# Backstepping Adaptive Neural Network Control for Electric Braking Systems of Aircrafts
## 1 Introduction  
With the development of aviation technology, the performance of modern aircraft has also greatly improved and the requirement of braking system performance is more stringent [1; 2; 3; 4; 5]. The electric braking system is a new type of braking system that uses electromechanical actuators instead of traditional hydraulic actuators. Compared with the hydraulic braking system, the electric braking system has advantages of light weight, small volume, and high reliability which make it the development direction of aircraft braking systems in the future [6; 7; 8; 9]. As a new type of actuator, the electromechanical actuator (EMA) is composed of a motor, reduction gear, and a ball screw. With the development of permanent magnet material technology, the brushless DC motor (BLPCM) has been widely used in many industrial and automotive applications. The BLDCM has the advantages of a high-power density, a compact structure, and high efficiency which make it suitable for driving the EMA [10; 11; 12]. From the analysis above, it can be noted that the electric braking system is a new kind of servo system with special applications. Therefore, an appropriate control strategy is needed to satisfy the high-performance requirement of the aircraft braking system. The EMA is a complex mechatronic transmission system that contains friction, backlash, hysteresis, and other nonlinear factors. These characteristics make it difficult to accurately describe the dynamic mathematical model of the EMA. In addition, aircrafts usually work in harsh environments, such as large fluctuations in temperature, strenuous vibrations, and damp conditions. For these reasons, it is impossible to obtain an accurate mathematical model of the EMA and is therefore difficult for the EMA to achieve the high precision and fast response of the braking pressure control effect with a traditional linear controller. To design an appropriate controller, the mathematical model of the EMA must be reasonably simplified, and many studies have been working on this issue [13; 14; 15]. Thecompound disturbance in the EMA is a combination of the internal deformation, external disturbance, time-varying parameters, and unmodeled dynamics, so an appropriate design idea is also essential to design the control law of the electric braking system [16; 17]. [PERSON] et al. proposed a sliding mode control method for the electromechanical braking system with a BLDCM, and the switching control law was adjusted by a fuzzy corrector [18]. [PERSON] et al. presented a dynamic surface-based control algorithm for solving the stability problem of slip ratio control in an electric braking system [19]. To improve the control ability and accuracy of the motor in a flexible-joint robot, a fuzzy PID control method was proposed in [20]. To overcome the parameter variability and unknown disturbance in the electric rudder servo system, [PERSON] et al. proposed a backstepping power fast terminal sliding mode control algorithm in [21]. [PERSON] et al. [22] designed an RBF neural network-based nonsingular fast terminal sliding mode control algorithm for braking systems with an EMA. The global stability of the control law was proved by using the Lyapunov function. In [23], [PERSON] et al. proposed a sliding-mode extremum seeking controller for the all-electric active braking system in unmanned aerial vehicles and validated the servo performance of the designed controller through HIL experiments. [PERSON] et al. [24] realized a non-mechanical antilock braking system (ABS) controller for the electric scooter, and the braking performance for the ABS action was further addressed via experiments. Furthermore, most of the existing studies have focused on improving the performance of the EMA controller, and the braking pressure-motor angle models in the literature are generally equivalent to a first-order proportional linear model. However, as shown in Figure 2, the real curve of the EMA is not the case.