J.J. Loiseau

Feedback realization of compensators for a class of time-delay systems

The ring of pseudopolynomials, i.e., entire functions which are rational in the variable s and its exponential, is the convenient concept for feedback control and stabilization of systems with commensurable delays, since it is a Bezout ring. Within this framework, conditions are derived for a compensator to be feedback realizable with internal stability. When these conditions hold, the compensator can be realized by a control law defined by a Volterra equation.

Pole Structure Assignment via Non-Regular Static State Feedback

Abstract The limits of static state feedback u =Fx + Gv, with G not necessarily nonsingular, in altering the transmission pole structure of a linear system ẋ =Ax +Bu are studied. A necessary and sufficient condition for a list of polynomials to be the denominator polynomials of the Smith-McMillan form of the closed-loop transfer matrix (sI - A - BF) -l BG is established. The condition involves the calculation of the infimal set of the controllability indices that the system can attain through feedback while satisfying Rosenbrocks inequalities.

CALIBRATION METHODS FOR THE TEST OF THE EQUIVALENCE PRINCIPLE

Abstract MICROSCOPE is a scientific space mission which aims to verify the Equivalence Principle with an accuracy of 10- 15 , 100 times better than the best current lab experiences. Special attention has been paid to the accelerometric environment of the satellite in order to decrease all the disturbing accelerations. The payload is the core of a complex servo system that allows the drag compensation and the attitude control of the satellite, that generates reference signals for the instrument calibration and gives the Equivalence Principle data. This paper focuses particularly on the development of servo manoeuvres needed for the calibration.

Realisation of precompensators for linear systems over a polynomial ring

We establish in this work the solution of the precompensator realisation problem for systems over a ring of polynomials in several variables. Due to the lemmas of the solution of P=XQ, these results are fully constructive.

Compensator realization through output feedback

Abstract The systems considered herein and their control laws are defined with point-wise commensurate delays and a class of distributed delays. At first, a description of these operators is provided, then the form of the systems and of the control laws is described. A procedure for the stabilization in this framework is recalled, before presenting a test for the realizability of a feedforward compensator by state feedback with internal stability. Eventually, an asymptotic observer for this type of system is introduced, allowing the extension of the previous result to output feedback.

Structure Assignment of State-Output Systems by Choice of the Output Equation

Abstract Necessary and sufficient conditions to assign a given finite and infinite zero structure to the state-output system E ẋ= Ax + Bu, y = Cx + Dv by choice of C and D are given.

ON VARIOUS INTERPRETATIONS OF ROSENBROCK'S THEOREM

Abstract We discuss the importance of Rosenbrocks theorem on pole placement for control theory

Eigenstructure Assignment by P and PD State Feedback in Linear Singular Systems

Abstract An overview of the results regarding the problem of eigenstructure assignment by proportional and proportional and derivative state feedback in linear implicit systems is provided and some open problems are pointed out