Control of Servo Systems Based on Differentiable Lugre Friction Model

This paper investigates the problem of high-precision tracking control of servos with nonlinear friction compensation. Although friction compensation based on the LuGre model has been widely applied in various industrial servo mechanisms, combining it with inverse design is challenging due to the piecewise continuous characteristics of the model. As a result, servo control based on nonlinear models rarely involves friction compensation for non-differentiable friction models such as the LuGre model and the Stribeck effect. This study introduces an enhanced particle swarm approach to adapt the conventional piecewise continuous LuGre model, leading to the development of a novel model, which is both nonlinear and continuously differentiable. Then it introduce an adaptive inverse controller that takes into account factors such as friction parameters and transmission clearance in the established nonlinear servo system. By means of Lyapunov analysis, the controller provides a theoretical assurance of asymptotic tracking performance even in the presence of parameter uncertainties, while also demonstrating robustness against unconsidered dynamics and external disturbances. The simulation results validate the effectiveness of the proposed controller. This research provides a new approach to nonlinear friction compensation and control of servo systems, with potential applications in various industries.