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Analysis of Linear Time Invariant and Time Varying Dynamic Systems via Taylor Series Using a New Recursive Algorithm

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Modelling and Simulation in Science, Technology and Engineering Mathematics (MS-17 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 749))

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Abstract

The paper presents a new recursive method using Taylor series to solve the states of time invariant as well as time varying control systems. In traditional approach, the Taylor series had been used by well known operational matrix for integration, whereas this proposition does not follow the same method. This approach is recursive in nature and thereby avoids the complexity of using operational matrix of fixed dimension. Additionally, computational burden and memory requirement is greatly reduced. If equal number of recursion points are considered, the second order Taylor series solution is always more efficient than the first order Taylor series solution. But, the first order Taylor series can approach the accuracy of the second order Taylor series solution at the cost of more recursion points, i.e., increasing the computational burden. This has been studied numerically. Three examples are treated and the results obtained are compared with the exact solutions via related tables and graphs. The present approach is attractive because of its straightforward approach.

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Authors and Affiliations

  1. Department of Electrical Engineering, Faculty, MCKV Institute of Engineering, 243, G. T. Road, Liluah, Howrah, 711204, India

    Suchismita Ghosh

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  1. Suchismita Ghosh
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Correspondence to Suchismita Ghosh .

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Editors and Affiliations

  1. Department of Electrical Engineering, Ghani Khan Choudhury Institute of Engineering and Technology, Malda, West Bengal, India

    Surajit Chattopadhyay

  2. Department of Electrical Engineering, MCKV Institute of Engineering, Howrah, West Bengal, India

    Tamal Roy

  3. University of Calcutta, Kolkata, West Bengal, India

    Samarjit Sengupta

  4. University of Lyon, Lyon, France

    Christian Berger-Vachon

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Ghosh, S. (2019). Analysis of Linear Time Invariant and Time Varying Dynamic Systems via Taylor Series Using a New Recursive Algorithm. In: Chattopadhyay, S., Roy, T., Sengupta, S., Berger-Vachon, C. (eds) Modelling and Simulation in Science, Technology and Engineering Mathematics. MS-17 2017. Advances in Intelligent Systems and Computing, vol 749. Springer, Cham. https://doi.org/10.1007/978-3-319-74808-5_34

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  • DOI: https://doi.org/10.1007/978-3-319-74808-5_34

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-74807-8

  • Online ISBN: 978-3-319-74808-5

  • eBook Packages: EngineeringEngineering (R0)

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