Civil aircraft anti-skid brake control method

Abstract

A method for controlling anti-skid braking in civil aircraft involves constructing an anti-skid braking model and flight dynamics and kinematics models of the aircraft to analyze the forces acting on the aircraft system and obtain the corresponding forces and torques. For the anti-skid braking system, a BSMC controller is designed to control the braking coefficient μ. Brake This invention controls the braking force to ultimately control the anti-skid braking system of civil aircraft. It uses a backstepping slip mode controller (BSMC) to control the aircraft's braking commands, ensuring the system maintains the optimal slip ratio during braking, maximizing braking efficiency, reducing wheel wear, and minimizing the cost of the aircraft's braking system.

Description

Technical Field

[0001] This invention relates to a technology in the field of flight control, specifically a method for anti-skid braking control of civil aircraft. Background Technology

[0002] Under various loads, complex weather conditions, or extreme operating conditions, the dynamics and kinematics of civil aircraft during ground taxiing become quite complex. To ensure the safety of aircraft taxiing on the ground during landing or takeoff, anti-skid braking systems are crucial. Relying solely on pilot experience or intermittent braking during deceleration can easily lead to excessive braking force, wheel lock-up, and tire wear and blowout. Therefore, an anti-skid braking control system is needed to prevent excessive braking force that could cause wheel slippage.

[0003] The slip ratio (σ) refers to the proportion of the aircraft's wheel-carrying motion to its total motion, and is a crucial indicator affecting braking efficiency. In anti-skid braking systems for civil aircraft, controlling the slip ratio near the optimal slip ratio ensures good braking performance. Commonly used anti-skid braking control algorithms include PID control and neural networks. PID control is easy to implement but has relatively low accuracy, while neural network methods require a large number of training samples, which is difficult to obtain and thus impractical in engineering. Summary of the Invention

[0004] To address the aforementioned shortcomings of existing technologies, this invention proposes a civil aircraft anti-skid braking control method. Specifically for the anti-skid braking system of civil aircraft, a backstepping sliding mode controller (BSMC) is employed to design the controller. By combining sliding mode control with backstepping techniques for anti-skid braking control, the system's tracking response speed is significantly improved, and the adjustment time is shortened, exhibiting excellent robustness.

[0005] This invention is achieved through the following technical solution:

[0006] This invention relates to a method for anti-skid braking control of civil aircraft. By constructing an anti-skid braking model and a flight dynamics and kinematics model of the aircraft, the force conditions of the aircraft system are analyzed to obtain the corresponding forces and torques. For the anti-skid braking system, a BSMC controller is designed to control the braking coefficient μ. Brake This is used to control the braking force, ultimately achieving control of the anti-skid braking system for civil aircraft.

[0007] The control method specifically includes:

[0008] Step 1) Construct an aircraft anti-skid braking model

[0009] in: This is the component of the frictional force of the nose landing gear in the x-direction. The friction of the main landing gear, X B For braking force; The first derivative of the braking force. For maximum braking force, τ B μ is the time constant of the braking module. Brake ω is the braking coefficient; ω is the rolling angular velocity of the aircraft wheels, J m Z is the moment of inertia of the aircraft wheels. Mt The supporting force of the main landing gear, r e The radius of the aircraft wheels is μ; μ is the coefficient of ground friction. Max A1 and A2 are constant coefficients in the wheel-tire model, where A1 is the maximum friction coefficient on the ground and A2 are constant coefficients. σ is the slip ratio of the system. V t This refers to the speed of the aircraft.

[0010] This invention addresses the slip ratio σ in anti-skid braking systems. Generally, when an aircraft's anti-skid system is in an optimal slip ratio state, the aircraft's braking efficiency is highest, brake pad wear is reduced, and wheel slippage during braking is prevented, thus enhancing aircraft safety during landing.

[0011] This invention changes the braking coefficient μ using a backstepping sliding mode control method. Brake To control the slip ratio of the entire aircraft system and ensure that the entire aircraft system is at the optimal slip ratio, so as to maximize the braking efficiency of the system.

[0012] Step 2) Construct the dynamics and kinematics model of the aircraft, specifically including:

[0013] Aircraft dynamics model:

[0014] Where: X, Y, and Z are the resultant external forces in the x, y, and z directions, respectively. φ, θ, and ψ are Euler angles, representing roll, pitch, and yaw angles, respectively. u, v, and w are the linear velocities in the x, y, and z directions in the body coordinate system. m is the mass of the entire aircraft system, and g is the local gravitational acceleration.

