# A Study of Friction Nonlinearity and Compensation for Turntable Servo Systems
## 1 Introduction
Inspired by the average deformation of the bristle model, the [PERSON] model was extended and the LuGre model was established in [7], which is more complete and easier to implement, making it the most widely used dynamical model. [PERSON] pointed out that the LuGre model does not describe the hysteresis phenomenon adequately and could not explain the non-local memory problem in the experiments, so he proposed the Leuven model [8], which is the most widely used dynamic model. And [PERSON] et al. proposed a generalized Maxwell sliding model based on the Leuven model [9]. Friction compensation is mainly divided into two ideas: friction model-based compensation and non-friction model-based compensation. The essence of the friction model-based compensation strategy is feedforward compensation: the fixed friction model parameters are obtained through offline experiments, or the friction parameters are recognized online through adaptive methods. Then, the friction torque is estimated according to the current state parameters, such as the system speed, and feedforward compensation is carried out. One study [10] used a simple static model (Coulomb + viscous hysteresis) and a Stribeck model for compensation, and the experimental results showed that the latter was more effective. Another study [11] used the LuGre model in the start-up phase and switched to the Stribeck model in the smooth operation phase, which reduced the average speed tracking error to a seventh of the original one. The study by [12] proposed an adaptive friction compensation scheme based on the LuGre model, in which the unknown dynamic parameters and the unmeasurable internal states are obtained by an observer. The essence of a compensation strategy that is not based on a friction model is to consider the friction as a disturbance in the system, and the disturbance is suppressed by algorithms such as nonlinear proportional integral derivative (PID) control, observer-based control, neural network control, variable structure control, or robust control. The study by [13] estimates the friction effect of a three-wheeled omni-directional mobile robot based on a reduced-order extended state observer, and a large number of experimentsdemonstrated the effectiveness and robustness of the control method. Since neural networks can approximate any nonlinear function, in the study by [14], an augmented neural network was used to achieve an accurate approximation of the discontinuous function using fewer nodes. Then, an integral sliding mode control was designed based on the system model and the friction model based on the neural network, with the sliding surface as a simple proportional integral function of the positional error, and the control rate obtained by the backpropagation method. The study by [15] improved the tracking response of a DC brushless linear motor by optimally tuning the parameters of a perturbation observer-based variable structure controller using particle swarm optimization (PSO). From the above literature review, it can be concluded that static friction models allow for easier modeling of friction without overly sacrificing accuracy. The suppression and compensation of unknown friction perturbations can be achieved through the introduction of ADRC. This study delves into the pervasive influence of friction on transmission mechanisms. Friction has a significant effect on fine positioning, leading to increased errors and motor stalls. Therefore, this paper no longer ignores the effect of friction in the transmission link. To address these challenges, a closed-loop structure with state feedback is proposed to compensate for mechanical gaps by enhancing friction through increased surface roughness. Offline identification of friction characteristics with a static friction model is carried out. Feedforward compensation for friction torque is also implemented.