Vol. 15, 1979, pp. 691-692.\n[15] A.K. Mittal, R. Prasad, and S.P. Sharma, \"Reduction of linear dynamic\nsystems using an error minimization technique\", Journal of Institution\nof Engineers IE(I) Journal – EL, Vol. 84, 2004, pp. 201-206.\n[16] J. Pal, \"Stable reduced order Pade approximants using the Routh urwitz\narray\", Electronic Letters , Vol. 15, No.8, 1979, pp. 225-226.\n[17] M. R. Chidambara, \"On a method for simplifying linear dynamic\nsystem\", IEEE Trans. Automat Control, Vol. AC-12, 1967, pp. 119-120.\n[18] L. S. Shieh and Y. J. Wei, \"A mixed method for multivariable system\nreduction\", IEEE Trans. Automat. Control, Vol. AC-20, 1975, pp. 429-\n432\n[19] Bistritz Y. and Shaked U., \"Stable linear systems simplification via pade\napproximation to Hurwitz polynomial\", Transaction ASME, Journal of\nDynamic System Measurement and Control, Vol. 103, 1981, pp. 279-\n284.\n[20] Girish Parmar and Manisha Bhandari, \"Reduced order modelling of\nlinear dynamic systems using eigen spectrum analysis and modified\ncauer continued fraction\" XXXII National Systems Conference, NSC\n2008, December 17-19, 2008.\n[21] R. Prasad and J. Pal, \"Use of continued fraction expansion for stable\nreduction of linear multivariable systems\", Journal of Institution of\nEngineers, India, IE(I) Journal – EL, Vol. 72, 1991, pp. 43-47."]}

The author presented a method for model order reduction of large-scale time-invariant systems in time domain. In this approach, two modified Hankel matrices are suggested for getting reduced order models. The proposed method is simple, efficient and retains stability feature of the original high order system. The viability of the method is illustrated through the examples taken from literature., {"references":["Therapos C. P., \"Balanced Minimal Realization of SISO Systems\", Electronics Letters, Vol. 19, No.11, pp. 424-426, 1983.","Rosza P. and Sinha N. K., \"Efficient Algorithm for Irreducible Realization of a Rational Matrix\", Int. Journal of Control, Vol. 20, pp. 739-751, 1974.","Shamash Y., \"Model Reduction Using Minimal Realization Algorithms\" Electronics Letters, Vol. 11, No. 16, pp. 385-387, 1975.","Parthasarathy R. and Singh H. \"Minimal Realization of a Symmetric Transfer Function Matrix Using Markov Parameters and Moments\", Electronics Letters, Vol. 11, No. 15, pp. 324-326, 1975.","Hickin J. and Sinha N. K. \"New Method of Obtaining Reduced Order Models for Linear Multivariable Systems\", Electronics Letters, Vol. 12, pp. 90-92, 1976.","Shrikhande V. L., \"Harpreet Singh and Ray L. M.: On Minimal Realization of Transfer Function Matrices Using Markov Parameters and Moments\", Proc. IEEE, Vol. 65, No. 12, pp. 1717-1719, 1978.","Sinha N. K. \"Minimal Realization of Transfer Function Matrices: A Comparative Study of Different Methods\", Int. Journal of Control, Vol. 22, No. 5, pp. 627-639, 1975.","Silverman L. M. \"Realization of Linear Dynamical Systems\", IEEE Trans. Automatic Control, Vol.16, pp. 554-567, 1971.","C.B Vishwakarma and R. Prasad, \"Order Reduction Using Modified Pole Clustering and Pade Approximations\", International Journal of Embedded Software and Open Source systems, Vol.1 , No. 1 , pp. 11-19, 2011.\n[10]\tC.B Vishwakarma & R. Prasad, \"Clustering Method for Reducing Order of Linear Systems Using Pade Approximations\", IETE Journal of Research, Vol.54, No.5, pp. 326-330, 2008.\n[11]\tSingh Nidhi, \"Ph. D thesis on Reduced Order Modeling and Controller Design\", Indian Institute of Technology, Roorkee, India, December 2007."]}

The author presented a method for model order reduction of large-scale time-invariant systems in time domain. In this approach, two modified hankel matrices are suggested for getting reduced order models. The proposed method is simple, efficient and retains stability feature of the original high order system. The viability of the method is illustrated through the examples taken from literature.

A mixed method is proposed for finding stable reduced order models of single-input- single-output large-scale systems using Pade approximation and the clustering technique. The denominator polynomial of the reduced order model is determined by forming the clusters of the poles of the original system, and the coefficients of numerator polynomial are obtained by using the Pade approximation technique. This method guarantees stability of the reduced order model when the original high order system is stable. The methodology of the proposed method is illustrated with the help of examples from literature.