This paper aims to develop a state estimate-based friction fuzzy modeling and robust adaptive control techniques for controlling a class of multiple degrees of freedom (MDOF) mechanical systems. A fuzzy state estimator is proposed to estimate the state variables for friction modeling. Under some conditions, it is shown that such a state estimator guarantees the uniformly ultimate boundedness (UUB) of the estimate error. Based on system input–output data and our proposed state estimator, a robust adaptive fuzzy output-feedback control scheme is presented to control multiple degrees of freedom system with friction. The adaptive fuzzy output-feedback controller can guarantee the uniformly ultimate boundedness of the tracking error of the closed-loop system. A typical mass-spring system is employed in our simulation studies. The results demonstrate that our proposed techniques in this paper have good potential in controlling nonlinear systems with uncertain friction.

Modeling of friction force has been a challenging task in mechanical engineering. Traditional way, such as mathematical modeling approaches, was found quite difficult to achieve satisfactory performances due to some immanent nonlinearity and uncertainties in systems. This paper aims to develop fuzzy modeling techniques to characterize the friction dynamics. The proposed fuzzy modeling approach has two folds, that is, extraction of fuzzy rules using data mining techniques; setup of static model based on the fuzzy rules. The results obtained demonstrate that our proposed method in this paper has good potential in many mechanical systems with unknown nonlinear friction.