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at - Automatisierungstechnik

Methoden und Anwendungen der Steuerungs-, Regelungs- und Informationstechnik

[AT - Automation Technology: Methods and Applications of Control, Regulation, and Information Technology
]

Editor-in-Chief: Jumar, Ulrich


IMPACT FACTOR 2018: 0.500

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2196-677X
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Volume 67, Issue 8

Issues

Tracking control of a heavy chain system

Trajektorienfolgeregelung für das Labormodell „Scheibe mit schwerer Kette“

Christoph Hinterbichler
  • Corresponding author
  • Johannes Kepler University Linz, Institute of Automatic Control and Control Systems Technology, Altenberger Straße 69, A-4040 Linz, Austria
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Jakob Brunner / Kurt Schlacher
  • Johannes Kepler University Linz, Institute of Automatic Control and Control Systems Technology, Altenberger Straße 69, A-4040 Linz, Austria
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2019-07-31 | DOI: https://doi.org/10.1515/auto-2019-0014

Abstract

This paper deals with the tracking control of a particular heavy chain system, which consists of a chain mounted onto a pivoted disk. To this end, the governing system of ordinary differential equations is derived and a trajectory is computed via numerical optimization. As the arising optimization problem is computationally complex, a multithreading algorithm for parallel computation of the required derivatives is presented. Furthermore, a stabilizing feedback controller, based on damping injection and an integrator backstepping approach, is derived. Finally, measurements of a laboratory experiment show an excellent performance of the proposed control concept.

Zusammenfassung

Dieser Beitrag befasst sich mit der Trajektorienplanung und Regelung für das Labormodell „Scheibe mit schwerer Kette“. Bei diesem speziellen Modell ist die Kette an einer drehbar gelagerten Scheibe montiert. Die Trajektorie wird durch numerisches Lösen eines Optimierungsproblems berechnet, welches auf Grund der hohen Modellordnung äußerst komplex ist. Um die Laufzeit des Optimierers signifikant zu verringern, wird ein Multithreading-Algorithmus zur parallelen Berechnung der benötigten Ableitungen vorgestellt. Zur Stabilisierung der berechneten Trajektorie wird eine Kombination aus passivitätsbasiertem Reglerentwurf und einem Backstepping-Regler verwendet. Abschließend wird anhand von Messergebnissen die ausgezeichnete Funktion des vorgeschlagenen Regelungskonzepts demonstriert.

Keywords: heavy chain system; nonlinear optimization; multithreading; passivity-based control; backstepping

Schlagwörter: Schwere Kette; Nichtlineare Optimierung; Multithreading; Passivitätsbasierter Reglerentwurf; Backstepping

References

  • 1.

    HSL. A collection of Fortran codes for large scale scientific computation. URL: http://www.hsl.rl.ac.uk/. [Accessed 5.2.2019].Google Scholar

  • 2.

    Maple 2017. Maplesoft, a division of Waterloo Maple Inc., Waterloo, Ontario.

  • 3.

    The supercomputer mach-2. URL: https://www3.risc.jku.at/projects/mach2/. [Accessed 5.2.2019].Google Scholar

  • 4.

    B. Bell. CppAD: A Package for Differentiation of C++ Algorithms. URL: https://www.coin-or.org/CppAD/. [Accessed 5.2.2019].Google Scholar

  • 5.

    J. Brunner. Simulation und Regelung eines Multipendels. Master’s thesis, Johannes Kepler Universität Linz, 2017.Google Scholar

  • 6.

    P. Deuflhard and F. Bornemann. Scientific Computing with Ordinary Differential Equations. Springer, 2002.Google Scholar

  • 7.

    G. Gaël, J. Benoît, et al. Eigen v3. URL: http://eigen.tuxfamily.org, 2010. [Accessed 5.2.2019].Google Scholar

  • 8.

    D. Gerbet and J. Rudolph. Redundante Koordinaten in der Modellbildung für ein schweres Seil. at – Automatisierungstechnik, 66(7):536–547, 2018.CrossrefGoogle Scholar

  • 9.

    A. Griewank and A. Walther. Evaluating Derivatives – Principles and Techniques of Algorithmic Differentiation (2nd Ed.). Society for Industrial and Applied Mathematics, 2008.Google Scholar

  • 10.

    H.K. Khalil. Nonlinear Systems (3rd Ed.). Prentice Hall, 2003.Google Scholar

  • 11.

