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Performance Evaluation of an LQG Controller of a Robotic Link with Fractional Dampers Based on Their Integer–Order Approximation

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Mechanism Design for Robotics (MEDER 2018)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 66))

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Abstract

Accurate modelling of robotic links may lead to fractional–order descriptions that complicate controller synthesis. This paper explores whether an LQG controller derived for an integer–order approximation can be applied to the original fractional–order model without appreciably degrading the system performance. Simulations show that this is the case for a fairly large range of orders of fractional derivatives and related combination coefficients.

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Notes

  1. 1.

    Bryson suggests to use diagonal matrices Q and R and to choose the diagonal entries according to the maximum acceptable values (m.a.v.). In particular, \(Q_{ii}=( m.a.v. of x_i)^{-2}\) and \(R_{ii}=( m.a.v. of u_i)^{-2}\).

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Author information

Authors and Affiliations

  1. Polytechnic Department of Engineering and Architecture, University of Udine, via delle Scienze 206, 33100, Udine, Italy

    Daniele Casagrande, Stefano Miani & Umberto Viaro

  2. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Wiesław Krajewski

Authors
  1. Daniele Casagrande
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  2. Wiesław Krajewski
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  3. Stefano Miani
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  4. Umberto Viaro
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Corresponding author

Correspondence to Stefano Miani .

Editor information

Editors and Affiliations

  1. Dipartimento Politecnico di Ingegneria e Architettura, Università degli Studi di Udine, Udine, Italy

    Alessandro Gasparetto

  2. Dipartimento di Ingegneria Meccanica e Civile, Università di Cassino e del Lazio Meridionale, Cassino, Italy

    Marco Ceccarelli

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Casagrande, D., Krajewski, W., Miani, S., Viaro, U. (2019). Performance Evaluation of an LQG Controller of a Robotic Link with Fractional Dampers Based on Their Integer–Order Approximation. In: Gasparetto, A., Ceccarelli, M. (eds) Mechanism Design for Robotics. MEDER 2018. Mechanisms and Machine Science, vol 66. Springer, Cham. https://doi.org/10.1007/978-3-030-00365-4_29

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