Metodologia nebulosa robusta para estimação da resposta em frequência de sistemas dinâmicos incertos.

Abstract

In this thesis, a robust fuzzy methodology for frequency response estimation of uncertain dynamic systems, based on experimental data, is presented. The thesis deals with two fundamental aspects: fuzzy modeling of uncertain dynamic systems and design, and implementation of robust controllers for uncertain dynamic systems, based on the Fuzzy Frequency Response (FFR), considered as the main contribution of this work. The fuzzy modeling of uncertain dynamic systems is performed by identification systems and Takagi-Sugeno (TS) fuzzy dynamic models, which allow the isolation of the uncertain dynamic system in linear sub-models and the concatenation of these sub-models into a single Takagi-Sugeno (TS) fuzzy inference structure. To obtain the rules base of Takagi-Sugeno (TS) fuzzy dynamic model, a fuzzy clustering algorithm to automatically generate the antecedent space and least squares algorithm to estimate the parameters of the linear sub-models the consequent space were used. From fuzzy modeling of uncertain dynamic systems a formulation for obtaining the frequency response of Takagi-Sugeno (TS) fuzzy dynamic models is presented as well as a Theorem, which shows that the graphical representation of the Fuzzy Frequency Response (FFR) is a family of frequency responses, of magnitude and phase, in the frequency domain. As a consequence of this Theorem , the Fuzzy Frequency Response (FFR) is defined as a region (bound) in Bode’s magnitude and phase graphs, obtained by the sub-models in the consequent space and based on the operation regions in the antecedent space of Takagi-Sugeno (TS) fuzzy dynamicmodel rules base. Experimental results obtained through the design and implementation of robust controllers for uncertain dynamic systems, based on the Fuzzy Frequency Response (FFR), in a control real-time platform, demonstrate the efficiency of the methodology in the analysis and/or design of robust controllers applied to the real dynamic systems.