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Robust continuous third-order finite time sliding mode controllers for exoskeleton robot

Fellag Ratiba, Guiatni Mohamed, Hamerlain Mustapha, Achour Noura

Archive of Mechanical Engineering

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2021

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LXVIII, nr 4

395--414

EN

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.

2

Theoretical study of heat transfer effects on flow past a parabolic started vertical plate in the presence of chemical reaction of first order

Muthucumaraswamy R., Velmurugan S.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 2

275--284

EN

An exact solution of an unsteady flow past a parabolic starting motion of an infinite vertical plate with variable temperature and mass diffusion, in the presence of a homogeneous chemical reaction of first order has been studied. The plate temperature as well as concentration level near the plate are raised linearly with time t. The dimensionless governing equations are solved using the Laplace-transform technique. The effects of velocity profiles are studied for different physical parameters such as the chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time. It is observed that the velocity increases with increasing values of the thermal Grashof number or mass Grashof number. The trend is just reversed with respect to the chemical reaction parameter.

3

Permutation Representation of 3 and 4-Homogenous Latin Bitrades

Lefevre J.G., Donovan D., Drápal A.

Fundamenta Informaticae

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2008

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Vol. 84, nr 1

99-110

EN

Cavenagh, Donovan and Drápal (2005) gave a construction for 3-homogeneous latin bitrades which was proved by Cavenagh (2006) to give every 3-homogeneous latin bitrade. A corollary is that every 3-homogenous latin bitrade may be partitioned into three disjoint transversals. Using a permutation representation for latin bitrades developed by Drápal, we provide a shorter proof of these results, and then give a construction for a family of separated 4-homogeneous latin bitrades.

4

Sur la méthode de l'intégrale particuliere et sur ses conséquences pour l'équation de Riccati et pour les équations différentielles linéaires et homogenes d'ordre supérieur

Kapcia A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2007

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Vol. 47, [Z] 2

255-283

EN

This paper presents the method of particular solution for solving the Riccati equation and linear homogenous equations of second and third order, as well as its certain application to linear homogenous equations of n-th order. The conditions of effective integrability for equations (0.1) and (0.2) are expressed in symbolic (operator) form and also for equation (0.3) in fully expanded form. There have been proved three theorems which state the following: for any subclass of differential equations of the form (0.1), (0.2), (0.3), if there are known, respectively: a particular solution y0, a particular solution u0, two linearly independent particular solutions u1, u2, then it is possible to construct superclasses of differential equations of the given class, using classes cited in [6, 7, 8, 9]. Moreover, one may obtain their effectively integrable generalizations. Numerous examples provided illustrate the above results. The article presents also a practical way of applying the method of particular solution to linear equations of n-th order. This method enables us to integrate more general equations than those described in [4, 5, 14] of the form (0.1), (0.2), (0.3), (0.4) for which the particular solutions are cited therein.

5

Numerical calculation of the steam condensing flow

Dykas S.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2001

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Vol. 5, No 4

519-535

EN

Considering the flow in the last stages of LP (low pressure) steam turbine the strong non-linearity of the thermal parameters of state and possibility of the two-phase flow have to be taken into account in the numerical calculation of the flow field. In this paper numerical calculations of the steam condensing flow for the turbine geometry are presented. The steam properties are described here on the basis of the IAPWS’97 formulation. The classical nucleation theory of Volmer and Frenkel was adapted for modelling of condensing flow. The droplet growth model of Gyarmathy is implemented. The calculations are based on the time dependent 3D Euler equations, which are coupled to three additional mass conservation equations for the liquid phase and are solved in conservative form.

6

Diffraction by a perfectly conducting open-ended waveguide in a homogeneous biisotropic medium

Aschar S., Hayat T.

Optica Applicata

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2000

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Vol. 30, nr 2-3

361-373

EN

In this paper, the diffraction of an electromagnetic wave within perfectly conducting parallel-plates embedded in a homogeneous biisotropic medium is examined. The vector diffraction problem is reduced to the scattering of a single scalar field, the latter being the normal component of either a left-handed or a right-handed Beltrami field. The scattering of the left-handed field component is explicitly analyzed, with that of the other scalar field being analogously tractable.