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Abstract

A substantial quantity of research on muffler design has been restricted to a low frequency range using the plane wave theory. Based on this theory, which is a one-dimensional wave, no higher order wave has been considered. This has resulted in underestimating acoustical performances at higher frequencies when doing muffler analysis via the plane wave model. To overcome the above drawbacks, researchers have assessed a three-dimensional wave propagating for a simple expansion chamber muffler. Therefore, the acoustic effect of a higher order wave (a high frequency wave) is considered here. Unfortunately, there has been scant research on expansion chamber mufflers equipped with baffle plates that enhance noise elimination using a higher-order-mode analysis. Also, space-constrained conditions of industrial muffler designs have never been properly addressed. So, in order to improve the acoustical performance of an expansion chamber muffler within a constrained space, the optimization of an expansion chamber muffler hybridized with multiple baffle plates will be assessed. In this paper, the acoustical model of the expansion chamber muffler will be established by assuming that it is a rigid rectangular tube driven by a piston along the tube wall. Using an eigenfunction (higher-order-mode analysis), a four-pole system matrix for evaluating acoustic performance (STL) is derived. To improve the acoustic performance of the expansion chamber muffler, three kinds of expansion chamber mufflers (KA-KC) with different acoustic mechanisms are introduced and optimized for a targeted tone using a genetic algorithm (GA). Before the optimization process is performed, the higher-order-mode mathematical models of three expansion chamber mufflers (A-C) with various allocations of inlets/outlets and various chambers are also confirmed for accuracy. Results reveal that the STL of the expansion chamber mufflers at the targeted tone has been largely improved and the acoustic performance of a reverse expansion chamber muffler is more efficient than that of a straight expansion chamber muffler. Moreover, the STL of the expansion chamber mufflers will increase as the number of the chambers that separate with baffles increases.
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Authors and Affiliations

Min-Chie Chiu
Ying-Chun Chang
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Abstract

The purpose of that paper is to develop of unified equations of electromechanical energy converters accounting for the magnetic non-linearity of the main magnetic circuit of a converter. The concept of applying higher order forms of winding currents for the description of the co-energy function is introduced in order to derive the structure of converter equations via mathematical analysis. Also, another concept of equivalent magnetizing currents is applied to determine the higher order forms for selected converters designs. The structure of circuital equations for converters with multiple windings has been unified by means of the introduction of matrices of dynamic and nonlinear inductances following the higher order forms of the co-energy function.
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Authors and Affiliations

Tadeusz Sobczyk
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Abstract

A boundary value problem for a non-linear difference equation of order three is considered. We show that this equation can be interpreted as the equation satisfied by the value function in a stochastic optimal control problem. We thus obtain an expression for the solution of the non-linear difference equation that can be used to find an explicit solution to this equation. An example is presented.
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Authors and Affiliations

Mario Lefebvre
1

  1. Department of Mathematics and Industrial Engineering,Polytechnique Montréal, C.P. 6079, Succursale Centreville, Montréal, Canada H3C 3A7, Canada
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Abstract

In this work, continuous third-order sliding mode controllers are presented to control a five degrees-of-freedom (5-DOF) exoskeleton robot. This latter is used in physiotherapy rehabilitation of upper extremities. The aspiration is to assist the movements of patients with severe motor limitations. The control objective is then to design adept controllers to follow desired trajectories smoothly and precisely. Accordingly, it is proposed, in this work, a class of homogeneous algorithms of sliding modes having finite-time convergence properties of the states. They provide continuous control signals and are robust regardless of non-modeled dynamics, uncertainties and external disturbances. A comparative study with a robust finite-time sliding mode controller proposed in literature is performed. Simulations are accomplished to investigate the efficacy of these algorithms and the obtained results are analyzed.
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Bibliography

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Authors and Affiliations

Ratiba Fellag
1 3
ORCID: ORCID
Mohamed Guiatni
2
ORCID: ORCID
Mustapha Hamerlain
1
Noura Achour
3

  1. Centre de Développement des Technologies Avancées, Alger, Algérie.
  2. Laboratoire LCS^2, Ecole Militaire Polytechnique, Alger, Algérie.
  3. Laboratoire LRPE, Université des Sciences et de la Technologie Houari Boumediene, Alger, Algérie.

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