Performances analysis of controlled interval systems using Hinf approach.
Résumé
Control strategies for dynamical systems are based on an appropriate model and often require a good knowledge of the system properties and its environment. However, the characteristics of the most physical systems are complex and non interpretable due to the nonlinearities, high-dimensional aspect, time-varying parameters and the complex sensitivity to the environmental conditions. For that, many simplifications are often introduced during the modeling in order to obtain usable models. As a result, the used models are subjected to uncertainties. These uncertainties present a challenge to control systems when particularly the objective is to achieve robust performances using limited information. One method to deal with uncertainty and robust control design is interval analysis where the parametric uncertainties are characterized by intervals. The principle of the control design consists to combine a linear theory of control with interval arithmetic. The controller design problem is based on a given interval model which represents a family of models and a wanted interval closed-loop (a family of models describing desired performances). Hence, interval techniques are automatically introduced to solve the problem and to compute the set solution of the controller parameters. In this talk, after designing a controller by combining interval arithmetic and a linear control theory, we perform the robust performances analysis of the closed-loop by means of the H∞; approach. The objective consists to check if the computed controller ensures the required performances for the uncertain system (interval system). The analysis is based on the H∞ standard problem which for its classical use consists to compute a controller C(s) such that ||Fl(P(s),C(s))||∞ where and Fl(P(s),C(s)) represents the interconnection between C(s) and the augmented plant P(s) that contains the system to be controlled and the weightings defining the specifications. An example is given via the control and robust performances analysis of piezoelectric cantilevers used to develop Microsystems.