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Observer-Controller Design for Three Dimensional Overhead Cranes Using Time-Scaling

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  • A. GIUA
  • M. SANNA
  • C. SEATZU

Abstract

In this paper we address the design of an observer-controller for a three degrees of freedom overhead crane. We consider a linear model of the crane where the length of the suspending rope is a time-varying parameter. The set of models given by frozen values of the rope length can be reduced to a single time-invariant reference model using suitable time-scalings. We construct a controller and an observer for the reference model assigning the desired closed loop eigenvalues for both system and estimation error. The time-scaling relations can be used to derive a control law for the time-varying system that implements an implicit gain-scheduling [6]. A second gain-scheduling is used to choose suitable closed-loop eigenvalues for different values of the load and lifting/lowering operations. Using a Lyapunov-like theorem, it is also possible to find relative upper bounds for the rate of change of the varying parameter that ensure the stability of the time-varying system.

Suggested Citation

  • A. Giua & M. Sanna & C. Seatzu, 2001. "Observer-Controller Design for Three Dimensional Overhead Cranes Using Time-Scaling," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 7(1), pages 77-107, March.
    • Handle: RePEc:taf:nmcmxx:v:7:y:2001:i:1:p:77-107
    DOI: 10.1076/mcmd.7.1.77.3634
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    Cited by:

    1. Alyazidi, Nezar M. & Hassanine, Abdalrahman M. & Mahmoud, Magdi S., 2023. "An Online Adaptive Policy Iteration-Based Reinforcement Learning for a Class of a Nonlinear 3D Overhead Crane," Applied Mathematics and Computation, Elsevier, vol. 447(C).

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