Adaptive Fuzzy Active-Disturbance Rejection Control-Based Reconﬁguration Controller Design for Aircraft Anti-Skid Braking System

: The aircraft anti-skid braking system (AABS) is an essential aero electromechanical system to ensure safe take-off, landing, and taxiing of aircraft. In addition to the strong nonlinearity, strong coupling, and time-varying parameters in aircraft dynamics, the faults of actuators, sensors, and other components can also seriously affect the safety and reliability of AABS. In this paper, a reconﬁguration controller-based adaptive fuzzy active-disturbance rejection control (AFADRC) is proposed for AABS to meet increased performance demands in fault-perturbed conditions as well as those concerning reliability and safety requirements. The developed controller takes component faults, external disturbance, and measurement noise as the total perturbations, which are estimated by an adaptive extended state observer (AESO). The nonlinear state error feedback (NLSEF) combined with fuzzy logic can compensate for the adverse effects and ensure that the faulty AABS maintains acceptable performance. Numerical simulations are carried out in different runway environments. The results validate the robustness and reconﬁguration control capability of the proposed method, which improves AABS safety as well as braking efﬁciency.


Introduction
An aircraft anti-skid braking system (AABS) with good performance is an important guarantee for the successful completion of flight missions [1]. It directly affects the safety of the aircraft and the crew on board. With the rapid development of the aviation industry, the demand for large-tonnage and high-velocity aircraft is increasing. In order to brake this type of aircraft in less time and over shorter distances, it is necessary to improve the efficiency and performance of AABS. Moreover, the AABS is highly non-linear and subject to many uncertainties including runway surface conditions, which makes the AABS controller design challenging [2].
The conventional PID + PBM control [3] method does not work well on runways with disturbances, and the aircraft suffers from low-speed slippage [4,5]. In response to these problems, many control schemes proposed by researchers have been widely applied in the field of AABS, such as mixed slip deceleration PID control [6], backstepping dynamic surface control [7], optimal fuzzy control [8], self-learning fuzzy sliding mode control [9], (i) It is a robust control strategy, in which the AABS model is extended with a new state variable. This state variable is the sum of all unknown dynamics and disturbances that are not noticed in the fault-free plant description, and it is estimated online using the designed extended state observer (ESO), which indirectly simplifies the model to a significant extent. (ii) An adaptive extended state observer (AESO) is proposed to estimate the new state variable. The method is based on online tuning of ESO parameters using an improved back propagation neural network (BPNN). It should be noted that the proposed AESO is an improvement on the one presented by Qi et al. [31]. The application of AESO not only eliminates the tedious manual tuning of the parameters, but also greatly enhances the adaptiveness and robustness of the proposed method in the face of faults and disturbances.
(iii) Fuzzy logic is introduced into the nonlinear state error feedback (NLSEF). The performance of the ADRC is heavily related to the selection of NLSEF parameters. ADRC with fixed parameters has limited robustness and anti-disturbance. It may lead to an unacceptable performance or even divergence in different fault perturbation cases. NLSEF combined with fuzzy logic can adjust the control law parameters online autonomously to meet the control performance requirements, which thereby improves controller robustness and parameter adaptiveness. It is worth mentioning that fuzzy logic is data-driven, making it immune to model errors caused by imprecise modeling. (iv) Additional fault detection and identification (FDI) modules are not required, and the controller parameters are adaptive. Therefore, the proposed AFADRC belongs to a novel combination of passive reconfiguration control and FDI-free reconfiguration control, which makes it an interesting solution in unknown fault conditions.
The paper is organized as follows. Section 2 describes AABS dynamics. The reconfiguration controller based on AFADRC is presented in Section 3. The simulation results are presented to demonstrate the merits of the proposed method in Section 4, and conclusions are drawn in Section 5.

