Adaptive friction compensation for a class of mechanical systems based on LuGre model

This paper deals with the problem of friction compensation for a class of uncertain mechanical systems based on LuGre model. The objective is to develop control laws such that the position variable of the system tracks a periodic desired signal or a constant desired signal. Since the friction behavior of the system with periodic desired signals is largely different from that of the system with constant desired signals, two different adaptive control methods are presented for the two cases, respectively. For the case of periodic desired signals, an adaptive repetitive learning control method is presented, and for the case of constant desired signals, an adaptive dynamic state feedback control method is presented. Both the control laws can guarantee that all the signals in the closed loop system are bounded and the tracking errors converge to zero. Several numerical simulations are carried out to show effectiveness of the proposed control algorithms.