New results and examples in nonlinear feedback stabilization
Systems & Control Letters
Adding an integrator for the stabilization problem
Systems & Control Letters
A toolkit for nonlinear feedback design
Systems & Control Letters
Nonlinear and Adaptive Control Design
Nonlinear and Adaptive Control Design
Modelling and control of an overhead crane with a variable length flexible cable
International Journal of Computer Applications in Technology
MATH'08 Proceedings of the 13th WSEAS international conference on Applied mathematics
Modelling, simulation and control of a heavy chain system
EUROCAST'11 Proceedings of the 13th international conference on Computer Aided Systems Theory - Volume Part II
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This paper deals with the uniform exponential stabilization of a hybrid PDE-ODE system which describes an overhead crane with flexible cable. A previous linear boundary feedback law (see d'Andrea-Novel, Boustany, Conrad & Rao (1994). MCSS Journal, 1, 1-22) depending on the platform position and velocity and on the angular displacement of the cable at the connection point to the platform, led to asymptotic stabilization but could not provide an exponential decay (see Rao (1993). European Journal of Applied Mathematics, 4, 303-319). Taking advantage of the ''cascaded'' structure of the hybrid system, we propose here a back-stepping approach leading to a linear boundary feedback which ''naturally'' depends in addition, on the angular velocity of the cable. We prove that this boundary feedback law produces uniform exponential stability and illustrative simulations are displayed. In d'Andrea-Novel & Coron ((1997). Proceedings of the IFAC SYROCO '97 Conference, Nantes) this result has been established under a small gain condition on the feedback stabilizing the subsystem made of the PDE. Here, by using a result of Datko (see Datko (1970). Journal of Mathematical Analysis and Application, 32, 610-616) we show that this condition can be relaxed.