The minimum norm multi-input multi-output receptance method for partial pole placement

A closed-form analytical solution is developed for the first time that fully addresses the problem of choosing feedback gains that minimize the control effort required for partial pole placement in multi-input, multi-output systems. The norm of the feedback gain matrix is shown to take the form of an inverse Rayleigh quotient, such that the optimal closed-loop system eigenvectors are given as a function of the dominant (highest)eigenvectors of the matrix in the quotient. The feedback gains that deliver the required pole placement with minimum effort may then be determined using standard procedures. The original formulation by the receptance method proposed an arbitrary choice of the closed loop eigenvectors that assigned the poles exactly but was generally wasteful of control effort that might otherwise be conserved or put to good use in satisfying additional control objectives. The analytical solution is validated against a set of numerical examples

Stochastic modeling and identification of an uncertain computational dynamical model with random fields properties and model uncertainties

International audienceThis paper is devoted to the construction and to the identification of a probabilistic model of random fields in presence of modeling errors, in high stochastic dimension and presented in the context of computational structural dynamics. Due to the high stochastic dimension of the random quantities which have to be identified using statistical inverse methods (challenging problem), a complete methodology is proposed and validated. The parametric-nonparametric (generalized) probabilistic approach of uncertainties is used to perform the prior stochastic models: (1) system-parameters uncertainties induced by the variabilities of the material properties are described by random fields for which their statistical reductions are still in high stochastic dimension and (2) model uncertainties induced by the modeling errors are taken into account with the nonparametric probabilistic approach in high stochastic dimension. The steps of the methodology are explained and illustrated through an application

Robustness analysis of an uncertain computational model to predict well integrity for geologic CO2 sequestration

International audienceGeologic storage of CO2 must respond to demonstrations of safety, control and acceptability with authorities and public. The wells are essential elements of the storage system and constitute the only man-made intrusive element in the geologic systems. The role of containment of components of wells must then be ensured for hundreds of years, despite degradation mechanisms that affect their properties. Probabilistic approaches are used to take into account the uncertainties on the quantities of CO2 which migrate from the reservoir of CO2 towards the surface and towards the aquifer. Uncertainties are taken into account by using the generalized probabilistic approach which allows both the system-parameter uncertainties and the model uncertainties induced by modeling errors to be performed in the stochastic computational model. These probabilistic tools, applied to industrial projects, allow owners and operators to set up decisions and provide a strong support to long term safety demonstration with a high level of confidence, even in presence of uncertainties in the computational models