Experiments with two formation controllers for marine unmanned surface vessels are reported. The formation controllers are designed using the nonlinear robust model-based sliding mode approach. The marine vehicles can operate in arbitrary formation configurations by using two leader-follower control schemes. For the design of these controller schemes 3 degrees of freedom (DOFs) of surge, sway, and yaw are assumed in the planar motion of the marine surface vessels. Each vessel only has two actuators; therefore, the vessels are underactuated and the lack of a kinematic constraint puts them into the holonomic system category. In this work, the position of a control point on the vessel is controlled, and the orientation dynamics is not directly controlled. Therefore, there is a potential for an oscillatory yaw motion to occur. It is shown that the orientation dynamics, as the internal dynamics of this underactuated system, is stable, i.e., the follower vehicle does not oscillate about its control point during the formation maneuvers. The proposed formation controller relies only on the state information obtained from the immediate neighbors of the vessel and the vessel itself. The effectiveness and robustness of formation control laws in the presence of parameter uncertainty and environmental disturbances are demonstrated by using both simulations and field experiments. The experiments were performed in a natural environment on a lake using a small test boat, and show robust performance to parameter uncertainty and disturbance.the first experimental verification of the above mentioned approach, whose unique features are the use of a control point, the zero-dynamic stability analysis, the use of leaderfollower method and a nonlinear robust control approach.
Shell structures are extensively used in engineering for constructions with light weight and high strength. Classical applications are covers in automotive industry, aero-and astronautics. For this purpose the dynamical behaviour is of interest for safety and comfort. The focus will be placed on rotating circumferential cylindrical shells. Starting with the geometrical nonlinear kinematics for the strains, the HAMILTON's principle is evaluated. In the followingup to the calculus of variation RITZ approach is used, to compute eigenfrequencies. Afterwards the results are discussed for certain examples and compared to FE-solutions. Mechanical modelStarting point is the mechanical model of a rotating cylindrical shell, how it is shown in figure 1. L is the length of the shell, R m the mean radius, h the wall thickness and Ω the constant angular velocity. The displacement of a arbitrary point on the middle surface P is given by the three functions u (X, φ, t), v (X, φ, t) and w (X, φ, t). Those functions depend on the LAGNRANGE parameters X, φ and the time t. For the description of the dynamical behaviour HAMILTON's principleis used. The kinetic energy is given by E kin and the potential energy by E pot . It is assumed, that there are no potential-free forces which are producing a additional virtual work (δW = 0). The kinetic energy of the rotating shell is given by(2)Fig. 1: Mechanical model of a rotating circumferential cylindrical shell.For the potential energy the stresses and strains of the shell are needed. HOOKE's law is assumed as well as the plain-stresstheory (h << R m , h << L), so that the non-zero strains are given byThe strain in thickness direction can be expressed as ZZ = −ν ( XX + φφ ) / (1 − ν). With the previous considerations the potential energy E potI = E 2 (1 − ν 2 ) L 0 2π 0 h/2 −h/2 2 XX + 2 ν XX φφ + 2 φφ (R m + Z) dZ dφ dX + E 1 + ν L 0 2π 0 h/2 −h/2 2 Xφ (R m + Z) dZ dφ dX (4)
The wire sawing technology plays an important role on the manufacturing of thin discs out of brittle materials and is used for example in the solar-and microelectronic industry. The surface of a wire sawn disc shows a characteristic geometry, which suggests the influence of oscillations during the slicing process. In order to examine the process a distinct-elementmodel is used to simulate the motion and the interaction of the abrasive particles with the moving wire and the workpiece. The simulation shows interesting phenomena like clustering of particles and reacting forces to the wire, which could be one reason for the observed oscillations in the process. Wire sawingThe wire sawing process is used for example in the photovoltaic industry to cut silicon into thin wafers. A moving wire, wounded for several times around some wire pulleys is used in addition with a slurry, which contains abrasive particles, to slice through the silicon ( The main material removal mechanism is represented by Moeller et al. [1]. He shows that the removal process can be understood as the sum of single indentations, which may be caused by a rolling particle motion. This motion can not be easily observed, so in this paper the Distinct-Element-Method (DEM) is used to investigate the motion of the particles and the influence of the interaction between particles in more detail. Distinct-element-model Particle interactionEssential for the simulation of the wire sawing process are the forces which act onto the surface of the sliced material. To calculate these forces, the interaction between the wire and the abrasive particles have to be considered under the influence of the slurry, which contains these abrasive particles. Therefore the used DEM-Code, which is originated from the Institute of Computational Physics in Stuttgart [2], was extended by a simple fluid model. It contains the influence of a shear flow between the wire and the ingot surface, leading to shear forces onto the particles and to a lift force in direction towards the wire (Fig. 2).The lapping particles are modeled as viscoelastic bodies. Therefor two-dimensional polygons are assigned with physical properties like mass, Young's modulus and shear modulus. The later two are used to calculate stiffness constants in order to model the viscoelastic material behavior (Fig. 3 and 4, Equations 1 and 2). The direction of the contact force is determined by the edges of the overlapping area and the center is used as the point of application of the forces.With n -normal direction, t -tangential direction A o -"overlap"-area, k (n,t) -stiffness constant, b (n,t) damping constant and v rel -relative velocity between colliding particles. The stiffness constant of such a contact depends on the Young's modulus
Until now several studies of rotating structures like rings or shells have been done. To model such problems in a right way, geometrical nonlinearity has to be considered. Different methods can be used, to solve the corresponding eigenvalue problem. In this article the focus will be placed on the finite element method. In contrast to flat elements curved ones can cause some numerical inconveniences. They include a tremendous loss of convergence on the one hand, on the other hand the appearance of zero energy modes. In addition, centrifugal and Coriolis effects have to be taken into account. For certain examples the results of different FE‐models are shown and compared with global approaches as well as measurement data.
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