Síntesis de controladores robustos mediante el análisis de la compatibilidad de especificaciones e incertidumbre

Résumé

This thesis is based upon the challenge of knowing and quantifying the control trade-offs in the synthesis of a unique robust feedback controller capable of solving simultaneously several control requirements in the presence of uncertainty. For this purpose, the Quantitative Feedback Theory (QFT) has been analysed in detail, particularly, the QFT bounds that represent the control specifications for each frequency including the system uncertainties. The robust feedback control requirements, whose representative bounds have been studied, have been clustered around five groups: complementary sensitivity, sensitivity at the plant input, sensitivity at the plant output, control effort, and two-degrees-of-freedom tracking specifications. Their contribution to the bound formulation (together with that of the plant uncertainty) has been analysed. As a result, three QFT bound typologies can be found whose complexity increases with the uncertainty size and the demands on performance specification. Then, the solution for the multiple objective feedback control problem lies firstly in the bound compatibility at each frequency and secondly, in the bound meeting for the whole set of frequencies during the controller loopshaping process. Through a careful study of the QFT bounds formulas it is possible to answer both questions before bound computation and loopshaping. The new formulation is useful not only to predict the simultaneous meeting of different feedback control specifications in the presence of uncertainty, but also to quantify the trade-offs amongst control goals in order to achieve the optimal feasible solution and/or obtain the maximum benefits at the lowest 'cost of feedback'. Otherwise it allows the quantification of the best way to divide the uncertainty space to improve the performance without excessive control bandwidth implementing robust-adaptive control structures