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Kharitonov Polynomial-Based Order Reduction of Continuous Interval Systems

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Abstract

In this contribution, two general expressions for Markov parameters (MPs) and time moments (TMs) of continuous interval systems (CISs) are proposed. The TMs and MPs are derived in such a way that they do not require the inversion of the denominator of the transfer function of a given system. Additionally, there is no requirement for the solution of interval equations for obtaining TMs and MPs. The applicability of derived TMs and MPs is shown with the help of CIS model order reduction (MOR). The method utilized for the CIS MOR is the Routh–Padé approximation. The whole MOR procedure is explained with the help of one test case where the third-order system is reduced to first-order and second-order models. To establish the efficacy of the proposed method, the step and impulse responses of the system and model are plotted. For a fair comparative study, time-domain specifications such as the peak value, rise time, settling time, peak time and steady-state value for the lower and upper limits of the model are presented. Furthermore, the integral square error, integral absolute error, integral of time multiplied absolute error and integral of time multiplied square error for the difference between the responses of the system and model are tabulated. The results presented prove the applicability and effectiveness of the proposed method.

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Abbreviations

\({G_n(s)}\) :

System transfer function

B :

System numerator coefficients

A :

System denominator coefficients

T :

System time moments (TMs)

M :

System Markov parameters (MPs)

\({H_p(s)}\) :

Model transfer function

\(b^*\) :

Model numerator coefficients

\(a^*\) :

Model denominator coefficients

\(t^*\) :

Model time moments (TMs)

\(m^*\) :

Model Markov parameters (MPs)

P(s):

Kharitonov polynomial coefficients

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Acknowledgements

This work is supported by the Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India (Grant No: ECR/2017/000212).

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Authors and Affiliations

  1. Department of Electrical Engineering, Malaviya National Institute of Technology Jaipur, Jaipur, India

    V. P. Meena & V. P. Singh

  2. Faculty of Computing and Information Technology in Rabigh, Rabigh, Saudi Arabia

    Lalbihari Barik

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  1. V. P. Meena
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  2. V. P. Singh
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  3. Lalbihari Barik
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Meena, V.P., Singh, V.P. & Barik, L. Kharitonov Polynomial-Based Order Reduction of Continuous Interval Systems. Circuits Syst Signal Process 41, 743–761 (2022). https://doi.org/10.1007/s00034-021-01824-4

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