AABS Dynamics
Previous studies have generally not considered the effect of the landing gear but have viewed the fuselage and landing gear as a rigid whole [11,12]. This simplified model of the brake system is not accurate enough to describe the actual system. In this paper, the dynamics modeling of an AABS generally includes aircraft fuselage dynamics, landing gear dynamics, individual main wheel braking dynamics, combination coefficients, and electrohydraulic actuators. The subsystems are strongly coupled and exhibit strong nonlinearity and complexity.

Aircraft Fuselage Dynamics
Based on the actual process of anti-skid braking and objective facts, some reasonable assumptions can be made: (i) The aircraft fuselage is ideal rigid one with a concentrated mass. (ii) The gyroscopic moment generated by the engine rotor is not considered in the aircraft braking process. (iii) The system ignores the crosswind effect. (iv) The system ignores the tire deformation.
(v) All wheels are the same and controlled synchronously.
The force diagram of the aircraft fuselage is shown in Figure 1, and the specific parameters described in the diagram are shown in Table 1. The force balance equation of the aircraft is:     According to the influence of aerodynamic properties, we have the following equation: The combination coefficient µ i is defined as: where i = 1, 2.

Landing Gear Dynamics
The main function of the landing gear is the support and buffer action, thus improving the vertical and longitudinal force situation. In addition to the wheel and braking device, struts, buffer, and torque arm are the main components of the landing gear. In this paper, it is assumed that the stiffness of the torque arm is large enough and the torsional freedom of the wheel with respect to the strut and the buffer is ignored, so the torque arm is not considered.

Buffer Modeling
The buffer can be reasonably simplified to a mass-spring-damper system [37]. The force acting on the fuselage by the buffer can be described as: whose parameters are shown in Table 2. Due to the nonrigid connection between the landing gear and aircraft, horizontal and angular displacements are generated under the action of braking force. However, the strut is a cantilever beam whose angular displacement is very small and negligible. The landing gear lateral stiffness model can be represented by the equivalent second-order equation as follows: whose parameters are shown in Table 3.

Wheel Dynamic
The force analysis diagram of the main wheel brake is shown in Figure 2. During the taxiing, the main wheel is subjected to a combination of braking torque M s and ground friction torque M j . In addition, since the effect of lateral stiffness is considered for the main landing gear, there exists a wheel axle velocity V zx along the longitudinal direction of the airframe, obtained by superimposing the aircraft speed V and the navigation vibration speed d V . The main wheel dynamics equation is: whose parameters are shown in Table 4.   [37].
In this paper, λ can be calculated as follows: The combination coefficient is related to the real-time runway status, aircraft speed, slip rate, and many other factors. In this paper, the magic formula given by Pacejka H. B. [38] is used to describe the model: where D is the peak factor, C is the stiffness factor, and B is the curve shape factor.
By changing these factors, different ground combination coefficients can be modeled. The  When the wheel is braked, a longitudinal force is applied to the tire, always making V > V w . This difference can be expressed in terms of the slip rate λ. For the main wheel, using V zx instead of V to calculate λ can avoid the false brake release caused by landing gear deformation, thus effectively reducing the landing gear walk situation [37]. In this paper, λ can be calculated as follows: The combination coefficient is related to the real-time runway status, aircraft speed, slip rate, and many other factors. In this paper, the magic formula given by Pacejka H. B. [38] is used to describe the model: where D is the peak factor, C is the stiffness factor, and B is the curve shape factor. By changing these factors, different ground combination coefficients can be modeled. The specific parameter values for several different runways are shown in Table 5.

