Online Neuro-Fuzzy Controller : projeto para estabilidade robusta

Abstract

Adaptive control is a control paradigm already established in the solution of problems involving nonlinearities, variance, or parametric uncertainty, known challenges in the practice of Control Engineering. An adaptive control system tries to simultaneously carry out the identification of a plant (implicitly or explicitly) and the recursive adjustment of the parameters of a controller designed to control that same plant. Due to the characteristic of universal approximators, Fuzzy systems serve as an element of an adaptive controller. The analysis of stability and robustness of an adaptive controller is a central problem in the development of these techniques and ordinarily, requires the use of non-linear analysis tools. The objective of this work was to investigate the stability problem of Online Neuro-Fuzzy Controller (ONFC), an adaptive controller based on Fuzzy systems with a simple structure and that can be applied to different types of processes. Its efficiency and low computational cost have enabled applications in several industrial plants to be successful. In spite of the fact that many works have improved the original version of the ONFC, a design procedure with formal stability guarantees was still pending. Besides, problems of robustness to disturbances and difficulties in tuning the parameters were pointed out in several practical applications. In this work, the conditions for the robust stability of the ONFC are presented, applied to a linear plant with a single entrance and single exit, considering the polytopic uncertainties of the system and external disturbances. A generalized model is proposed, based on Model Reference Adaptive Control (MRAC), which includes a way of specifying the desired dynamic performance. A new rule for adapting the controller parameters is proposed, with dynamic adaptation gain, which ensures stability and robustness to measurement noise and presents better performance compared to the original version. The threshold conditions are given in the form of an LMI (Linear Matrix Inequality) problem, based on Lyapunov’s direct method for the discrete case. Objective ONFC design guidelines have been developed for application in a partially unknown linear plant, using only output feedback. Numerical tests were performed by applying the proposed controller and other competitors in typical problems to indicate their application possibilities. The simulation results show that the proposed modifications retain the simplicity and low computational cost of the ONFC while giving it a significant performance gain in controlling different types of problems and design formalism.