Friction dynamics identification based on quadratic approximation of LuGre model

In mechanical transmission servo systems, where friction is the primary disturbance, such as robot joints, dynamic friction is considered the leading cause of control inaccuracy in low-speed regions and during velocity direction changes. The LuGre model is a well-established dynamic friction model that has proved successful in describing dynamic frictional phenomena in such systems. However, most identification methods of the LuGre model rely on the prior knowledge of the inner parameters, and the internal state is difficult to observe. These factors make the friction dynamics identification become very cumbersome. On the other hand, we have discovered that the LuGre model exhibits redundancy in predicting friction dynamics. Therefore, in this article, the LuGre model is remodeled as a dynamic neuron by its recurrent quadratic approximation to expose high-order hidden parameters. On the basis of this modeling approach, a direct adaptive control architecture is proposed to identify all unknown parameters without any prior knowledge. In this scheme, a self-tuning combined error neuron is designed whose signal–noise ratio is maximized by principle component analysis. Besides, a kernel function-based stabilizing term is introduced in the update laws to suppress the oscillation during transient response. The feasibility of the strategy is verified through stability analysis. Simulation results show that the estimated LuGre model correctly reveals the actual behavior of friction dynamics. Finally, comparative experiments are carried out on a rotary actuator. The results show that the proposed adaptive control-based learning strategy significantly enhances position tracking performance, especially in the processes of slow crawling and switching in speed direction.