Hydraulic Servo System Modeling
AABS working principle is introduced in advance: the controller controls the hydraulic servo system according to the error between the wheel speed and the aircraft speed, thus changing the brake pressure and realizing brake control. Since the structure of the hydraulic servo system is complex, in this paper, some simplifications have been made that only electro-hydraulic servo valve and pipes are considered. The transfer functions of them are expressed as follows: whose parameters are shown in Table 6. It should be noted that the controller should realize both brake control and anti-skid control. To this end, there is an approximately relationship between the brake pressure P and the control current I c , which can be described as follows: The braking device serves to convert the brake pressure into brake torque, and its calculation is as follows: M s = µ mc N mc PR mc (12) whose parameters are also shown in Table 6. The hydraulic servo system, as the actuators of AABS, is inevitably subject to potential faults. Problems such as hydraulic oil mixing with air, internal leakage, and vibration seriously affect the efficiency of the hydraulic servo system [13,14]. Therefore, in this paper, loss of effectiveness (LOE) is introduced to represent typical AABS actuator faults. The LOE fault is characterized by a decrease in the actuator gain from its nominal value [35]. In the case of an actuator LOE fault, the brake pressure generated by the AABS deviates from the commanded output expected by the controller. In other words, one instead has: where P f ault refers to the actuator actual output, P is the commanded output by the controller, k LOE represents the LOE fault gain, and k LOE ∈ (0, 1).

Remark 2.
It should be noted that if the actuator does not have the same characteristics as fault-free, it is necessary to establish the fault model. Not only does this provide an accurate model for the next controller design, but it also ensures that the adverse effects caused by faults can be effectively estimated and compensated for.
Thus, Equation (12) can be rewritten as follows: where M s is the actual brake torque. (1)-(12), the fault-free AABS is nonlinear and highly coupled. The occurrence of the faults leads to a jump in the model parameters with greater internal perturbation compared to the no-fault case. Meanwhile, the external disturbance cannot be ignored.

Overall Components of Aircraft Anti-Skid Braking System
The overall components of AABS and the interaction between each part are summarized in Figure 3. It can be seen that AABS is a complex nonlinear system, whose variables affect and constrain each other. The controller design for AABS will be more challenging if actuator faults are considered.
where s M′ is the actual brake torque. (1)-(12), the fault-free AABS is nonlinear and highly coupled. The occurrence of the faults leads to a jump in the model parameters with greater internal perturbation compared to the no-fault case. Meanwhile, the external disturbance cannot be ignored.

Overall Components of Aircraft Anti-Skid Braking System
The overall components of AABS and the interaction between each part are summarized in Figure 3. It can be seen that AABS is a complex nonlinear system, whose variables affect and constrain each other. The controller design for AABS will be more challenging if actuator faults are considered.

Aircraft Fuselage Dynamics
Braking device

Landing Gear and Wheel
Hydraulic Servo System Controller Runway Status

Reconfiguration Controller Design
ADRC inherits the advantage of PID control, which is error-driven rather than modelbased. There are some unique qualities in ADRC [35,39]: it offers an observer to estimate the disturbance; it combines the state feedbacks in a nonlinear way, allowing for a wide range of parameter adaptation; it is a digital control technique developed from the experimental platform rooted in computer simulations. The normal ADRC consists of a tracking differentiator (TD), a nonlinear state error feedback (NLSEF), and an extended state observer (ESO). However, the fixed controller parameters may not perform well in the face of faults that cause large jumps in model parameters. The normal ADRC requires many parameters to be tuned, which will increase the difficulty of engineering applications. Motivated by these facts, an AFADRC reconfiguration controller is proposed in this section-that is, using AESO instead of ESO to estimate the perturbations adaptively, and combining NLSEF with fuzzy logic to meet the control performance requirements under different fault and disturbance conditions.
Although the aircraft has three degrees of freedom, only longitudinal taxiing is focused on in AABS. According to Section 2, the AABS model can be written as follows: ..
where f (·) is the uncertainty item, represents the total perturbations, b x = 1 m . Since AABS in this paper adopts the slip speed control type [1], system (15) can be rewritten as follows: .
The structure of the AFADRC proposed in this paper is shown in Figure 4. For AABS, v 0 = V, u = I c and y = V w + V n , where V n denotes measurement noise. The design process is described in detail next. a wide range of parameter adaptation; it is a digital control technique developed from the experimental platform rooted in computer simulations. The normal ADRC consists of a tracking differentiator (TD), a nonlinear state error feedback (NLSEF), and an extended state observer (ESO). However, the fixed controller parameters may not perform well in the face of faults that cause large jumps in model parameters. The normal ADRC requires many parameters to be tuned, which will increase the difficulty of engineering applications. Motivated by these facts, an AFADRC reconfiguration controller is proposed in this section-that is, using AESO instead of ESO to estimate the perturbations adaptively, and combining NLSEF with fuzzy logic to meet the control performance requirements under different fault and disturbance conditions.
Although the aircraft has three degrees of freedom, only longitudinal taxiing is focused on in AABS. According to Section 2, the AABS model can be written as follows: where ( ) f ⋅ is the uncertainty item, ϖ represents the total perturbations, 1 Since AABS in this paper adopts the slip speed control type [1], system (15) can be rewritten as follows: where The structure of the AFADRC proposed in this paper is shown in Figure 4. For AABS,

