Finite-time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time. In this paper, we use the notion of finitetime stability to apply it to the problem of coordinated motion in multiagent systems. Specifically, we consider a group of fully actuated agents described by Euler-Lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady-state distances between the neighboring agents in finite time. We use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph Laplacian matrix. Furthermore, using sliding mode control approach, we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state. Sliding mode control is known to drive the system states to the sliding surface in finite time.The key feature of our approach is in the design of non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time, thus ensuring finite-time coordination among the agents in the network.
Calculation of fiber orientation distribution is the reference standard for determining the numerous physical and mechanical properties of injection molded short fiber reinforced thermoplastics. On the other hand, most of the properties of these composites depend on their fiber orientation pattern, which can be represented by tensorial notation, aij. This work focuses on numerical calculation of a fiber orientation tensor of an injection molded short glass fiber polystyrene (SGF-PS) composite part, shaped as a rectangular plate. In this study, the effects of some parameters of the injection molding process including injection flow rate, mold wall temprature, packing pressure and also fiber content on the changes of fiber orientations of this specimen are investigated. Our studies are concentrated on determining the changes of the first orientation tensor component in the flow direction due to different injection parameters. In addition, the changes on tensile modulus of the injected part are simulated in every condition. The simulations show how these molding parameters can influence both fiber orientation and tensile modulus of injection molded parts. At the first step, in order to be confident about the software results, they are validated by experimental data in two cases.
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