Airplane anti-skid brake control method based on model prediction

Abstract

The invention provides an aircraft anti-skid brake control method based on model prediction, and belongs to the technical field of brake control, and the method comprises the steps: an aircraft enters a landing grounding state, and control parameters are initialized; key signals needed by braking control are collected in real time, the real-time slip rate, the instantaneous friction coefficient and the optimal slip rate are calculated, and the runway working condition is recognized; a prediction model is constructed, specifically, a hydraulic brake actuator model and a slip dynamics model are constructed, a multi-objective weighted optimization objective function is constructed, and a constraint set is set; adaptively selecting a control mode, dynamically adjusting and optimizing each target weight in the target function, converting into a standard quadratic programming problem, and solving to obtain an absolute pressure instruction; the absolute pressure instruction is updated to a hydraulic brake actuator model, and the real-time state parameters are updated to a slip dynamic model; and when the braking termination condition is met, the braking process is ended. According to the method, the robustness and the real-time performance of anti-skid brake control are improved.

Description

Technical Field

[0001] This application relates to the field of braking control technology, and in particular to an aircraft anti-skid braking control method based on model prediction. Background Technology

[0002] Aircraft require braking systems to decelerate and stop during takeoff and landing. Especially during the landing roll, aircraft speeds are high, and runway friction conditions can be highly uncertain, such as rain, snow, icing, or runway contamination. In such conditions, improper braking force distribution or severe tire slippage can not only increase braking distance but also cause excessive tire wear, tread abrasion, or even accidents. Therefore, achieving efficient and stable anti-skid braking control under complex conditions has always been a crucial research issue in the field of aircraft braking.

[0003] Most existing aircraft anti-skid braking systems employ proportional-integral control, fuzzy logic control, or threshold-based slip ratio control methods. While these methods can suppress tire slippage to some extent, they generally suffer from slow response lag and insufficient robustness. Furthermore, aircraft landing gear typically has a multi-wheel configuration, resulting in complex tire forces and placing higher demands on the robustness and real-time performance of braking control. Therefore, there is an urgent need for a control method suitable for aircraft that can maintain a stable slip ratio and shorten braking distance under multiple constraints. Summary of the Invention

[0004] In view of this, embodiments of this application provide a model prediction-based aircraft anti-skid braking control method, which at least partially solves the problems in the prior art such as poor stability of braking control under all operating conditions and the occurrence of excessively fast or slow pressure adjustment.

[0005] This application provides a model-predictive-based aircraft anti-skid braking control method, the method comprising: When the aircraft is determined to be in the landing touchdown state, the control parameters are initialized; Real-time acquisition of key signals required for braking control, and preprocessing of the acquired key signals; Based on the preprocessed key signals, the real-time slip ratio, instantaneous friction coefficient and optimal slip ratio are calculated, and the runway operating conditions are identified based on the instantaneous friction coefficient. Construct predictive models, including constructing a hydraulic brake actuator model and a sliding motion mechanics model; Based on the prediction model and the optimal slip ratio, a multi-objective weighted optimization objective function is constructed, and a set of constraints for the optimization objective function is set. Based on real-time slip ratio, instantaneous friction coefficient and runway conditions, the control mode is adaptively selected, and the weights of each objective in the objective function are dynamically adjusted and optimized according to the selected control mode. The optimized objective function and constraint set after weight adjustment are transformed into a standard quadratic programming problem, and optimized to obtain the absolute pressure command for controlling the execution of braking pressure. The absolute pressure command is updated to the hydraulic brake actuator model, and the real-time state parameters are updated to the sliding motion mechanics model to provide the initial state for the rolling optimization of the next cycle. When the braking termination condition is met, the braking process ends, the slip ratio-based active control exits, and the system switches to low-speed parking or ground coasting control, and data is recorded.

[0006] According to a specific implementation of an embodiment of this application, the key signals include wheel speed, wheel brake pressure, hydraulic system oil temperature, aircraft ground speed, wheel load, and wheel turning angle.

