# High-Fidelity Fin-Actuator System Modeling and Aeroelastic Analysis Considering Friction Effect
## 1 Introduction
Therefore, the prediction of the stability boundary of a fin-actuator aeroelastic system is not enough. In fact, in engineering, the friction can be changed by adjusting the preload, the roughness of the friction surface, lubrication, material, temperature, and other factors that cannot be represented fully by simple models. Therefore, a model that can more accurately reflect the friction characteristics is introduced into the aeroelastic analysis model to improve the model's accuracy, study further the influence mechanism of the above factors on the aeroelastic stability, and give some guidance suggestions. The friction models that are currently used are mainly separated into two main types: the static model and the dynamic model [22]. The static model may include different components such as viscous friction, Coulomb friction, the Stribeck effect, and static friction. However, the static friction model cannot describe the influence of friction when the contact surfaces are relatively static. Some experiments show that some phenomena of friction can only be reproduced by dynamic models with memory, such as hysteresis, rate-dependence, and pre-displacement. The dynamic friction model can reflect the friction phenomenon more accurately, and therefore has more application value. Many researchers have developed a variety of dynamic models, mainly including the Dahl model [23], the LuGre model [24,25], the Leuven model [26,27], the Generalized Maxwell-Slip (GMS) model [28,29], and two-state friction model (2 SEP) [30]. The Dahl model is not accurate enough when the velocity is low, and it cannot capture stick-slip motion. The LuGre friction model extends the Dahl model, which was proposed by [PERSON] and his companions [24; 25; 31; 32; 33; 34]. It can reflect the complex processes of friction static and dynamic characteristics, including viscous friction, Stribeck effect, variable static friction, memorial friction, and pre-sliding displacement. The disadvantage of the LuGre model is that the hysteresis behavior does not have nonlocal memory characteristics in the pre-sliding regime, which has attracted some attention in the field of precise control. The Leuven model can reflect this characteristic, but it is difficult to implement. The same author also proposed the GMS model. Compared with the Leuven model, the GMS model can more accurately reflect the physical mechanism of friction, but the model is also more complex, which leads to difficulties in implementation or identification. The 2 SEP model considers to a greater extent the micro-scale elastoplasticity, which is not the focus of this paper. A comparison of these models is shown in Table 1.  
It is worth noting that when choosing a model, a proper trade-off must be made between model fidelity and implementation. The accuracy of the LuGre model is sufficient for the problem we want to study. The parameters' physical meaning of the LuGre model is clear, and thus can easily match experimental data. It is a first-order model, which is more convenient to use and analyze than other second-order models [35]. Various benefits make this model widely used in control systems [36; 37; 38; 39; 40], which means it is easy to integrate into the actuator model based on SIMULINK, launched by MathWorks company, and it is also convenient for subsequent work with which to perform active flutter suppression. Using more complex models to consider the effect of friction in a more micro and accurate way can be an open question for future investigations. The LuGre model contains only six parameters, which are \(\sigma_{0}\), \(\sigma_{1}\), \(\sigma_{2}\), \(F_{\rm c}\), \(F_{\rm s}\), and \(V_{\rm s}\). Many researchers have proposed effective LuGre parameters identification methods [31; 41; 42; 43]. Based on interpreting the asperities contact, the LuGre model uses elastic spring-like bristles with damping to accurately represent the asperities between two contact surfaces.