Implicit Euler numerical simulations of sliding mode systems

In this report it is shown that the implicit Euler time-discretization of some classes of switching systems with sliding modes, yields a very good stabilization of the trajectory and of its derivative on the sliding surface. Therefore the spurious oscillations which are pointed out elsewhere when an explicit method is used, are avoided. Moreover the method (an {\em event-capturing}, or {\em time-stepping} algorithm) allows for accumulation of events (Zeno phenomena) and for multiple switching surfaces (i.e., a sliding surface of codimension $\geq 2$). The details of the implementation are given, and numerical examples illustrate the developments. This method may be an alternative method for chattering suppression, keeping the intrinsic discontinuous nature of the dynamics on the sliding surfaces. Links with discrete-time sliding mode controllers are studied

Analysis of explicit and implicit discrete-time equivalent-control based sliding mode controllers

Different time-discretization methods for equivalent-control based sliding mode control (ECB-SMC) are presented. A new discrete-time sliding mode control scheme is proposed for linear time-invariant (LTI) systems. It is error-free in the discretization of the equivalent part of the control input. Results from simulations using the various discretized SMC schemes are shown, with and without perturbations. They illustrate the different behaviours that can be observed. Stability results for the proposed scheme are derived

Energy conservation and dissipation properties of time-integration methods for the nonsmooth elastodynamics with contact

This research report is devoted to the study of the conservation and the dissipation properties of the mechanical energy of several time-integration methods dedicated to the elasto- dynamics with unilateral contact. Given that the direct application of the standard schemes as the Newmark schemes or the generalized-α schemes leads to energy blow-up, we study two schemes dedicated to the time-integration of nonsmooth systems with contact: the Moreau-Jean scheme and the nonsmooth generalized-α scheme. The energy conservation and dissipation properties of the Moreau-Jean is firstly shown. In a second step, the nonsmooth generalized-α scheme is studied by adapting the previous works of Krenk and Høgsberg in the context of unilateral contact. Finally, the known properties of the Newmark and the Hilber-Hughes-Taylor (HHT) scheme in the unconstrained case are extended without any further assumptions to the case with contact.Ce rapport de recherche propose une étude des propriétés de conservation et de dissipation de l'énergie mécanique pour différents schémas d'intégration en temps de la dynamique élastique avec du contact unilatéral. Sachant que l'application directe des schémas standards de type Newmark et des schémas α-généralisés conduisent à des explosions de l'énergie mécanique, on étudie deux schémas dédiés à l'intégration en temps des systèmes non réguliers avec contact : le schéma de Moreau-Jean et le schéma α-généralisé non-régulier. La conservation de l'énergie et les propriétés de dissipation du schéma de Moreau-Jean sont d'abord démontrées. Dans un second temps, le schéma α-généralisé non-régulier est étudié en adaptant les travaux précurseurs de Krenk et Høgsberg dans le contexte du contact unilatéral. Finalement, les propriétés connues du schéma de Newmark et du schéma Hilber-Hughes-Taylor (HHT) dans le cas régulier sont étendues dans le cas avec contact sans hypothèses supplémentaires

Miopatia induzida pelo vírus influenza A (H1N1): uma complicação extrapulmonar importante

Universidade Federal de São Paulo (UNIFESP), Escola Paulista de Medicina (EPM) Department of Neurology and NeurosurgeryUNIFESP, EPM, Department of Neurology and NeurosurgerySciEL

The nonsmooth generalized-α scheme with a simultaneous enforcement of constraints at position and velocity levels.

International audienceIn this work, we present a formalism for the numerical time integration of nonsmooth dynamical systems composed of rigid and flexible bodies, kinematic joints and frictionless contact conditions. The proposed algorithm guarantees the exact satisfaction of the bilateral and unilateral constraints both at position and velocity levels, extending a previous work on the development of the generalized-α scheme for computational contact mechanics. Following the idea of Gear, Gupta and Leimkuhler, the equation of motion is reformulated so that the bilateral and unilateral constraints appear both at position and velocity levels which amounts to solving two complementarity conditions at both position and velocity levels at each iteration using a monolithic semi-smooth Newton procedure

Non-smooth contact dynamics approach of cohesive materials

International audienceThe main features of the non-smooth contact dynamics (NSCD) method—the dynamical equation, the Signorini relation as a non-smooth modelling of unilateral contact, and the frictional Coulomb's law, treated with fully implicit algorithms— are briefly presented in this paper. By mere changes of variables, it appears that a large class of interface problems, including cohesive interface problems, may be solved using Signorini, Coulomb and standard NSCD algorithms. Emphasis is put on contact between deformable bodies. Examples illustrating numerical simulation are given for fibre-reinforced materials and for buildings made of blocks

An open question : How to solve efficiently 3D frictional contact problem ?

International audienceIn this talk, we want to discuss possible numerical solution procedures for the following discrete frictional contact problem. We will recall a result for the problem in (1) which ensures that a solution exists [3]. In this framework, we will list several algorithms that have been previously developed for solving the SOCCP (1) mainly based variational inequality and nonsmooth equations reformulations. On one hand, we will show that algorithms based on Newton methods for nonsmooth equations solve quickly the problem when they succeed, but suffer from robustness issues mainly if the matrix H has not full rank. On the other hand, the iterative methods dedicated to solving variational inequalities are quite robust but with an extremely slow rate of convergence. To sum up, as far as we know there is no option that combines time efficiency and robustness. To try to answer to this question, we develop an open collection of discrete frictional contact problems called FCLIB http://fclib.gforge.inria.fr in order to offer a large library of problems to compare algorithms on a fair basis. In this work, this collection is solved with the software Siconos and its component Siconos/Numerics http://siconos.gforge.inria.fr

Comments on "Chattering-free digital sliding-mode control with state observer anddisturbance rejection''

International audienceAn unfortunate mistake in the proof of Proposition 1 in V. Acary, B. Brogliato, Y. Orlov, IEEE Transactions on Automatic Control, 57(5) 1087-1101, 2012, is corrected

Analysis of collocated feedback controllers for four-bar planar mechanisms with joint clearances

International audienceThis article presents an analysis of two-dimensional four-bar mechanisms with joint clearance, when one joint is actuated by collocated open-loop or state feedback controllers (proportional-derivative, state feedback linearization, passivity-based control). The study is led with numerical simulations obtained with a projected Moreau-Jean's event-capturing algorithm. The contact/impact model uses kinematic coefficients of restitution, and Coulomb's friction. The focus is put on how much the performance deteriorates when clearances are added in the joints. It is shown that collocated feedback controllers behave in a very robust way

Periodic motions of coupled impact oscillators

International audienceIn this work, we study the existence and stability of time-periodic oscillations in a chain of linearly coupled impact oscillators reminiscent of a model analyzed in [2], for rigid impacts without energy dissipation. We introduce a numerical method allowing to compute branches of time-periodic so- lutions when an arbitrary number of nodes undergo rigid impacts. For this purpose, we reformulate the search of periodic solutions as a boundary value problem incorporating unilateral constraints. We illustrate this numerical approach by computing some families of nonlinear spatially localized modes (breathers) and extended modes