Mounir HAMMOUCHE : "Robust and optimal control via interval techniques for microsystem contro"

Work thesis of  Mounir Hammouche : "Robust and optimal control via interval techniques for microsystem control"

Abstract : Piezoelectric actuators are widely used at micro/nanoscale because of their simple configuration, high resolution (subnanometric),high speed (large bandwidth up to 1kHz), and high force density. However, they are characterized by some ,nonlinearities such as hysteresis, internal friction and creep,...etc. These characteristics considerably impact the dynamics of the piezoactuators which makes the control of these systems not a trivial task. Various robust controllers have
been developed to control piezoelectric actuators. These include high gain feedback approach, H1 approach, disturbance observer based control approach,...etc. Those techniques demonstrated a significant improvement of the control performance, but they often derive controllers with high-order which are difficult for implementation. To bypass this limitation, we focus on the thesis on combining interval analysis with classical controller design techniques to obtain a low order controllers. The main advantage of intervals is that they permit to model parametric uncertainties easily by bounding them. Furthermore, the process of modeling the system uncertainties by intervals makes the synthesis of robust controller with low order relatively easy. The state of the art on the use of interval techniques to design and derive robust controllers for uncertain system can be divided into two categories: interval transfer functions based approaches and interval state-space representation based approaches. Interval transfer functions based designs have been widely used to model and to control SISO (Single Input single Output) systems subjected to uncertainties. These approaches make the synthesis of robust controllers for such systems easy with providing good performance. However, the current work that use interval transfer functions are limited to systems in SISO case. In the other side, the state-space based approaches have been shown to be well adapted to synthesis robust controllers for multivariable systems. Nevertheless, the exciting works are limited to systems with state and input matrices of special structures. Furthermore, they address only the degree of stability of the closed-loop system without discussing performance specification. In order to make the design of robust controller using interval state-space approach possible for any interval state-space structure, this thesis will explore the interval state-space control design using robust pole assignment technique. This proposed approach will guarantee the stability and the desired performance of the closed-loop system also it allows to obtain a low order controller. For this matter, an algorithm based on Set Inversion Via Interval Analysis (SIVIA) combined with interval
eigenvalues computation is proposed to seek for a set of robust gains. This recursive SIVIA-based algorithm allows to approximate with subpaving the set solutions [K] that satisfy the inclusion of the eigenvalues of the closed-loop system in a desired region in the complex plan. Furthermore, simple algorithms are proposed to find the optimal feedback gains among the range of robust gains [K] as well as the range of the gains that satisfy input constraints, all with the help of interval analysis. Finally, in order to improve the controller performance, we were directed our attention to nonlinear control approaches and especially interval sliding mode control (ISMC) design using interval observers. The effectiveness of the proposed approaches are tested by a real experimentation on several platforms developed in our laboratory to achieve robust performance.

Localisation : Amphithéâtre Jules Haag - ENSMM - 26, Rue de l'Epitaphe - Besançon