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Register a new userFinite-time stabilization of an overhead crane with a flexible cable submitted to an affine tension
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The paper is concerned with the finite-time stabilization of a hybrid PDE-ODE system describing the motion of an overhead crane with a flexible cable. The dynamics of the flexible cable is described by the wave equation with a variable coefficient which is an affine function of the curvilinear abscissa along the cable. Using several changes of variables, a backstepping transformation, and a finite-time stable second-order ODE for the dynamics of a conveniently chosen variable, we prove that a global finite-time stabilization occurs for the full system constituted of the platform and the cable. The kernel equations and the finite-time stable ODE are numerically solved in order to compute the nonlinear feedback law, and numerical simulations validating our finite-time stabilization approach are presented.
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Equations of motion and dynamics of a quadrotor transporting a load with a flexible cable modeled as a chain pendulum is obtained using Euler-Lagrange equations by taking variations on manifolds. An arbitrary number of links considered in a series models the flexible cable connecting the load to the quadrotor while the whole system can undergo complex motion in 3D. Geometric nonlinear control asymptotically stabilizes the load and cable bellow the quadrotor. A linearization about the equilibrium and the corresponding lyapunov stability analysis is provided. We produced numerical simulations and validated our work experimentally using a quadrotor UAV.
A system of partial differential equations describing the spatial oscillations of an Euler-Bernoulli beam with a tip mass is considered. The linear system considered is actuated by two independent controls and separated into a pair of differential equations in a Hilbert space. A feedback control ensuring strong stability of the equilibrium in the sense of Lyapunov is proposed. The proof of the main result is based on the theory of strongly continuous semigroups.
We derived a coordinate-free form of equations of motion for a complete model of a quadrotor UAV with a payload which is connected via a flexible cable according to Lagrangian mechanics on a manifold. The flexible cable is modeled as a system of serially-connected links and has been considered in the full dynamic model. A geometric nonlinear control system is presented to exponentially stabilize the position of the quadrotor while aligning the links to the vertical direction below the quadrotor. Numerical simulation and experimental results are presented and a rigorous stability analysis is provided to confirm the accuracy of our derivations. These results will be particularly useful for aggressive load transportation that involves large deformation of the cable.
The frequency-based method is the most commonly used method for measuring cable tension. However, the calculation formulas for the conventional frequency-based method are generally based on the ideally hinged or fixed boundary conditions without a comprehensive consideration of the inclination angle, sag-extensibility, and flexural stiffness of cables, leading to a significant error in cable tension identification. This study aimed to propose a frequency-based method of cable tension identification considering the complex boundary conditions at the two ends of cables using the particle swarm optimization (PSO) algorithm. First, the refined stay cable model was established considering the inclination angle, flexural stiffness, and sag-extensibility, as well as the rotational constraint stiffness and lateral support stiffness for the unknown boundaries of cables. The vibration mode equation of the stay cable model was discretized and solved using the finite difference method. Then, a multiparameter identification method based on the PSO algorithm was proposed. This method was able to identify the tension, flexural stiffness, axial stiffness, boundary rotational constraint stiffness, and boundary lateral support stiffness according to the measured multiorder frequencies in a synchronous manner. The feasibility and accuracy of this method were validated through numerical cases. Finally, the proposed approach was applied to the tension identification of the anchor span strands of a suspension bridge (Jindong Bridge) in China. The results of cable tension identification using the proposed method and the existing methods discussed in previous studies were compared with the on-site pressure ring measurement results. The comparison showed that the proposed approach had a high accuracy in cable tension identification.
In this article we study how bad can be the singularities of a time-optimal trajectory of a generic control affine system. In the case where the control is scalar and belongs to a closed interval it was recently shown in [6] that singularities cannot be, generically, worse than finite order accumulations of Fuller points, with order of accumulation lower than a bound depending only on the dimension of the manifold where the system is set. We extend here such a result to the case where the control has an even number of scalar components and belongs to a closed ball.
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