[0007] According to a specific implementation of an embodiment of this application, the preprocessing of the acquired key signals includes: Based on a unified clock, time synchronization and interpolation resampling are performed on each key signal, and then normalization is performed. The rotational speed and wheel load of each turbine are filtered using a combination of band-limited low-pass filtering and median pulse removal. The components containing power frequency interference are superimposed with notch filters; First-order hysteresis correction and temperature compensation are introduced for the braking pressure of each wheel and the oil temperature of the hydraulic system.

[0008] According to a specific implementation of an embodiment of this application, the calculation of real-time slip ratio, instantaneous friction coefficient, and optimal slip ratio, and the identification of runway operating conditions based on the instantaneous friction coefficient, includes: Calculate the real-time slip ratio based on the aircraft's ground speed and wheel speed; Calculate the instantaneous friction coefficient based on the current wheel brake pressure and wheel load; Based on historical data pairs of slip ratio and friction coefficient, a dynamic adaptive sliding window combined with the least squares method is used to fit and calculate the parameters of the Burckhardt model, thereby obtaining the Burckhardt model expression. The dynamic adaptive sliding window adaptively adjusts the sampling period according to the drastic change in friction coefficient and the variance of slip ratio fluctuation. The window slides successively with the sampling period. When the drastic change in friction coefficient is detected to be greater than the first preset threshold, the window is immediately reset, historical data is cleared, and new data with the minimum window length is re-collected to ensure that the fitting parameters quickly adapt to the new working conditions. Based on the Burckhardt model expression, the optimal slip ratio and its corresponding peak friction coefficient are calculated. Based on the instantaneous friction coefficient, calculate whether the difference between the average friction coefficients of the left and right wheels or the front and rear wheels in the runway area is greater than or equal to the second preset threshold. If so, determine that the current runway condition is the μ-split condition.

[0009] According to a specific implementation of an embodiment of this application, the expression for the hydraulic brake actuator model is: u i (k+1)=(1-T s / τ)·u i (k)+(T s / τ)·y i (kd)+w i (k), Among them, u i (k) represents the braking pressure at time k, u i (k+1) represents the braking pressure at time k+1, T s The sampling period is τ, the actuator time constant is y i (kd) is the output of the hydraulic brake controller command at time kd, where d is the lag step number, and w i (k) represents the random disturbance term.

[0010] According to a specific implementation of an embodiment of this application, the construction of the sliding motion mechanics model includes: Based on the discretization of the angular momentum balance equation, the wheel speed prediction formula is obtained: ω i (k+1)=ω i (k)+(T s / I)·(μ i (k)Fz i (k)r-Ku i (k)r), Where, ω i (k) represents the rotational speed of the turbine wheel at time k, ω i (k+1) represents the wheel speed at time k+1, I represents the tire moment of inertia, and μ i (k) is the friction coefficient at time k, Fz i (k) represents the wheel load at time k, r is the effective rolling radius of the tire, and μ i (k)Fz i (k)r represents the ground friction torque, K is the pressure-force conversion coefficient of the braking system, and Ku i (k)r represents the braking torque, T s / I represents the first time coefficient after discretization; Based on the discretization of the longitudinal force balance equation, the ground speed prediction formula is obtained: v(k+1)=v(k)-(T s / m)·∑ i μ i (k)Fz i (k), Where v(k) is the aircraft ground speed at time k, v(k+1) is the aircraft ground speed at time k+1, m is the aircraft mass, and ∑ i μ i (k)Fz i (k) represents the resultant force of all wheels' ground friction, T s / m is the second time coefficient after discretization; Based on the wheel speed prediction formula and the ground speed prediction formula, the sliding motion mechanical model is obtained. The expression of the sliding motion mechanical model is: λ i (k+1)=[v(k+1)-ω i (k+1)r] / max(v(k+1),ε), Where, λ i (k+1) represents the slip ratio at time k+1, and ε is the minimum value.

