A novel order reduction procedure for linear time invarient interval systems using SGO algorithm
-
2018-02-09 https://doi.org/10.14419/ijet.v7i1.8.9986 -
Social Group Optimization, Reduced Order Model, Optimal Approximation, Integral Square Error, Impulse Response Energy Error, Interval Systems. -
Abstract
In this paper, the authors presented a new algorithm for the reduction of high order linear time interval systems. In the proposed method, the Reduced Order Interval Model (ROIM) denominator and numerator polynomials are determined based on minimization ofobjective function comprising of Integral Squared Error r using Social Group Optimization (SGO). The SGO technique is found to be simple, easy in implementation and provides the optimal solution. Applicability and effectiveness of the proposed method are illustrated through a DC motor speed control system and a typical Seventh order system taken from the literature.
-
References
[1] Y Shamash (1974), Stable reduced order models using Pade type approximation, IEEE Trans. on Automatic Control, vol. 19, no. 5, pp.615-616.https://doi.org/10.1109/TAC.1974.1100661.
[2] M F Hutton and B Friedland (1975), Routh Approximation for reducing order of linear time invariant system, IEEE Trans. on Automatic Control, vol. 20, no. 3, pp. 329-337.https://doi.org/10.1109/TAC.1975.1100953.
[3] T.C. Chen, C.Y. Chang and K.W. Han (1979), Reduction of transfer functions by the stability-equation method, J. Frankl. Inst., 8, 389–404.https://doi.org/10.1016/0016-0032(79)90066-8.
[4] B Bandyopadhyay, O Ismail and R Gorez (1994), Routh-Pade approximation for interval systems, IEEE Trans. on Automatic Control, vol. 39, no. 12, pp. 2454 - 2456.
[5] B Bandyopadhyay, Avinash Upadhye and Osman Ismail (1997), Routh Approximation for Interval Systems, IEEE Trans.on Automatic Control, vol.42, no. 8, pp. 1126-1130.https://doi.org/10.1109/9.362850.
[6] V L Kharitonov (1979), Asymptotic stability of an equilibrium position of a family of systems of linear differential equations, Differentsial’nye Uraveniya, vol. 14, no. 11, pp. 2086-2088.
[7] Devender kumar saini and Dr. Rajendra prasad (2010), Mixed evolutionary techniques to reduce order of linear interval systems using generlized routh array, International Journal of Engineering science and technology, vol. 2, no. 10, pp. 5197-5205.
[8] G V K R Sastry and P Mallikarjuna Rao (2003), A New Method for Modelling of Large Scale Interval Systems, IETE Journal of Research, vol 49, no6, 423-430.https://doi.org/10.1080/03772063.2003.11416366.
[9] G V K R Sastry and M Siva Kumar (2008), High -order MIMO interval system reduction using direct routh approximation method, International Journal of Engineering Reasearch Indus. Appls.,vol.1, no.4, pp 45-54.
[10] G V K R Sastry and M Siva Kumar (2010), Direct Routh Approximation method for linear SISO uncertain systems Reduction, International Journal of Applied Engineering Reasearch, vol .5, no.1, pp. 96-98.
[11] N Selvaganesan (2007), Mixed Method of Model Reduction for Uncertain Systems, Serbian Journal of Electrical Engineering, vol. 4, no. 1, pp. 1-12.https://doi.org/10.2298/SJEE0701001S.
[12] D Kranti Kumar, S K Nagar and J P Tiwari (2011), Model Order reduction of Interval systems using Routh approximation and Cauer second form, International journal of Advances in science and technology, vol. 3, no. 2, pp. 35-41.
[13] B.Chen, M.Nordin and P.O.Gutman (1995), Recursive grid method to compute value set of Transfer function with parametric uncertainiity,In Proc of ACC ,3861-3865.
[14] Suresh Satapath and Anima Naik(2016) , Social group optimization (SGO): a new population evolutionary optimization technique, Complex and intelligent systems, Volume 2, Issue 3, pp 173–203, Oct. 2016
[15] A Naik, S C Satapathy and A S Ashour et al., Social group optimization for global optimization of multimodal functions and data clustering problems, Neural Computation &Applications,
Doi.org/10.1007/s00521-016-2686-9.
-
Downloads
-
How to Cite
Anand N, V., Kumar M, S., & Rao R, S. (2018). A novel order reduction procedure for linear time invarient interval systems using SGO algorithm. International Journal of Engineering & Technology, 7(1.8), 118-122. https://doi.org/10.14419/ijet.v7i1.8.9986Received date: 2018-03-08
Accepted date: 2018-03-08
Published date: 2018-02-09