On the ill-posedness of observation problems

Observation problems are restricted here to problems of estimation of state variables (or more generally, internal variables) from two sources of information: online measurements of some variables and the dynamic model relating the quantities to be estimated and the measurements. In the control theory engineering literature the tremendous success of the Kalman filter has left little room to numerical analysis approaches to observation problems. This work is a contribution to the building of a tunnel between numerical analysis and control theory literature on observation problems. The first brick is the statement that state estimation is an ill-posed inverse problem. In the present communication attention is focused on linear systems (with constant or non constant coefficients) for which popular asymptotic estimators (Luenberger observer and Kalman observer) are shown to be regularizations of the ill-posed estimation problem

Dynamic estimation of specific growth rates and concentrations of bacteria for the anaerobic digestion

The paper proposes an observability analysis and estimation schemes for specific growth rates and biomass concentrations of the anaerobic digestion process. A 3-stage model of 5 dynamic states is assumed, describing the hydrolysis, acidogenesis and methanogenesis of two different populations of microorganisms (acidogenic and methanogenic). The main result is that the specific growth rates of the two populations of bacteria can be stability estimated only from easily measured quantities -- the dilution rate and the flow rates of methane and carbon dioxide in the biogas. The estimation schemes thus obtained have quite interesting features one of which is their freeness of most yield coefficients often hard to identify. The analysis rests on the differential algebraic approach of observation problems. The results are currently being confronted to experimental data from a 100m3 pilot bioreactor fed with cattle dung. Realistic simulations are presented in this paper as illustrations of the estimator performance

On a differential algebraic system structure theory

International audienceThe structure at infinity and the essential structure are two control theory notions which were first defined for linear, then for the so-called affine, systems. And they were shown to be useful tools for the study of the fundamental problem of noninteracting control. They also appeared as related to the solutions of other important control problems such as disturbance decoupling. Their definitions are however entirely in terms of an algorithm, namely the so-called structure algorithm. The present work proposes new definitions with some advantages: they extend the class of systems from linear and affine systems to systems which may be described by algebraic differential equations, they are not tied to specific algorithms, and finally they provide more information on system structure. Let a system be a set of differential equations in variables which are grouped as m inputs, p outputs and n latent variables. To each input component is attached a rational integer, which, for a single input single output system defined by a single differential equation, is the difference between the order in the output and the order in the input of the differential equation defining the system. The m-tuple of these rational integers is the new structure at infinity of the system. Associated to the structure at infinity is also defined a p-tuple of rational integers representing a new notion of essential structure. The old structure at infinity is shown to be recoverable from the new one. Computations of system structure based upon the suggested definitions are quite complex. The present paper focuses on proofs of algorithms which attempt to reduce the complexity of these computations

A semi-active controller tuning and application to base seismically-isolated structures

International audienceThis paper proposes a modified version of Leitmann and co-authors' classical result on the stabilization of uncertain nonlinear systems. In particular, for usual models of structure dynamics in earthquake engineering it is shown that applying a specific control law drives the state variables into a ball around the origin (arbitrarily chosen) in finite time as long as the radius of the ball is not lower than a limiting value. In addition estimates of this limiting ball radius and the time limit for arbitrary ball radius are provided. The semi-active control thus provides the control designer with interesting design parameters. It is also an attempt to explicitly use pseudoacceleration floor response spectrum as a performance criterion. Though not limited to twodegree- of-freedom structures, this semi-active control is applied to these plant models for simplicity and illustrated through simulations

A robust nonlinear semi-active control for base seismically-isolated structures

This paper proposes a robust nonlinear semi-active control for base seismically-isolated structures. The control is based upon an extension of works of Leitmann et al. on the stabilization of nonlinear systems with uncertain models. For usual models of structure dynamics it is shown that applying a specific control law drives the state variables into a ball of specified radius in finite time. The radius of the ball may be arbitrarily chosen as long as it is not lower than a limiting value. In addition, estimates of this limiting ball radius is provided. The time to reach the ball is also provided. The semi-active control thus provides the control designer with interesting design parameters. The efficacy of proposed semiactive control is illustrated by its application to simple models of structures focusing in particular to the attenuation of excitation transmitted from floor to equipment mounted on them

