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

Expressing an observer in preferred coordinates by transforming an injective immersion into a surjective diffeomorphism

When designing observers for nonlinear systems, the dynamics of the given system and of the designed observer are usually not expressed in the same coordinates or even have states evolving in different spaces. In general, the function, denoted $\tau$ (or its inverse, denoted $\tau^*$) giving one state in terms of the other is not explicitly known and this creates implementation issues. We propose to round this problem by expressing the observer dynamics in the the same coordinates as the given system. But this may impose to add extra coordinates, problem that we call augmentation. This may also impose to modify the domain or the range of the augmented" $\tau$ or $\tau^*$, problem that we call extension. We show that the augmentation problem can be solved partly by a continuous completion of a free family of vectors and that the extension problem can be solved by a function extension making the image of the extended function the whole space. We also show how augmentation and extension can be done without modifying the observer dynamics and therefore with maintaining convergence.Several examples illustrate our results.Comment: Submitted for publication in SIAM Journal of Control and Optimizatio

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

Enterprise model verification and validation : an approach

This article presents a verification and validation approach which is used here in order to complete the classical tool box the industrial user may utilize in enterprise modeling and integration domain. This approach, which has been defined independently from any application domain is based on several formal concepts and tools presented in this paper. These concepts are property concepts, property reference matrix, properties graphs, enterprise modeling domain ontology, conceptual graphs and formal reasoning mechanisms

Local and global electrochemical impedances applied to the corrosion behaviour of an AZ91 magnesium alloy

The electrochemical behaviour of an AZ91 magnesium alloy was investigated in a low aggressive medium by means of local and global electrochemical impedance measurements. The results were compared to those obtained on a pure magnesium sample. It was possible to show the individual contribution of each phase constituting the alloy, and it was observed that the corrosion mechanism of the two phases was the same, controlled by the Mg dissolution. However, local impedance diagrams clearly indicated that the kinetics dissolution of the b-phase was slower than that of the a-phase, which was in good agreement with SEM observations

Decision map for spatial decision making in urban planning

In this paper, we introduce the concept of decision map and illustrate the way this new concept can be used effectively to support participation in spatial decision making and in urban planning. First, we start by introducing our spatial decision process which is composed of five, non-necessary sequential, phases: problem identification and formulation, analysis, negotiation, concertation, and evaluation and choice. Negotiation and concertation are two main phases in spatial decision making but most available frameworks do not provide tools to support them effectively. The solution proposed here is based on the concept of decision map which is defined as an advanced version of conventional geographic maps which is enriched with preferential information and especially designed to clarify decision making. It looks like a set of homogenous spatial units; each one is characterised with a global, often ordinal, evaluation that represents an aggregation of several partial evaluations relative to different criteria. The decision map is also enriched with different spatial data exploration tools. The procedure of the construction of a decision map contains four main steps: definition of the problem (i.e. generation of criteria maps), generation of an intermediate map, inference of preferential parameters, and generation of a final decision map. The concept of decision map as defined here is a generic tool that may be applied in different domains. This paper focuses on the role of the decision map in supporting participation in spatial decision making and urban planning. Indeed, the decision map is an efficient communication tool in the sense that it permits to the different groups implied in the spatial decision process to ‘think visually’ and to communicate better between each other.ou

Galvanic coupling between copper and aluminium in a thin-layer cell

The Al/Cu coupling was investigated in a thin-layer cell formed by a large Cu electrode and an Al microelectrode embedded in an insulator placed above the Cu electrode. By using a scanning electrochemical microscope (SECM) the thickness of the thin layer was perfectly controlledwith a precision in the micrometer range. A copper deposit on an electrochemical quartz crystal microbalance (EQCM) was also used as SECM substrate to quantify the copper dissolution rate. It was shown that such an experimental set-up allows to mimic the galvanic corrosion of intermetallic particles embedded in the aluminium matrix of the 2XXX series aluminium alloys. The combination of the SECM and the EQCM permitted the evaluation of the corrosion rate of copper at the corrosion potential of the 2024 Al alloy, whereas cyclic voltammetry performed on the SECM tip indicated the enrichment in Cu2+ ions in the thin electrolyte layer

Electrodynamic guiding and deceleration of polar diatomic molecules

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