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A novel and computationally efficient algorithm for stability analysis of multi input-multi output process control systems

  • Process Systems Engineering, Process Safety
  • Published:
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Abstract

An efficient method based on the Faddeev-Leverrier algorithm combined with the Adomian decomposition method is devised to facilitate the stability analysis of multi-input multi-output control systems. In contrast to prior eigenvalue algorithms, our method affords all eigenvalues of the state matrix, either real or complex. Specifically, the calculation of the complex eigenvalues is made possible through special canonical forms, mainly involving square root operators, of the characteristic equation of the state matrix. Moreover, the proposed method does not require an initial guess, which is often a matter of concern since an inappropriate guess can cause failure in such available schemes. For the sake of illustration, a number of numerical examples, including chemical reaction processes, are also provided that demonstrate the efficiency of our new technique.

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Authors and Affiliations

  1. Center for Separation Processes Modeling and Nano-Computations, School of Chemical Engineering, College of Engineering, University of Tehran, Tehran, 11155-4563, Iran

    Hooman Fatoorehchi & Hossein Abolghasemi

  2. Advanced Process Control Research Laboratory, School of Chemical Engineering, College of Engineering, University of Tehran, Tehran, 11155-4563, Iran

    Hooman Fatoorehchi, Hossein Abolghasemi & Reza Zarghami

  3. Multiphase Systems Research Laboratory, School of Chemical Engineering, College of Engineering, University of Tehran, Tehran, 11155-4563, Iran

    Reza Zarghami

  4. The George Adomian Center for Applied Mathematics, 316 South Maple Street, Hartford, Michigan, 49057-1225, USA

    Randolph Rach

  5. Institute for Control Engineering of Machine Tools and Manufacturing Units (ISW), University of Stuttgart, Stuttgart, 70174, Germany

    Sebastian von Freeden

Authors
  1. Hooman Fatoorehchi
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  2. Hossein Abolghasemi
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  3. Reza Zarghami
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  4. Randolph Rach
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  5. Sebastian von Freeden
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Correspondence to Hossein Abolghasemi.

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Fatoorehchi, H., Abolghasemi, H., Zarghami, R. et al. A novel and computationally efficient algorithm for stability analysis of multi input-multi output process control systems. Korean J. Chem. Eng. 32, 1733–1743 (2015). https://doi.org/10.1007/s11814-014-0385-8

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  • DOI: https://doi.org/10.1007/s11814-014-0385-8

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