Commande de systèmes d'isolation antisismique mixte

Nous nous intéressons aux méthodes de contrôle de vibrations de modèles réduits de structures à n degrés de liberté, sismiquement isolées au niveau de la base par des systèmes d'isolation mixte.Le mouvement provoqué par une sollicitation sismique horizontale a lieu dans le plan vertical.Nous avons construit un problème de contrôle semi-actif de systèmes incertains soumis à des perturbations inconnues, mais bornées. Dans le langage de l'automatique, il s'agit d'un problème d'atténuation de perturbations.Le résultat principal de cette thèse porte sur la construction d'une version modifiée des résultats de Leitmann et de ses collaborateurs sur la stabilisation de systèmes non linéaires incertains. Le théorème proposé repose sur une loi de commande par retour d'état qui assure en boucle fermée les propriétés de "uniform boundedness" et "uniform ultimate boundedness".En particulier, il peut être appliqué à la résolution de problèmes de contrôle semi-actif, qui sont actuellement traités en génie parasismique.L'objectif du contrôle est d'améliorer le comportement (i.e. la réponse) de structures isolées pour faire face aux perturbations externes, c'est-à-dire les séismes. Plusieurs points différencient notre problème de la majorité que l'on trouve dans la littérature: (i) on ne s'intéresse pas seulement à la protection de la structure isolée, mais aussi aux équipements situés à l'intérieur de la structure, et (ii) au lieu d'utiliser des indicateurs de performance habituels exprimés en termes de déplacement relatif de la base versus des accélérations absolues des planchers, nous utilisons uniquement le spectre de plancher en pseudo-accélération, comme il a été proposé dans des travaux précédents par Politopoulos et Pham. Ce travail est une tentative d'utiliser explicitement les spectres de plancher comme critère de performance.Concernant la procédure d'application, plusieurs étapes intermédiaires ont été détaillées:(i) modélisation de signaux sismiques;(ii) réglage des paramètres de la loi de commande utilisant la théorie des vibrations;(iii) validation et test du comportement en boucle fermée à travers des simulations numériques: pour des raisons de simplicité, on se limite au cas n=2.Cette procédure peut être utilisée sur des structures en industrie nucléaire, mais aussi en génie civil.D'autres sujets traités incluent une tentative d'utiliser les outils temps-fréquence, et en particulier la distribution de Wigner-Ville, pour la synthèse de lois de commande, en espérant pouvoir mieux contrôler les composants transitoires des signaux de perturbation (les entrées) et des variables d'état (les sorties).Vibration attenuation control designs are proposed for reduced plant models consisting of n-degree-of-freedom base seismically-isolated structures (i.e., a specific type of earthquake-resistant design), modeled by uncertain nonlinear systems and subjected to one-dimensional horizontal ground acceleration (i.e. the earthquake signal), treated as unknown disturbance but assumed to be bounded.In control systems literature, this is a perturbation attenuation problem.The main result of this PhD is the development of a modified version of Leitmann and co-authors' classical result on the stabilization of uncertain nonlinear systems. The proposed theorem consists of a bounded nonlinear feedback control law that is capable of ensuring uniform boundedness and uniform ultimate boundedness in closed-loop. In particular, it can be applied to solving semi-active control design problems, which are currently dealt with in earthquake engineering.The control objective is to improve the behavior (i.e. response) of mixed base-isolated structures to external disturbance, namely earthquakes. What differentiates our problem from the majority to be found in the literature is that: (i) attention is being paid to the protection of equipment placed inside the structure an not only to the structure itself; (ii) instead of using regular performance indicators expressed in terms of relative base displacement versus floors accelerations, we use solely the pseudo-acceleration floor response spectra, as it was proposed in previous recent works by Politopoulos and Pham.Actually, this work is an attempt to explicitly use floor response spectra as performance criterion.Concerning the application procedure, some of the topics that were detailed are:(i) modeling of earthquake signals;(ii) tuning of control law parameters based on vibration theory;(iii) validation and testing of the closed-loop behavior using numerical simulations: for simplicity reasons, we take n=2.This procedure can be used on structures of both nuclear industry as well as civil engineering.Other topics include an attempt to using time-frequency concepts and in particular the Wigner-Ville distribution to the control law design procedure, in order to better control transitory components of both perturbation (the input) and state variables signals (the output).PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF

Une nouvelle structure d'observateur

An observer structure has been proposed with features such as "nonpeaking", "bounded" and with quasi explicit algorithms for its design. These new potentialities are attribuable to both the structure of the data feedback and the introduction of regularized numerical differentiation schemes of sampled data

A differential algebraic approach of systems theory

International audienceDifferential algebraic geometry (and differential algebra) [1,2] was earlier recognized as particularly adapted as a language for the description of some of the systems theory problems. See the pioneering works by Jean-François Pommaret [3] and Michel Fliess [4]. In the latter paper the notion of invertibility, which was long studied in the control literature, was given a better clarification. And in [5] differential algebraic elimination theory was invoked as, not only a better description of questions in the control literature, but a constructive answer, too. One of the fundamental notions of systems theory, that of observability, was also given a differential algebraic geometry description which clarified many aspects of that questions [6]. This contribution is a tentative comprehensive expose of differential algebraic geometry known answers to some of the systems theory questions. The latter include previously mentioned ones, and notions of invariants, structural issues, and constructivity

On sensor selection for differential algebraic systems observability

International audienceWe address the problem of selecting sensors, that is, output equations, in order to endow dynamic equations of a system with some properties. Among all such desirable properties is the basic one of observability and/or identifiability. Once such a problem is solved one may ask how to choose sensors in order to improve estimation algorithms in terms of reliability, robustness, or simply, low complexity. First, what is the minimal number of sensors that make the dynamics observable? Second, when the sensors are bound to measure state components, what is their minimum number? Third, how may the observability margin be improved by selecting the sensors? In this communication we provide an overview of these questions in the differential algebraic approach of observation problems