Tracking-Differentiator (TD)
The main role of the TD is twofold: the first is to arrange the transition process for the system; the second is to filter the signal and obtain the differentiated signal. This effectively solves the conflict between rapidity and overshoot. A second-order TD can be designed as follows:

Tracking-Differentiator (TD)
The main role of the TD is twofold: the first is to arrange the transition process for the system; the second is to filter the signal and obtain the differentiated signal. This effectively solves the conflict between rapidity and overshoot. A second-order TD can be designed as follows: where v 0 is the desired output, v 1 is the transition process of v 0 , v 2 is the derivative of v 1 , r and h are adjusted accordingly as filter coefficients. The function fhan(·) is defined as follows: Actuators 2021, 10, 201

Adaptive-Extended-State-Observer (AESO)
ESO is the core of ADRC, which estimates the system states and the total disturbance in real time based on the control quantity u and the plant output y. The normal ESO can be designed as follows: where ε is error of estimation, z 1 is the estimated state, z 2 is the derivative of z 1 , z 3 is the extended state which is an estimate of the total system perturbations, b e is an adjustable parameter with a value close to b v , and (β 01 , β 02 , β 03 , δ) are positive scalars; the function f al(·) is defined as follows: From Equation (20), it can be seen that the three important parameters (β 01 , β 02 , β 03 ) directly affect the accuracy of the estimated states (z 1 , z 2 , z 3 ). In particular, z 3 directly determines the perturbation compensation accuracy, which further comes to affect the overall control performance. For AABS with potential faults, the normal ESO may have the following issues: (i) Manual tuning of parameters is tedious and not conducive to engineering applications. (ii) An ESO with fixed (β 01 , β 02 , β 03 ) may not accurately estimate the perturbations or even converge when faults occur. (iii) If the ESO estimations are not optimal, this may result in less-than-satisfactory control.
Motivated by the above analysis, in this paper, a three-layer BPNN-based AESO is designed that can be adaptively tuned to parameters with plant changes and disturbances. It is equivalent to system identification, which can improve the robustness, the estimated accuracy, and the control performance. The internal AESO structure is shown in Figure 5. (e 1 , e 2 , y, 1) and (β 01 , β 02 , β 03 ) are the input and output of the BPNN, respectively. The number of hidden nodes is determined to be 5 in combination with the plant and after several attempts. designed that can be adaptively tuned to parameters with plant changes and disturbances. It is equivalent to system identification, which can improve the robustness, the estimated accuracy, and the control performance. The internal AESO structure is shown in Figure 5. β β β are the input and output of the BPNN, respectively.
The number of hidden nodes is determined to be 5 in combination with the plant and after several attempts. The inputs of the input layer are: and the input layer nodes correspond to 1 2 ( , , ,1) e e y .
The inputs and outputs of the hidden layer are: The inputs of the input layer are: and the input layer nodes correspond to (e 1 , e 2 , y, 1). The inputs and outputs of the hidden layer are: whereω hid ij is the connection weight of the hidden layer. The inputs and outputs of the output layer are: whereω out li is the connection weight of the output layer, the output layer nodes correspond to (β 01 , β 02 , β 03 ), and the activation functions of neurons in the hidden layer and output layer are taken as follows: To derive the error back-propagation process, the error energy function is defined as follows: where rin is system command value, yout is system output, i.e., rin = v 0 and yout = y. Slow learning speed and easy to fall into local minima are two typical disadvantages of traditional BPNN [40]. In this paper, we introduce an adaptive learning rateη(k) and an inertia termα that makes the search converge quickly to the full drama minimum. The connect weight can be adjusted byÊ(k) in the negative gradient direction (steepest descent method), which can be defined as follows: where ∂Ê(k) ∂ω out where ∆Ê(k) =Ê(k) −Ê(k − 1),â andb can be adjusted depending on the actual application system to ensure the stability of the network training process. This method has been proved to be effective in improving the network convergence speed [41]. Since ∂yout(k) ∂O out l (k) is unknown, it can be approximated by sgn( . Then, the network output layer connect weight learning algorithm can be derived as: Similarly, the network hidden layer connect weight learning algorithm can be obtained as follows: After giving the initial values (β 01_I NT , β 02_I NT , β 03_I NT ), AESO can update them autonomously to achieve the optimal estimation. This method is more convenient and has better observational performance than the traditional trial-and-error method.
In normal applications, (k 1 , k 2 ) need to be tuned manually according to the actual situation. ADRC with fixed (k 1 , k 2 ) can perform well when the system is in normal operation. Once abrupt faults occur, large system parameter jumps are caused. At this point, the fixed (k 1 , k 2 ) may not maintain an acceptable performance. To improve the robustness and parameter adaptiveness of the controller, fuzzy logic is introduced to adjust the control law online. The controller thus has the reconfiguration capability to cope well with the fault conditions.
Remark 4. TD, AESO, and NLSEF with fuzzy logic together constitute the AFADRC controller. Compared to normal ADRC, AFADRC realizes the parameter adaption that makes the controller reconfigurable. The robustness and immunity are greatly improved. It can effectively compensate the adverse effects caused by the total perturbations including faults.

