Contribution à l'identification et au réglage robustes

The parametric uncertainty is defined as the gap between the complete model of a dynamical process and its simplified nominal one which is normally used to investigate the properties of the system. It is because of this model mismatch that the role of sensitivity in designing control systems becomes very important. In robust control, the parametric uncertainty is taken into account in both the analysis and the synthesis phases of the closed-loop system. In this thesis, first, robustness to small parameter variation is studied using differential sensitivity functions. A combined diagram is used to generate relative sensitivity functions which can be used for improving existing controllers. Several control structures which are suitable for the design of zero-sensitivity control systems are presented. Then, as a framework for studying large parameter uncertainty, the RST controller has been chosen. Robustness criteria, based on parameter uncertainty, have been established. Two complementary ways to robustify a nominal RST controller are presented. First, the pole placement characteristic polynomial is augmented in the second approach, we try to compensate the supplementary signal due to the parametric uncertainty. This signal causes the nominal system misfunction. Instead of estimating this generalized perturbation, various block-diagrams are used to emulate it. As far as identification is concerned, a new method of robust identification which reinforces the tracking capability of RLS algorithm for a nonstationary system is presented. Normally, the gain matrix of RLS has to be adjusted when parameter variations are detected. In this work, an on-line estimation of the parameter covariance as an additional gain matrix is proposed for this adjustment on the basis of the prediction error. Then, the diagonal elements of this computed covariance matrix are used to calculate an on-line estimation of the parameter uncertainty.

Related material