[0015] The dynamic model of angular motion is:

[0016] Where L, M, and N represent the rolling moment, pitching moment, and yaw moment, respectively. Since the aircraft is taxiing on the ground, it does not experience rolling motion along the x-direction; therefore, the rolling moment L = 0. xx I yy I zzand I zx Let be the moments of inertia along each axis. p, q, and r represent the angular velocities, respectively.

[0017] The kinematic equations for angular motion are:

[0018] The equations of motion for the aircraft are:

[0019] Step 3) Based on the model established in Step 2, analyze the force situation of the aircraft's ground system to obtain the corresponding net external force and net external moment, specifically: the aircraft is subjected to the supporting force Z, horizontal force X, lateral force Y, and aerodynamic force F. aero And the corresponding torque in the vertical direction, the torque generated by the force in the horizontal direction, the torque generated by the lateral force of the aircraft, and the torque N generated by the aerodynamic force. Aer .

[0020] The supporting force Z on the aircraft is Z = Z N +Z Mt , where: Z N For the support force of the aircraft's nose landing gear, Z Mt The supporting force of the main landing gear, Z Mt =2·Z N And Z N This refers to the support force of a single main landing gear of an aircraft.

[0021] The torque M corresponding in the vertical direction Ver =Z N ·l N -Z Mt ·l M , where: l N It is the longitudinal distance from the center of gravity of the nose landing gear to the center of gravity of the entire aircraft. M The longitudinal distance from the main landing gear to the center of gravity of the entire aircraft system.

[0022] The horizontal force on the aircraft in: This is the component of the frictional force of the nose landing gear in the x-direction. The friction of the main landing gear, X B For braking force, X P For aircraft engine thrust, This is the component of the lateral force of the front landing gear in the x-direction.

[0023] The torque generated by the force in the horizontal direction includes: Where: z is the height of the aircraft's center of gravity above the ground, μ is the coefficient of ground friction, and δ N This refers to the angle of deflection of the front landing gear.

[0024] The lateral force experienced by the aircraft in: and The sideslip friction of the nose landing gear in the x and y axis directions. This refers to the sideslip friction of the aircraft's main landing gear.

[0025] The torque generated by the lateral force of the aircraft includes:

[0026] The aerodynamic forces acting on the aircraft Where: Y r It is the lateral force caused by the yaw rate. For the aerodynamic force generated by rudder deflection, Y β The lateral force generated during the aircraft's sideslip. These are the corresponding aerodynamic derivatives. r is the yaw rate, and δ is the aerodynamic derivative. r β is the rudder deflection angle of the aircraft, and β is the sideslip angle of the aircraft. Where S is the dynamic pressure and S is the aircraft area.

[0027] The torque generated by the aforementioned aerodynamic force in: is the corresponding aerodynamic moment coefficient. b is the wing span.

[0028] The resultant external force includes: The corresponding net external torque includes

[0029] Technical effect

[0030] This invention addresses the problem of pilots relying solely on their experience to operate the braking system, which can easily lead to excessive braking force, wheel lock-up, and ultimately, tire blowout. By employing a backstepping sliding mode (BSMC) method to control the anti-skid braking system, the safety factor of the aircraft during ground deceleration is improved. Even in the presence of external interference such as noise, the designed method exhibits good robustness to the aircraft braking system, enhancing its reliability and safety. Attached Figure Description

[0031] Figure 1 This is a flowchart of the present invention;

[0032] Figure 2 A schematic diagram of the vertical support force of an aircraft landing gear;

[0033] Figure 3 A schematic diagram of the horizontal forces acting on the aircraft;

[0034] Figure 4 This is a schematic diagram of the lateral forces acting on an aircraft landing gear.

[0035] Figure 5 For the aircraft speed tracking response in scenario A;

[0036] Figure 6 For the slip rate tracking response of the aircraft anti-skid braking system in scenario A;

[0037] Figure 7 This refers to the speed response of the aircraft in scenario B during high-speed taxiing.

[0038] Figure 8 The braking efficiency of the aircraft braking system in scenario B;

[0039] Figure 9 The slip rate response of the anti-skid braking system in scenario B, where the aircraft is taxiing at high speed.