Simulation Results
To validate the fault recovery and disturbance rejection capabilities of the proposed reconfiguration controller for AABS, the corresponding simulations are performed in this section. AFADRC parameters are shown in Table 8. The initial states of the aircraft are set as follows: (1) initial speed of aircraft landing V(0) = 72 m/s; (2) initial values of pitch angle and velocity θ 0 = 0.02 rad, . θ 0 = 0 rad/s; (3) initial height of the center of gravity Hh = 2.178 m; (4) initial speed of wheel V w (0) = 72 m/s. The anti-skid brake control is considered to be over when V is less than 1 m/s. To prevent deep wheel slippage as well as tire blowout, the wheel speed is kept to follow the aircraft speed quickly at first and the brake pressure is applied only after 1.5 s. This is also a concise protection measure.
In this paper, the pressure efficiency method [42] is used to calculate the brake efficiency η, which can be described as follows: where S peak is the square of the area between the peak point connection and the horizontal coordinate, S 0 is the square of the area between the actual brake pressure trace and the horizontal coordinate. The details are shown in Figure 6.
where peak S is the square of the area between the peak point connection and the horizontal coordinate, 0 S is the square of the area between the actual brake pressure trace and the horizontal coordinate. The details are shown in Figure 6.

Case 1: Fault-Free and External Disturbance-Free in Dry Runway Condition
The simulation results of the dynamic braking process for different control schemes are shown in Figure 7 and Table 9. From Figure 7a,b, compared with the traditional PID + PBM control, ADRC and AFADRC effectively shorten the braking time and the braking distance. In Figure 7c the slip ratio is depicted. In the initial stage of braking, i.e., the highspeed phase of the wheel, there is a brief slippage of PID + PBM. In contrast, the braking efficiencies of ADRC and AFADRC are greatly improved, and the wheel slippages are clearly reduced with satisfactory control effects. As shown in Figure 7d, AESO automatically adjusts the observer parameters during the braking process to achieve optimal observation. The control currents for the three methods are clearly shown in Figure 7e. It can be seen that the controller is constantly performing release and brake operations during the braking process. Figure 7f shows that ADRC and AFADRC can effectively estimate the disturbances generated inside the system during braking. It should be noted that AESO and fuzzy logic constantly update the parameters online to improve the estimation and compensation accuracy, which makes AFADRC braking performance better than ADRC.

Case 1: Fault-Free and External Disturbance-Free in Dry Runway Condition
The simulation results of the dynamic braking process for different control schemes are shown in Figure 7 and Table 9. From Figure 7a,b, compared with the traditional PID + PBM control, ADRC and AFADRC effectively shorten the braking time and the braking distance. In Figure 7c the slip ratio is depicted. In the initial stage of braking, i.e., the high-speed phase of the wheel, there is a brief slippage of PID + PBM. In contrast, the braking efficiencies of ADRC and AFADRC are greatly improved, and the wheel slippages are clearly reduced with satisfactory control effects. As shown in Figure 7d, AESO automatically adjusts the observer parameters during the braking process to achieve optimal observation. The control currents for the three methods are clearly shown in Figure 7e. It can be seen that the controller is constantly performing release and brake operations during the braking process. Figure 7f shows that ADRC and AFADRC can effectively estimate the disturbances generated inside the system during braking. It should be noted that AESO and fuzzy logic constantly update the parameters online to improve the estimation and compensation accuracy, which makes AFADRC braking performance better than ADRC.

