Estimação e compensação de atrito em um pêndulo invertido

Abstract

The inverted pendulum is a mechanical system underactuated, inherently unstable in openloop, with nonlinear dynamics, being a classic benchmark for the study of control problems. The motivation behind this interest is the growing number of precise positioning applications in mechanical systems. The application of control techniques without taking into consideration friction can produce limit cycles. In this work, methods for modeling, quantification and compensation of friction are analyzed and applied to the inverted pendulum. Techniques recently proposed in the literature are adapted to the system under study. Models of Coulomb, Karnopp and LuGre are discussed and methods are analyzed to obtain the parameters via identification in open loop and closed loop and quantification fitting ellipses to input versus output data. Friction quantified via different models are compared. These models are used to compensate the friction present in the cart of the pendulum. The non-model based methods of compensation called continuous reinforcement and knocker are also applied. Their performances are evaluated and compared using three performance indexes, through their application to a real pendulum.