Analytic hierarchy process based approximation of high-order continuous systems using TLBO algorithm

  • S. P. Singh
  • Varsha Singh
  • V. P. Singh


This paper presents an analytic hierarchy process based approach for approximation of stable high-order systems using teacher–learner-based-optimization (TLBO) algorithm. In this method, the stable approximant is derived by minimizing the errors of time moments and of Markov parameters of system and its approximant. Being free from algorithm-specific parameters, the TLBO algorithm is used for minimizing the objective function. The Hurwitz criterion is used to ensure the stability of approximant. The first time moment of the system is retained in approximant to guarantee the matching of steady states of system and approximant. The distinctive feature of this work is that the multi-objective problem of minimization of errors of time moments and of Markov parameters is converted into single objective problem by assigning some weights to different objectives using analytic hierarchy process. Also, the proposed method always produces stable approximant for stable high-order system. The results of proposed approach are compared with other existing techniques. To conclude the superiority of proposed approach, a comparative study is performed using the step responses and time domain analysis. The efficacy and systematic nature of proposed approach is shown with the help of two test systems.


Analytic hierarchy process Model reduction Padé approximation Routh approximation Teacher–learner-based-optimization 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical EngineeringIndian Institute of TechnologyKanpurIndia
  2. 2.Department of Electrical EngineeringNational Institute of TechnologyRaipurIndia

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