[0040] Figure 10 The response of the aircraft anti-skid braking system to the slip rate and the noisy slip rate in scenario C;

[0041] Figure 11 The simulation results show the comparison between the backstepping sliding mode controller and the PID controller in the aircraft anti-skid braking system of scenario C. Detailed Implementation

[0042] like Figure 1 As shown, this embodiment relates to a method for controlling anti-skid braking of a civil aircraft, specifically including:

[0043] Step 1) Construct a model of the aircraft's anti-skid braking system.

[0044] in: This is the component of the frictional force of the nose landing gear in the x-direction. The friction of the main landing gear, X B For braking force; The first derivative of the braking force. For maximum braking force, τ B μ is the time constant of the braking module. Brake ω is the braking coefficient; ω is the rolling angular velocity of the aircraft wheels, J m Z is the moment of inertia of the aircraft wheels. Mt The supporting force of the main landing gear, r e The radius of the aircraft wheels is μ; μ is the coefficient of ground friction. Max A1 and A2 are constant coefficients in the wheel-tire model, where A1 is the maximum friction coefficient on the ground and A2 are constant coefficients. σ is the slip ratio of the system. V t This refers to the speed of the aircraft.

[0045] Step 2) Construct a six-degree-of-freedom dynamics and kinematics model for a civil aircraft, specifically including:

[0046] Dynamic model of linear motion Where: X, Y, and Z are the resultant external forces in the x, y, and z directions, respectively. φ, θ, and ψ are Euler angles, representing roll, pitch, and yaw angles, respectively. u, v, and w are the linear velocities in the x, y, and z directions in the body coordinate system. m is the mass of the entire aircraft system, and g is the local gravitational acceleration.

[0047] Dynamic model of angular motion Where L, M, and N represent the roll moment, pitch moment, and yaw moment, respectively. Since the aircraft is taxiing on the ground, the roll moment L = 0. xx I yy I zz and I zx Let be the moment of inertia along each axis. p, q, and r represent the roll rate, pitch rate, and yaw rate, respectively.

[0048] The kinematic equations for angular motion are:

[0049] The equations of motion for the aircraft are:

[0050] Step 3) Based on the model established in Steps 1) and 2), perform a force analysis on the civil aircraft ground system to calculate the forces and moments in the model. Specifically, the aircraft is subjected to the following forces: support force Z, horizontal force X, lateral force Y, and aerodynamic force F. aero And the torque corresponding to the vertical direction, the torque generated by the horizontal direction, the torque generated by the lateral force of the aircraft, and the torque generated by the aerodynamic force.

[0051] like Figure 2 As shown, the supporting force Z on the aircraft is Z = Z N +Z Mt , where: Z N For the support force of the aircraft's nose landing gear, Z Mt The supporting force of the main landing gear, Z Mt =2·Z N And Z N This refers to the support force of a single main landing gear of an aircraft.

[0052] The torque M corresponding in the vertical direction Ver =Z N ·l N -Z Mt ·l M , where: l N It is the longitudinal distance from the center of gravity of the nose landing gear to the center of gravity of the entire aircraft. M The longitudinal distance from the main landing gear to the center of gravity of the entire aircraft system.

[0053] like Figure 3 As shown, the horizontal force acting on the aircraft in: This is the component of the frictional force of the nose landing gear in the x-direction. The friction of the main landing gear, X B For braking force, X P For aircraft engine thrust, This is the component of the lateral force of the front landing gear in the x-direction.

[0054] The torque generated by the force in the horizontal direction includes: Where: z is the height of the aircraft's center of gravity above the ground, δ N Let μ be the front wheel deflection angle, and μ be the coefficient of ground friction: μ = μ Max ·sin(A1·arctan(A2·σ)), where: μ Max σ is the maximum friction coefficient on the ground, A1 and A2 are constants in the tire model, and σ is the slip ratio of the system.

[0055] like Figure 4 As shown, the lateral force acting on the aircraft in: and The sideslip friction of the nose landing gear in the x and y axis directions. This refers to the sideslip friction of the aircraft's main landing gear.

[0056] The torque generated by the lateral force of the aircraft includes:

[0057] The aerodynamic forces acting on the aircraft Where: Y r It is the lateral force caused by the yaw rate. For the aerodynamic force generated by rudder deflection, Y β The lateral force generated during the aircraft's sideslip. These are the corresponding aerodynamic derivatives. r is the yaw rate, and δ is the aerodynamic derivative. r β is the rudder deflection angle of the aircraft, and β is the sideslip angle of the aircraft. Where S is the dynamic pressure and S is the aircraft area.

[0058] The torque generated by the aforementioned aerodynamic force in: is the corresponding aerodynamic moment coefficient. b is the wing span.

