Utilisation de correcteurs d'ordre non entier pour la simplification de la résolution de problèmes d'optimisation paramétrique

Abstract

In automatic control the determination of the controller parameters during the design presents a major interest of the research work to develop new efficient control algorithms. In this work our interest is focused on determination of controller's parameters using optimization technique. In close loop, qualitative specifications of the process are generally well-known. The difficulty appears when these specifications are to be transcribed in a mathematical formalism suitable for the resolution methods. Classically, the specifications are used to write an optimization criterion with some constraints. But satisfactory solutions to the optimization problems are not necessarily. Satisfactory for the original control problem. This is precisely due to the fact that the transcription is not reliable or imprecise. Is interested in the most reliable transcription of specification as they are given by industrials, without major care about the possible complexity of the obtained optimization problem. Once this is accomplished, we consider the resolution of the optimization problem. The specifications, depending their nature are transcribed as conventional constraints or functional constraints, this latter have analytical properties making the obtained optimization problem a semi-infinite problem with inequality constraints. Algorithms solving such problems are complexes and take long time to converge. Our contribution is to solve this problem by trying to simplify it by exploiting the properties of fractional order controllers. Indeed, the maximum overshoots of the response of such controller are independent of their parameters, these properties permit to transform the functional constraints on conventional constraints, which allows us to use simple algorithm to obtain an optimal controller. Then, we will have only to find an equivalent integer order controller to the obtained fractional order controller