Littérature scientifique sur le sujet « Uncertain and disturbed dynamical SISO systems »

In this work, a Nonlinear Higher Order Extended State Observer (NHOESO) is presented to replace the Linear Extended State Observer (LESO) used in Conventional Active Disturbance Rejection Control (C-ADRC) solutions. In the NHOESO, the standard LESO is completed with a two-term smooth nonlinear function with saturation-like characteristics. The proposed novel NHOESO enables precise observation of the generalized disturbances with higher-order derivatives. The stability of the NHOESO is examined with the aid of the Lyapunov method. A simulation of an uncertain nonlinear Single-Input–Single-Output (SISO) system with time-varying external disturbances confirms that the proposed NHOESO copes well with the generalized disturbance, which is not true for other ESOs.

This paper focuses on the robust control of fractional-order economical chaotic system (FOECS) with parametric uncertainties and external disturbances. The dynamical behavior of FOECS is studied by numerical simulation, and circuit implementations of FOECS are also given. Based on fractional-order Lyapunov stability theorems, a robust adaptive controller, which can guarantee that all signals remain bounded and the tracking error tends to a small region, is designed. The proposed method can be used to control a large range of fractional-order systems with system uncertainties. Fractional-order adaptation laws are constructed to update the estimation of adaptive parameters. Finally, the robustness and effectiveness of our control method are indicated by simulation results.

Uncertain dynamical system driven by Liu process is of importance to depict the operation laws of real systems disturbed by human epistemic uncertainty. This paper mainly investigates the finite‐time attractivity of uncertain dynamical systems. New concepts of the finite‐time attractivity are first introduced for uncertain dynamical systems from different perspectives, and the relationships among these types of concepts are revealed based on uncertainty theory. The judgement theorems for ensuring the finite‐time exponential attractivity of two classes of uncertain dynamical systems are proposed, respectively. Several examples are provided to illustrate the main concepts and results derived. Finally, the uncertain mean‐reverting process with time‐varying parameters is considered as an application.

Cette thèse est une contribution à la métrologie des faibles forces qui s'inscrit dans la continuité des activités de recherche menées au département AS2M de l'institut FEMTO-ST. Ce manuscrit présente la conception et la mise en œuvre expérimentale d'un accéléromètre pendulaire triaxial qui mesure les composantes non filtrées du régime sismique, puisque ces dernières sont susceptibles de perturber le fonctionnement d'une balance de micro-nanoforce électromagnétique actuellement en développement. Une méthodologie alternative de calcul est également proposée dans ce manuscrit afin d'estimer spécifiquement la valeur et l'incertitude associée à une ou plusieurs grandeurs d'intérêt inconnues, par l'intermédiaire d'un système dynamique SISO dont le comportement est incertain et perturbé. Cette approche repose sur la représentation exacte de ce système grâce à une entrée correctrice virtuelle qui contient les grandeurs d'intérêt. Cette entrée est estimée puis mise en forme afin de déterminer l'incertitude associée à ces grandeurs d'intérêt, en utilisant les outils de l'analyse par intervalles. La méthodologie proposée est validée à partir de simulations de l'accéléromètre en modes actif et passif, puis illustrée sur le dispositif expérimental. Une étude en simulation du fonctionnement couplé de la future balance de micro-nanoforce électromagnétique avec l'accéléromètre triaxial est également réalisée. L'approche proposée est mise en œuvre lors d'un essai simulé visant à caractériser la raideur mécanique d'un levier élastique
This PhD thesis is a contribution to small force metrology, in line with the research activities carried out in the AS2M department of the FEMTO-ST institute. This manuscript presents the design and experimental implementation of a triaxial pendulous accelerometer, which measures the unfiltered seismic activity, since the latter is likely to interfere with the operation of an electromagnetic micro-nanoforce balance currently under development. An alternative methodology is also proposed in this manuscript to specifically estimate the value and uncertainty associated with one or more unknown quantities of interest, using a dynamical SISO system whose behavior is uncertain and disturbed. This approach is based on the exact representation of this system by means of a virtual corrective input containing the quantities of interest. This input is estimated and then shaped to determine the uncertainty associated with these quantities of interest, using the tools of interval analysis. The proposed methodology is validated on the basis of simulated accelerometer responses in active and passive modes, then illustrated on the experimental setup. A simulation study of the coupled operation of the future electromagnetic micro-nanoforce balance with the triaxial accelerometer is also carried out. The proposed approach is implemented in a simulated test aiming at characterizing the mechanical stiffness of an elastic cantilever