Stability Study of an Observer-Based Controlled Wind Turbine

In this paper, the problem of stabilizing uncertain systems with time delay by low order controllers is considered. The set of all stabilizing controllers, having three parameters, are determined for this class of time delay systems. First, the D-decomposition method is employed to solve the problem for plants without uncertainty. The approach consists of using two subsidiary quasi-polynomials. Next, the convex direction concept together with Kharitonov plants are used to solve the original problem. Examples are given to illustrate the application of the proposed method.The aim of this paper is to analyze the quadratic stability of a gain scheduled observer-based state feedback controlled wind turbine. The designed control law consists in a linear quadratic regulator combined to a multimodel approach to deal with the high nonlinearity of the studied plant. Since the state variables of the considered process are not all measureable, a state observer is necessary to estimate the immeasurable ones. Hence the asymptotic stability study of the augmented system is considered by using the Lyapunov direct method associated to the resolution of an LMI feasibility problem.