[0011] According to a specific implementation of an embodiment of this application, the expression of the multi-objective weighted optimization objective function is as follows: J=∑_{i=1}^{N p}[w_λ·(λ i (k+i|k)-λ * (k)) 2 +w a ·(ä_d es -ä act (k+i|k)) 2 +w_Δu·(Δu i (k+i|k)) 2 ], Where J is the objective function, N p For prediction in the time domain, λ i (k+i|k) represents the predicted slip ratio for the i-th prediction step, and w_λ is the slip ratio tracking weight. * (k) represents the optimal slip ratio, ä_d es To decelerate the target, ä act (k+i|k) represents the actual predicted deceleration value for the i-th prediction step, w a For deceleration tracking weights, Δu i (k+i|k) represents the brake pressure increment command for the i-th prediction step, and w_Δu is the weight of the control command change rate. The constraint set includes actuator constraints, overall machine stability constraints, and safety protection constraints. Actuator constraints include brake pressure increment Δu iMeets the acceleration / deceleration rate limit, Δu i ∈[-u down T s ,u up T s ], u up For the maximum boost rate, u down This is the maximum pressure relief rate; Overall machine stability constraints include ensuring the symmetry of the brake pressure difference between the left and right wheels. left -u right |≤Δu sYm u left For the left wheel brake pressure, u right The right wheel brake pressure, Δu sYm The threshold is set to be symmetry-based. Safety protection constraint: when the slip ratio λ i >λ hi At that time, the forced braking pressure increment Δu i ≤0,λ hi This is the high slip ratio threshold.

[0012] According to a specific implementation of an embodiment of this application, the control mode includes torque tracking mode, anti-slip priority mode, and hybrid mode. The method adaptively selects the control mode based on real-time slip ratio, instantaneous friction coefficient, and runway conditions, and dynamically adjusts and optimizes the weights of each objective in the objective function according to the selected control mode, including: When the instantaneous friction coefficient μ i (k)≥μ and the real-time slip ratio is within the normal range λ low <λ i (k)<λ hi When μ is the threshold value of the friction coefficient, λ low To achieve a low slip threshold, torque tracking mode is selected, and the weights of each objective in the optimization objective function are adjusted as follows: w a =0.8, w_λ=0.3, w_Δu=0.1; When the real-time slip ratio λ i (k)>λ hi Or wheel speed ω i ≤ω th When, ω th Given the wheel speed threshold, the anti-slip priority mode is selected, and the weights of each objective in the objective function are adjusted as follows: w a =0.1, w_λ=0.9, w_Δu=0.1; When the runway operating condition is μ-split, a hybrid mode is selected. This hybrid mode includes: when the instantaneous friction coefficient μ... i (k)≥μ av9 At that time, the weights of each objective in the objective function are adjusted as follows: wa =0.8, w_λ=0.3, w_Δu=0.1; when the instantaneous friction coefficient μ i (k)<μ av9 At that time, the weights of each objective in the objective function are adjusted as follows: w a =0.1, w_λ=0.9, w_Δu=0.1, μ av9 The average coefficient of friction for the left and right wheels; When switching control modes, the current control mode must be held for a preset time, and the slip ratio must exceed the hysteresis threshold.

[0013] According to a specific implementation of an embodiment of this application, the step of transforming the weighted optimization objective function and constraint set into a standard quadratic programming problem, and then optimizing and solving it to obtain the absolute pressure command for controlling brake pressure execution, includes: The weighted objective function and constraint set are transformed into a standard quadratic programming problem. The interior point method is used to optimize and solve the standard quadratic programming problem to obtain the pressure increment command for each turbine. The pressure increment command of each wheel is converted into an absolute pressure command to control the brake pressure, and the absolute pressure command is ensured to comply with the actuator constraint by limiting the amplitude.

[0014] According to a specific implementation of an embodiment of this application, the method further includes: When an abnormal situation occurs during the optimization process, a safety degradation mode is immediately triggered, and the braking pressure is forcibly adjusted according to preset rules. The forced adjustment of the braking pressure according to preset rules includes: When it is λ i (k)>λ hi In overslip scenarios, a pressure relief strategy proportional to the degree of overslip is adopted, as shown in the formula: Δu i =-α·(λ i (k)-λ hi )·T s , Wherein, α is the pressure relief gain; When it is v(k) <v min In vulgar scenes, v min To achieve the minimum ground speed for the aircraft, low-speed safety pressure control is employed, using the following formula: u i (k)=min(u i (k-1)+β·T s ,u low ), Where β is the low-speed boost rate, u low This represents the maximum braking pressure at low speeds.

