# High-Fidelity Fin-Actuator System Modeling and Aeroelastic Analysis Considering Friction Effect
## 1 Introduction  
Flutter is a critical problem in modern flight vehicle design. To pursue lighter weight, wings and control surfaces tend to be more flexible, which may lead to flutter. Flutter instability will seriously affect aircraft performance and flight safety [1]. The conventional aeroelastic analysis of the control surface often focused only on the surface itself, and the actuator supporting the surface was regarded as a linear torsion spring with constant stiffness [2], as shown in Figure 0(a). In fact, many experiments have proved that the actuator itself has dynamic characteristics, especially electromechanical servo actuators. Electromechanical servo actuators have good maintainability, low static power consumption, and storage convenience, so they have been widely used in missile control fin position servo systems [3]. Thus, they are the modeling objects of this paper. An electromechanical actuator consists of multiple components that can be classified as the moment of inertia (MOI), elastic spring, and damper, as shown in Figure 0(b), which means that the actuator should not be over-simplified as a linear spring. Moreover, the stiffness of the actuator will change according to the change in the external load, which is called dynamic stiffness. In addition, the actuator has control algorithms and electrical and mechanical nonlinearities such as current/voltage saturation, freeplay, and friction [4]. The analysis of the fin-actuatorsystem, considering the dynamic characteristics of the actuating system, makes the results different from those of wings only [5], which will affect the flutter boundary of the system. Both the dynamics and structural nonlinearity of the actuator will greatly affect the aeroelastic characteristics of the system [6; 7]. In the field of aeroelasticity, there are some studies that model the actuator and perform flutter analysis while considering the actuator dynamics and structural nonlinearities. [PERSON] et al. [5] performed an aeroelastic analysis of the missile fin with a nonlinear pneumatic actuator and proposed a flutter suppression method. [PERSON] and the team [8] analyzed the flutter characteristics of the control fin of a rocket considering dynamic actuator characteristics. [PERSON] et al. [6] established a basic framework for obtaining the aeroelastic stability results of a fin-actuator system considering the actuator's dynamic characteristics. They found that the flutter boundary could be increased in this way. In the same year, [PERSON] et al. [9] investigated the same system with the consideration of actuator nonlinearities, such as freeplay, backlash, and transmission error. The results show that both the freeplay and backlash may influence the actuator dynamic stiffness. They also found that the nonlinearity and gear reductions can greatly affect the limit cycle oscillation (LCO) characteristics. [PERSON] et al. [7] obtained the aeroelastic characteristics of the fin-actuator system containing preload freeplay and found that an appropriate preload angle can suppress LCOs. [PERSON] and his team [10] analyzed the influence of actuator parameters on the dynamic stiffness. The results show that factors such as inertia of the motor rotor, connection stiffness between different levels of reducers, reduction ratio of each level of reducer, and the damping at the actuator fin shaft have significant effects. It can be seen that the studies above only considered freeplay or other nonlinearities in the actuator and rarely analyzed the friction. Friction actually has a great influence on aeroelastic properties, which exists widely and can be used to improve aeroelastic properties. Therefore, it was innovative and necessary to add a friction nonlinearity module to the model in this paper. Moreover, the previous work was only for a specific actuator, which is often too simplified, and the reliability of the model was not easy to guarantee. Furthermore, they often used the dynamic differential equations of the actuator to carry out modeling and analysis.