Case 2: Actuator LOE Fault and Measurement Noise in Dry Runway Condition
The fault considered here assumes a 20% actuator LOE at 5 s and escalate to 40% LOE at 10 s. The band-limited white noise with noise power 6 5 10 − × is applied to describe the measurement noise. The simulation results are shown in Figure 8 and Table 10. As can be seen in Figure 8a,b, the PID + PBM continuously performs a large braking and releasing operation under the combined effect of fault and disturbance. This makes braking much less efficient and risks dragging and flat tires. Although ADRC can maintain high braking efficiency, the braking time and distance are greatly increased. Moreover, Figure 8c shows

Case 2: Actuator LOE Fault and Measurement Noise in Dry Runway Condition
The fault considered here assumes a 20% actuator LOE at 5 s and escalate to 40% LOE at 10 s. The band-limited white noise with noise power 5 × 10 −6 is applied to describe the measurement noise. The simulation results are shown in Figure 8 and Table 10. As can be seen in Figure 8a,b, the PID + PBM continuously performs a large braking and releasing operation under the combined effect of fault and disturbance. This makes braking much less efficient and risks dragging and flat tires. Although ADRC can maintain high braking efficiency, the braking time and distance are greatly increased. Moreover, Figure 8c shows that there is a high frequency of wheel slip in the low-speed phase of the aircraft. In contrast, the proposed AFADRC can still efficiently and rapidly control the brakes, since it can remarkably handle the completely unknown uncertainties from both the internal and external. From Figure 8d,f, it can be seen that these uncertainties are estimated fast and accurately based on AESO. Meanwhile, NLSEF with fuzzy logic adaptively adjusts the control law parameters according to the magnitude of the state errors and reconfigures the control to compensate for faults and measurement noise. The comparison between Case 1 and Case 2 illustrates that AFADRC not only ensures the braking performance of fault-free AABS, but also greatly improves the robustness and immunity of AABS in fault-perturbed conditions. The fault considered here assumes a 20% actuator LOE at 5 s and escalate to 40% LOE at 10 s. The band-limited white noise with noise power 6 5 10 − × is applied to describe the measurement noise. The simulation results are shown in Figure 8 and Table 10. As can be seen in Figure 8a,b, the PID + PBM continuously performs a large braking and releasing operation under the combined effect of fault and disturbance. This makes braking much less efficient and risks dragging and flat tires. Although ADRC can maintain high braking efficiency, the braking time and distance are greatly increased. Moreover, Figure 8c shows that there is a high frequency of wheel slip in the low-speed phase of the aircraft. In contrast, the proposed AFADRC can still efficiently and rapidly control the brakes, since it can remarkably handle the completely unknown uncertainties from both the internal and external. From Figure 8d,f, it can be seen that these uncertainties are estimated fast and accurately based on AESO. Meanwhile, NLSEF with fuzzy logic adaptively adjusts the control law parameters according to the magnitude of the state errors and reconfigures the control to compensate for faults and measurement noise. The comparison between Case 1 and Case 2 illustrates that AFADRC not only ensures the braking performance of fault-free AABS, but also greatly improves the robustness and immunity of AABS in faultperturbed conditions.

