Multibody System Dynamics

, Volume 42, Issue 1, pp 1–17 | Cite as

Real-time trajectory control of an overhead crane using servo-constraints

  • Svenja Otto
  • Robert Seifried


In this paper, the system dynamics of an overhead crane are inverted by servo-constraints. The inversion provides a feedforward control for trajectory tracking of the system output. The overhead crane is inherently underactuated and modeled as a two-dimensional mechanical system with nonlinear system dynamics. Actuators are modeled as first-order systems to simplify implementation and account for velocity-controlled drives. The control based on servo-constraints is shown to be an effective method of trajectory control for overhead cranes. It will be demonstrated that the formulation is solvable in real-time using linear implicit Euler integration. The feedforward solution is made robust by an augmentation with LQR as well as a sliding mode controller. Experiments are conducted on a laboratory crane of 13 m motion range.


Servo-constraints Feedforward control Overhead crane Trajectory tracking Underactuated systems 


Compliance with ethical standards

The authors declare that they have no conflict of interest.


  1. 1.
    Abdel-Rahman, E.M., Nayfeh, A.H., Masoud, Z.N.: Dynamics and control of cranes: a review. J. Vib. Control 9(7), 863–908 (2003) zbMATHGoogle Scholar
  2. 2.
    Ashrafiuon, H., Erwin, R.S.: Sliding mode control of underactuated multibody systems and its application to shape change control. Int. J. Control 81(12), 1849–1858 (2008) MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Betsch, P., Altmann, R., Yang, Y.: Numerical integration of underactuated mechanical systems subjected to mixed holonomic and servo constraints. In: Multibody Dynamics, pp. 1–18 (2016) Google Scholar
  4. 4.
    Blajer, W., Kolodziejczyk, K.: A geometric approach to solving problems of control constraints: theory and a DAE framework. Multibody Syst. Dyn. 11(4), 343–364 (2004) MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Blajer, W., Kołodziejczyk, K.: Improved DAE formulation for inverse dynamics simulation of cranes. Multibody Syst. Dyn. 25(2), 131–143 (2011) CrossRefGoogle Scholar
  6. 6.
    Boustany, F., D’Andrea-Novel, B.: Adaptive control of an overhead crane using dynamic feedback linearization and estimation design. In: Robotics and Automation, 1992, Proceedings, 1992 IEEE International Conference, pp. 1963–1968 (1992) CrossRefGoogle Scholar
  7. 7.
    Brogan, W.L.: Modern Control Theory. Prentice Hall, New York (1991) zbMATHGoogle Scholar
  8. 8.
    Campbell, S.L.: High-index differential algebraic equations. Mech. Struct. Mach. 23(2), 199–222 (1995) MathSciNetCrossRefGoogle Scholar
  9. 9.
    Castillo, I., Vazquez, C., Fridman, L.: Overhead crane control through LQ singular surface design Matlab toolbox. In: American Control Conference (ACC), 2015, pp. 5847–5852 (2015) CrossRefGoogle Scholar
  10. 10.
    Fliess, M., Lévine, J., Martin, P., Rouchon, P.: Flatness and defect of non-linear systems: introductory theory and examples. Int. J. Control 61(6), 1327–1361 (1995) MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Hairer, E., Wanner, G.: Stiff and Differential-Algebraic Problems, 2nd edn. Springer, Berlin (1996) zbMATHGoogle Scholar
  12. 12.
    Otto, S.: Nonlinear trajectory control of a gantry crane. Master thesis MSC-001, Institute of Mechanics and Ocean Engineering, Hamburg University of Technology (2016) Google Scholar
  13. 13.
    Schiehlen, W., Eberhard, P.: Technische Dynamik Rechnergestützte Modellierung mechanischer Systeme im Maschinen- und Fahrzeugbau, 4th edn. Springer, Wiesbaden (2014) Google Scholar
  14. 14.
    Seifried, R., Blajer, W.: Analysis of servo-constraint problems for underactuated multibody systems. Mech. Sci. 4(1), 113–129 (2013) CrossRefGoogle Scholar
  15. 15.
    Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice Hall International, Englewood Cliffs (1991) zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Institute of Mechanics and Ocean EngineeringHamburg University of TechnologyHamburgGermany

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