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Geometry and flatness of m-crane systems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We propose a class of m-crane control systems that generalizes two- and three-dimensional crane systems. We prove that each representant of the described class is feedback equivalent to the second order chained form with drift. In consequence, we prove that it is differentially flat. Then we investigate its control properties and derive a control law for tracking control problem.
Rocznik
Strony
893--903
Opis fizyczny
Bibliogr. 18 poz., rys., tab.
Twórcy
autor
  • Poznan University of Technology, Institute of Automatic Control and Robotic, Piotrowo 3a, 61-138 Poznań, Poland
  • Normandie Université, INSA de Rouen, Laboratoire de Mathématiques, 76801 Saint-Etienne-du-Rouvray, France
autor
  • Normandie Université, INSA de Rouen, Laboratoire de Mathématiques, 76801 Saint-Etienne-du-Rouvray, France
autor
  • Poznan University of Technology, Institute of Automatic Control and Robotic, Piotrowo 3a, 61-138 Poznań, Poland
  • Poznan University of Technology, Institute of Automatic Control and Robotic, Piotrowo 3a, 61-138 Poznań, Poland
Bibliografia
  • [1] C. Cheng and C. Chen, “Controller design for an overhead crane system with uncertainty”, Control Engineering Practice 4(5), 645‒653, 1996.
  • [2] B. d’Andréa-Novel and J. Lévine, “Modelling and Nonlinear Control of an Overhead Crane”, In: Kaashoek M.A., van Schup-pen J.H., Ran A.C.M. (eds) Robust Control of Linear Systems and Nonlinear Control. Progress in Systems and Control Theory, vol 4. Birkhäuser Boston, 1990.
  • [3] M. Fliess, J. Lévine, P. Martin, and P. Rouchon, “Sur les systemes non linéaires différentiellement plats”, C. R. Acad. Sci. Paris Sér. I Math., 315, pp. 619–624, 1992.
  • [4] M. Fliess, J. Lévine, P. Martin, and P. Rouchon, “Flatness and defect of non-linear systems: introductory theory and examples”, International Journal of Control (61)6, 1327‒1361, 2007
  • [5] M. Fliess, J. Lévine, and P. Rouchon, “A simplified approach of crane control via a generalized state-space model”, Decision and Control, Proceedings of the 30th IEEE Conference on, 736‒741 vol. 1. 10.1109/CDC.1991.261409, 1992.
  • [6] A. Isidori, Nonlinear Control Systems, 3rd edition, Springer- Verlag, London, 1995.
  • [7] B. Jakubczyk, “Invariants of dynamic feedback and free sys-tems”, in Proc. ECC, pp. 1510–1513, 1993.
  • [8] J. Lévine, Analysis and Control of Nonlinear Systems: A Flat-ness-Based Approach, Springer Science&Business Media, p. 184‒186, 2009.
  • [9] J.E. Marsden and T.S. Ratiu, Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems, Springer Publishing Company, Incorporated, 10.1016/0967‒0661(96)00046‒9, 2010.
  • [10] R.M. Murray, M. Rathinam, and W. Sluis, “Differential Flatness of Mechanical Control Systems: A Catalog of Prototype Sys-tems”, Proceedings of the 1995 ASME International Congress and Exposition, 1995.
  • [11] F. Nicolau and W. Respondek, “Flatness of multi-input contro-laffine systems linearizable via one-fold prolongation”, SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics 55(5), 3171‒3203, 2017.
  • [12] F. Nicolau and W. Respondek, “Flatness of mechanical systems with 3 degrees of freedom”, IFAC-PapersOnLine 48(13), 19‒24, 2015.
  • [13] H. Nijmeijer and A.J. van der Schaft, “Nonlinear Dynamical Control Systems”, Springer-Verlag, New York, 1990.
  • [14] J. Pomet, “A differential geometric setting for dynamic equivalence and dynamic linearization”, Banach Center Publ., (32), 319–339, 1995.
  • [15] J. Pomet, “On dynamic feedback linearization of fourdimensional affine control systems with two inputs”, ESAIM Control Optim. Calc. Var, 2, 151–230, 1997.
  • [16] J. Smoczek, “Interval arithmetic-based fuzzy discrete-time crane control scheme design”, Bull. Pol. Ac.: Tech. (61)4, 863‒870, 2013.
  • [17] W. Respondek, “Symmetries and minimal flat outputs of nonlinear control systems”, In New Trends in Nonlinear Dynamics and Control and their Applications, volume LNCIS 295, pp. 65–86. Springer, 2003.
  • [18] S.S. Vlase, “A Method of Eliminating Lagrangian Multipliers from the Equation of Motion of Interconnected Mechanical Systems”, ASME. J. Appl. Mech. 54(1), 235‒237. DOI: 10.1115/1.3172969, 1987.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-370f3ebb-e2fb-4057-8cf5-18e2c3097597
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