[0059] The resultant external force includes: The corresponding net external torque includes

[0060] Step 4) Based on the model obtained in Step 3), the civil aircraft anti-skid system model can be rewritten as follows: Where: system state x1=σ, is the derivative of the slip ratio; u is the braking coefficient of the anti-skid braking system, which controls the braking force through control commands to brake the aircraft wheels; in the system

[0061] The aforementioned civil aircraft anti-skid braking control method, wherein the control input of the designed civil aircraft anti-skid braking system is: Where: ε, c1, λ1 are constants, and ε > 0, c1 > 0, λ1 > 0; z1 is the slip ratio error of the aircraft anti-skid braking system. The first derivative of the slip ratio error. For the desired slip ratio z d The second derivative, sliding surface: s = λ1z1 + z2, virtual control input For the desired slip ratio z d The first derivative.

[0062] This embodiment simulates scenario A, a low-speed taxiing run without interference. Specifically, under ideal, undisturbed conditions, the aircraft decelerates and taxis in a straight line at a low speed on the ground. This includes:

[0063] Initialization: The initial velocity of the aircraft is V. t0 =30m / s, initial yaw angle is ψ0=0°, aircraft wheel rolling angular velocity is ω0=75rad / s, wheel radius r e =0.4m, then the initial rolling linear velocity of the wheel is

[0064] For aircraft anti-skid braking systems, μ brake This is the control input for the anti-skid braking system. The optimal slip ratio for the aircraft anti-skid braking system in this invention is 0.117, at which point the braking effect is best.

[0065] The design parameters of the BSMC controller are: [c1, λ1, ε] = [1619, 58, 15].

[0066] like Figure 5 As shown, the aircraft is on the ground with an initial velocity of V. t0 =30m / s for deceleration and gliding motion.

[0067] like Figure 6As shown. Under the action of the backstepping sliding mode controller, the system response fluctuates somewhat in the early stage. After stabilization, the aircraft's slip ratio stabilizes at around 0.117, and the steady-state error of slip ratio tracking is 0. Its overshoot is 12.48%, and the root mean square error (RMSE) of the slip ratio is RMSE. σ =0.0169, indicating that the controller has good control effect.

[0068] This embodiment simulates scenario B, a high-speed taxiing operation without interference. Specifically, under ideal, interference-free conditions, the aircraft performs high-speed, variable-speed taxiing motions on the ground, including:

[0069] Initialization: The initial velocity of the aircraft is V. t0 =100m / s. The initial yaw angle ψ0 = 0°, and the aircraft maintains this initial angle at 0 degrees throughout its variable-speed linear motion. The initial roll velocity of the wheels is ω0 = 250rad / s, and the linear velocity of the wheels is...

[0070] like Figure 7 As shown, the aircraft performs variable-speed linear taxiing motion within a speed range of 95–105 m / s.

[0071] The design parameters of the BSMC controller are: [c1, λ1, ε] = [250, 180, 1.3].

[0072] like Figure 8 As shown, the braking efficiency of the aircraft anti-skid braking system is close to 100% under the control of the backstepping sliding mode algorithm proposed in this invention.

[0073] like Figure 9 The simulation results show a comparison between the BSMC controller and the PID controller in an aircraft anti-skid braking system. The settling time of the backstepping sliding mode controller is 1.4677 s, while that of the PID controller is 8.8045 s. The overshoot of the backstepping sliding mode controller is only 0.6865%, while that of the PID controller is 38.4904%. The data comparison also shows that the control algorithm proposed in this invention has a better control effect on the anti-skid braking system.

[0074] This embodiment simulates a high-speed taxiing scenario (Scenario C) with interference. In actual aircraft runway operations, the smoothness and slip resistance of the runway are inconsistent, leading to noise interference. Therefore, in this simulation scenario, under interference, the aircraft performs high-speed linear acceleration-variable taxiing motion on the ground, specifically including:

[0075] Initialization: The initial velocity of the aircraft is V. t0=100m / s. The initial yaw angle ψ0 = 0°, and the aircraft maintains this initial angle at 0 degrees throughout its variable-speed linear motion. The initial roll velocity of the wheels is ω0 = 250rad / s, and the linear velocity of the wheels is...

[0076] like Figure 10 The figure shows the slip ratio response of the anti-skid braking system of a civil aircraft after being disturbed. The design parameters of the BSMC controller are: [c1, λ1, ε] = [374, 41.5, 0.02].

