Discrete-time output feedback sliding-mode control design for uncertain systems using linear matrix inequalities

An output feedback-based sliding-mode control design methodology for discrete-time systems is considered in this article. In previous work, it has been shown that by identifying a minimal set of current and past outputs, an augmented system can be obtained which permits the design of a sliding surface based upon output information only, if the invariant zeros of this augmented system are stable. In this work, a procedure for realising discrete-time controllers via a particular set of extended outputs is presented for non-square systems with uncertainties. This method is applicable when unstable invariant zeros are present in the original system. The conditions for existence of a sliding manifold guaranteeing a stable sliding motion are given. A procedure to obtain a Lyapunov matrix, which simultaneously satisfies both a Riccati inequality and a structural constraint, is used to formulate the corresponding control to solve the reachability problem. A numerical method using linear matrix inequalities is suggested to obtain the Lyapunov matrix. Finally, the design approach given in this article is applied to an aircraft problem and the use of the method as a reconfigurable control strategy in the presence of sensor failure is demonstrated

Relation Structure moléculaire - Odeur Utilisation des Réseaux de Neurones pour l’estimation de l’Odeur Balsamique

Les molécules odorantes (parfums ou flaveurs) sont utilisées dans une grande variété de produits de consommation, pour inciter les consommateurs à associer les impressions favorables à un produit donné. La Relation Structure moléculaire-Odeur (SOR) est cruciale pour la synthèse de ces molécules mais est très difficile à établir due à la subjectivité de l’odeur. Ce travail présente une approche de prédiction de l'odeur des molécules basée sur les descripteurs moléculaires. Les techniques d’analyse en composantes principales (PCA) et de d’analyse de colinéarité permettent d’identifier les descripteurs les plus pertinents. un réseau de neurones supervisé5 à deux couches (cachée et sortie) est employé pour corréler la structure moléculaire à l’odeur. La base de données décrite précédemment est utilisée pour l’apprentissage. Un ensemble de paramètres est modifié jusqu’à la satisfaction de la meilleure régression. Les résultats obtenus sont encouragent, ainsi les descripteurs moléculaires convenables corrèlent efficacement l'odeur des molécules. C’est la première étape d’un modèle générique en développement pour corréler l'odeur avec les structures moléculaire

A canonical form for the design of unknown input sliding mode observers

International audienceIn this work, a new approach to solve the problem of designing an unknown input observer for linear systems is developed. An algorithm is given in order to find a suitable change of coordinates for the design of a step-by-step second order sliding mode observer. This observer provides, by usingthe equivalent output injections, a finite time estimation of both state and unknown inputs. Since the observer is based on second order sliding mode algorithms, the equivalent output injections are obtained in a continuous way without any use of low pass filters

Fast state estimation in linear time-varying systems: an algebraic approach

International audienceIn this note, an algebraic approach for state estimation of linear time-varying (LTV) systems is introduced. This approach is based on the following mathematical tools: Laplace transform, Leibniz formula, operational calculus and distribution theory. A generalized expression of the state variables as a function of the integrals of the output and the input is obtained. The example of a DC motor system and some simulation results are given to illustrate the performance of the proposed approach

Fast state estimation in linear time-invariant systems: an algebraic approach

International audienceIn this note, an algebraic approach for state estimation of linear time invariant systems is developed. This approach is based on the following mathematical tools: Laplace transform, Leibniz formula and operational calculus. A generalized expression of the state variables in function of the integrals of the output and the input is obtained. The example of a DC motor system and simulation results are given to illustrate the performance of the proposed approach

Commande sans capteur du moteur pas-à-pas à base de modes glissants d'ordre supérieur

International audienceNous proposons une commande robuste du moteur pas-à-pas sans capteur de position ni de vitesse, et ne nécessitant que des mesures des courants et des tensions. Nous présentons dans un premier temps des observateurs basés sur des modes glissants du 2ème ordre estimant la position et la vitesse du rotor, puis nous établissons une loi de commande robuste, elle même basée sur des modes glissants, et faisant intervenir ces estimations. La stabilité des observateurs et de la loi de commande est ensuite traitée. Des résultats obtenus en simulation démontrent l'intérêt et la robustesse de ces méthodes

Estimation des paramètres des systèmes linéaires : approche algébrique

International audienceLe développement de deux expressions formelles d'estimation des paramètres par une approche algébrique constitue la principale motivation de cet article, ces deux expressions étant obtenues en suivant les idées introduites par M. Fliess et H. Sira-Ramirez parues dans [1], [2]. Cette approche est dédiée à une classe générale de systèmes linéaires stationnaires. Nous présentons deux expressions formelles des paramètres inconnus en fonction d'intégrales portant sur la sortie et sur l'entrée. Pour ce faire, on applique certains outils mathématiques : la transformation de Laplace, la formule de Leibniz et les outils issus du calcul opérationnel. Un example en dimension trois d'un moteur à courant continu et les simulations sont donnés afin d'illustrer les performances de cette approche

Nonlinear control for linear motors with friction - Application to an inverted pendulum system

International audienceA linear motor is used here as an actuator for a cart-pendulum system. The global, upward stabilization of the inverted position is aimed at. In such an under-actuated situation, (i) constraints on the motor motion (limited length) have to be taken into account and (ii) friction effects may have a strong influence (limit cycles). A two-step path planning-plus-tracking strategy allows for dealing with constraint (i). Regarding point (ii), and since friction effects are hardly modeled, a second-order sliding mode algorithm is chosen. The resulting controller is designed without any knowledge of neither the electromagnetic circuits of the linear motor (the model is a simple gain), nor the friction models (only upper bounds for the friction forces acting on both the linear motor and pendulum are required). Experimental results show good performances in tracking and regulation, both for the swing-up and stabilization phases of the inverted pendulum

Tire/Road Contact Condition Identification Using Algebraic Numerical Differentiation

International audienceIn this paper, a realistic simulation model for Wheeled Mobile Robot (WMR) is given by a dynamical system that switches between three models corresponding to three different tire/road contact conditions: ideal condition, skidding condition and slipping condition. Then, an algebraic based numerical identification for the discrete state (tire/road contact condition) of this switching system is proposed. Finally, specific estimators for the uncertain parameters encountered in the identification scheme are given

Computer Aided Aroma Design. II. Quantitative structure-odour relationship

Computer Aided Aroma Design (CAAD) is likely to become a hot issue as the REACH EC document targets many aroma compounds to require substitution. The two crucial steps in CAMD are the generation of candidate molecules and the estimation of properties, which can be difficult when complex molecular structures like odours are sought and their odour quality are definitely subjective or their odour intensity are partly subjective as stated in Rossitier’s review (1996). The CAAD methodology and a novel molecular framework were presented in part I. Part II focuses on a classification methodology to characterize the odour quality of molecules based on Structure – Odour Relation (SOR). Using 2D and 3D molecular descriptors, Linear Discriminant Analysis (LDA) and Artificial Neural Network are compared in favour of LDA. The classification into balsamic / non balsamic quality was satisfactorily solved. The classification among five sub notes of the balsamic quality was less successful, partly due to the selection of the Aldrich’s Catalog as the reference classification. For the second case, it is shown that the sweet sub note considered in Aldrich’s Catalog is not a relevant sub note, confirming the alternative and popular classification of Jaubert et al., (1995), the field of odours