    T. Knüppel and F. Woittennek. Control design for quasi-linear hyperbolic systems with an application to the heavy rope. IEEE Transactions on Automatic Control, 60(1):5–18, 2015.CrossrefWeb of ScienceGoogle Scholar

  • 12.

    T. Knüppel and F. Woittennek. Flatness based control design for a nonlinear heavy chain model. In 8th IFAC Symposium on Nonlinear Control Systems, 2010.Google Scholar

  • 13.

    M. Krstić, I. Kanellakopoulos and P. Kokotović. Nonlinear and Adaptive Control Design. John Wiley & and Sons, 1995.Google Scholar

  • 14.

    P. Ludwig, K. Rieger and K. Schlacher. Modelling, simulation and control of a heavy chain system. In Computer Aided Systems Theory – EUROCAST 2011, 2012.Google Scholar

  • 15.

    A. Machelli. Port Hamiltonian Systems: A unified approach for modeling and control finite and infinite dimensional physical systems. PhD thesis, University of Bologna, 2002.Google Scholar

  • 16.

    R.M. Murray, M. Rathinam and W. Sluis. Differential flatness of mechanical control systems: A catalog of prototype systems. In ASME International Mechanical Engineering Congress and Exposition, 1995.Google Scholar

  • 17.

    M. Papageorgiou. Optimierung: Statische, dynamische, stochastische Verfahren für die Anwendung. R. Oldenbourg Verlag, 1991.Google Scholar

  • 18.

    N. Petit and P. Rouchon. Flatness of heavy chain systems. In Proceedings of the 41st IEEE Conference on Decision and Control, 2002.Google Scholar

  • 19.

    H. Schättler and U. Ledzewicz. Geometric Optimal Control. Springer, 2012.Google Scholar

  • 20.

    M. Schöberl and A. Siuka. On Casimir functionals for field theories in port-Hamiltonian description for control purposes. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, 2011.Google Scholar

  • 21.

    M. Schöberl and A. Siuka. Modelling and control of infinite-dimensional mechanical systems: A port-Hamiltonian approach. In Multibody System Dynamics, Robotics and Control, chapter 5, pages 75–93. Springer, 2013.Google Scholar

  • 22.

    M.W. Spong and M. Vidyasagar. Robot Dynamics and Control. John Wiley & Sons, 1989.Google Scholar

  • 23.

    D. Stürzer, A. Arnold and A. Kugi. Closed-loop stability analysis of a gantry crane with heavy chain and payload. International Journal of Control, 91:1931–1943, 2017.Web of ScienceGoogle Scholar

  • 24.

    D. Thull, D. Wild and A. Kugi. Infinit-dimensionale Regelung eines Brückenkranes mit schweren Ketten. at – Automatisierungstechnik, 53(8):400–410, 2005.Google Scholar

  • 25.

    A. Wächter and L.T. Biegler. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical Programming, 106(1):25–57, 2006.CrossrefGoogle Scholar

About the article

Christoph Hinterbichler

Christoph Hinterbichler received his diploma in Mechatronics from the Johannes Kepler University Linz (JKU), Austria, in 2016. Since then, he has been pursuing his PhD at the Institute of Automatic Control and Control Systems Technology. His research focuses on the industrial application of advanced control concepts and numerical optimization.

Jakob Brunner

Jakob Brunner received his diploma in Mechatronics from the Johannes Kepler University Linz (JKU), Austria, in 2017. He is currently employed as NVH (Noise, Vibration, Harshness) engineer at BRP Rotax GmbH & Co KG.

Kurt Schlacher

O. Univ.-Prof. Dipl.-Ing, Dr. techn. Kurt Schlacher is head of the Institute of Automatic Control and Control Systems Technology, Johannes Kepler University Linz, Austria. Main research topics and areas of work: Modeling and control of nonlinear lumped and distributed parameter systems having regard to industrial applications and deploying differential-geometric and computer algebra based methods.


Received: 2019-02-06

Accepted: 2019-05-26

Published Online: 2019-07-31

Published in Print: 2019-08-27


Citation Information: at - Automatisierungstechnik, Volume 67, Issue 8, Pages 693–702, ISSN (Online) 2196-677X, ISSN (Print) 0178-2312, DOI: https://doi.org/10.1515/auto-2019-0014.

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