[0077] like Figure 11 The figure shows the simulation results of the system response under the backstepping sliding mode controller and the PID controller after disturbance. The settling time of the backstepping sliding mode controller is 1.2243s, while that of the PID controller is 4.4869s. The overshoot of the backstepping sliding mode controller is only 1.4182%, while that of the PID controller is 42.0771%. The data comparison results show that the controller designed in this invention has better control performance.

[0078] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. A method of anti-skid braking control for a civil aircraft, characterized in that, By constructing the civil aircraft anti-skid brake model and the aircraft flight dynamics and kinematics model, the force on the aircraft system is analyzed to obtain the corresponding force and torque; for the anti-skid brake system, the BSMC controller is constructed to control the brake coefficient and the brake force, so as to ultimately realize the control of the civil aircraft anti-skid brake system. The aircraft anti-skid brake model comprises: wherein: is a component of the friction force in the x direction for the front landing gear, is a friction force for the main landing gear, is a brake force, is an aircraft engine thrust; is a first derivative of the brake force, is a maximum brake force, is a time constant of the brake module, is a brake coefficient; is a roll angular velocity of the aircraft wheel, is a moment of inertia of the aircraft wheel, is a support force of the main landing gear, is a radius of the aircraft wheel; is a ground friction coefficient, is a maximum ground friction coefficient, and is a constant coefficient in the wheel tire model, is a slip ratio of the system , is a speed of the aircraft.

2. The method of claim 1, wherein, The aircraft flight dynamics and kinematics model comprises: Aircraft dynamics model: ,in: They are respectively The resultant external force in three directions; These are Euler angles, specifically roll and pitch angles; In body coordinate system Linear velocity in three directions; Let g be the mass of the entire aircraft system, and g be the local gravitational acceleration. The dynamic model of angular motion is: wherein: L, M, N are respectively the roll moment, the pitch moment and the yaw moment; since the aircraft is taxiing on the ground, the roll moment L = 0; and are respectively the moment of inertia of each axis; respectively represent the angular velocity; The kinematic equation for the angular motion is: ; The position kinematic equation of the aircraft is: wherein: is the yaw angle.

3. The method of claim 2, wherein, The force conditions of the aircraft system include: support force , horizontal force , lateral force , aerodynamic force ; The corresponding moment includes: a corresponding moment in a vertical direction , a moment generated by a horizontal force, a moment generated by a lateral force of the aircraft, and a moment generated by the aerodynamic force .

4. The method of claim 3, wherein, The support force received by the aircraft wherein: respectively the support force of the front landing gear of the aircraft; The moment of force corresponding in the vertical direction wherein: is the longitudinal distance from the front landing gear center of mass to the overall aircraft center of mass, is the longitudinal distance from the main landing gear to the overall aircraft system center of mass; the horizontal force received by the aircraft , is the component of the friction force in the x direction for the nose landing gear, is the friction force for the main landing gear, is the brake force, is the aircraft engine thrust, is the component of the side slip force in the x direction for the nose landing gear; The moment of the force in the horizontal direction includes: wherein: is the height of the center of gravity of the aircraft from the ground, is the angle of deflection of the nose landing gear; The lateral force to which the aircraft is subjected wherein: and is the side slip friction in the direction of the axis of the nose landing gear, is the side slip friction in the direction of the axis of the nose landing gear, is the side slip friction of the main landing gear of the aircraft; The moment of the lateral force generated by the aircraft includes: ; The aerodynamic forces on the aircraft wherein: is the lateral force due to yaw rate, is the aerodynamic force due to rudder deflection, is the lateral force due to sideslip of the aircraft; the moment generated by the aerodynamic force wherein: is the corresponding aerodynamic moment coefficient; is the yaw rate, is the rudder deflection angle of the aircraft rudder, is the sideslip angle of the aircraft, is the dynamic pressure, is the aircraft area, is the wingspan; The resultant force on the aircraft includes: The corresponding resultant moment includes .

5. The method of claim 1, wherein, The BSMC controller is specifically: wherein: system state , is the derivative of slip ratio; is the brake coefficient of the civil aircraft anti-skid brake system: , , the brake coefficient of the civil aircraft anti-skid brake system: wherein: is a constant, and , , is the slip ratio error of the aircraft anti-skid brake system, is the first-order derivative of the slip ratio error, is the second-order derivative of the desired slip ratio slip surface: , virtual control input , is the first-order derivative of the desired slip ratio .

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