Case 3: Actuator LOE Fault and Measurement Noise in Mixed Runway Condition
The mixed runway structure is as follows: dry runway in the interval of 0-5 s, wet runway in the interval of 5-10 s, and snow runway after 10 s. Fault and disturbance conditions are the same as Case 2. The simulation results are shown in Figure 9 and Table 11. It can be clearly seen from Figure 9a,b that the PID + PBM control cannot brake the aircraft to stop in a limited time, which may lead to serious consequences. Compared with ADRC, AFADRC can better adapt to the runway changes. Figure 9d shows that AESO can still realize parameter adaption in the mixed runway case. The total perturbations can be accurately estimated: see Figure 9f. Under fault-perturbed conditions, AFADRC can still brake fast with high efficiency, which improves the environmental adaptability and reliability of AABS.
to stop in a limited time, which may lead to serious consequences. Compared with ADRC, AFADRC can better adapt to the runway changes. Figure 9d shows that AESO can still realize parameter adaption in the mixed runway case. The total perturbations can be accurately estimated: see Figure 9f. Under fault-perturbed conditions, AFADRC can still brake fast with high efficiency, which improves the environmental adaptability and reliability of AABS.

Conclusions
In this paper, a novel reconfiguration controller based on AFADRC is proposed to meet the higher performance requirements of AABS in fault-perturbed conditions. An AESO is designed to rapidly and adaptively estimate the states and disturbances of the plant, while an NLSEF incorporating fuzzy logic is developed to actively suppress perturbations and adapt to actuator faults. The proposed reconfiguration controller can perform brake anti-skid control well under faults, perturbations as well as runway changes. The simulation results verify that the proposed method can effectively improve the robustness and environmental adaptability of AABS, which in turn improves the safety and reliability of the whole aircraft. Since ADRC does not limit the specific mathematical form of uncertainty, it poses a great difficulty for the theoretical analysis, which becomes more complicated if a nonlinear mechanism is used. Therefore, the stability of the closed-loop system is difficult to prove. It would be the focus of future work.

Conclusions
In this paper, a novel reconfiguration controller based on AFADRC is proposed to meet the higher performance requirements of AABS in fault-perturbed conditions. An AESO is designed to rapidly and adaptively estimate the states and disturbances of the plant, while an NLSEF incorporating fuzzy logic is developed to actively suppress perturbations and adapt to actuator faults. The proposed reconfiguration controller can perform brake anti-skid control well under faults, perturbations as well as runway changes. The simulation results verify that the proposed method can effectively improve the robustness and environmental adaptability of AABS, which in turn improves the safety and reliability of the whole aircraft. Since ADRC does not limit the specific mathematical form of uncertainty, it poses a great difficulty for the theoretical analysis, which becomes more complicated if a nonlinear mechanism is used. Therefore, the stability of the closed-loop system is difficult to prove. It would be the focus of future work.

Conflicts of Interest:
The authors declare no conflict of interest.