[0015] Beneficial effects: The model-predictive anti-skid braking control method in this application embodiment achieves precise control of the slip ratio under complex runway conditions by constructing a predictive model and a multi-objective weighted optimization objective function, effectively improving braking performance. This method can collect and process key signals required for braking control in real time, calculating the real-time slip ratio, instantaneous friction coefficient, and optimal slip ratio based on these signals, thereby accurately identifying runway conditions. By adaptively selecting the control mode and dynamically adjusting the weights of each objective in the optimization objective function, it ensures that the optimal braking pressure command can be obtained under different operating conditions. Furthermore, this method considers actuator dynamic constraints, overall aircraft stability constraints, and safety protection constraints, obtaining the absolute pressure command for controlling braking pressure execution through optimization, significantly improving the robustness and real-time performance of anti-skid braking control. When abnormal conditions occur during the optimization process, a safety degradation mode can be immediately triggered, forcibly adjusting the braking pressure according to preset rules, further enhancing system safety. Therefore, the model-predictive anti-skid braking control method in this application embodiment provides an efficient and stable solution for the field of aircraft braking. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a schematic flowchart of a model prediction-based aircraft anti-skid braking control method according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the control architecture of a model-predictive aircraft anti-skid braking control method according to an embodiment of the present invention. Figure 3 This is a control mode switching logic diagram according to an embodiment of the present invention. Detailed Implementation

[0018] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0019] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0021] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0022] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0023] The applicant's research found that currently, the most widely used anti-skid braking system in aircraft based on slip ratio employs a threshold-based proportional-integral (PI) control method. This type of method typically calculates the real-time slip ratio by measuring the difference between wheel speed and aircraft ground speed, and compares it to a set threshold. When the slip ratio exceeds the threshold, the controller adjusts the hydraulic braking pressure to reduce tire slippage. Its basic control flow includes: Real-time acquisition of signals such as wheel speed, aircraft speed, and hydraulic braking pressure; The tire slip ratio is obtained through calculation; When the slip ratio exceeds the set range, the proportional-integral controller outputs an adjustment signal to drive the electro-hydraulic valve to adjust the brake pressure. After the wheel slip rate returns to normal, gradually increase the braking force to ensure braking efficiency.

[0024] This design is simple in structure and easy to implement, and therefore it is widely used in current civil aircraft and some military aircraft.

[0025] Because the proportional-integral controller relies on feedback signals, its adjustment speed is affected by the dynamic hysteresis of the hydraulic actuator. When the runway friction coefficient changes abruptly (e.g., in rain, snow, or on icy surfaces), the tire slip ratio may rapidly exceed the control range, and the controller response lags, leading to an increase in braking distance. Secondly, this method fails to explicitly consider physical constraints such as the pressure build-up rate and maximum braking torque of the hydraulic brake. When the actuator approaches saturation, control oscillations are prone to occur, causing periodic fluctuations in brake pressure and affecting braking stability.

[0026] Furthermore, on runways where the friction coefficients of the left and right wheels are inconsistent, this method often relies solely on a global threshold, lacking a coordination mechanism to address the differences between the left and right wheels. This leads to uneven braking performance and may cause aircraft yaw. These shortcomings primarily stem from the fact that a single feedback adjustment method cannot predict future states and fails to integrate actuator dynamics with multi-wheel constraints into a unified model for optimization.

[0027] The applicant also found that some studies propose applying fuzzy logic control to aircraft anti-skid braking systems. This type of method, by introducing fuzzy rules, attempts to achieve better control performance under different friction coefficients. Its basic steps are as follows: Collect wheel speed, ground speed, and braking pressure signals; Dynamically estimate tire-track friction using fuzzy inference; Adjust the braking pressure regulation rate according to the estimated results to avoid prolonged slippage; When the slip ratio approaches the set target, gradually restore the braking pressure.

[0028] This method improves the control effect on low-friction road surfaces to some extent and enhances the adaptability of the controller.

[0029] The design of fuzzy rules and adaptive laws relies on experience or experimental calibration, lacks systematicity, and is difficult to guarantee stability and optimality under all operating conditions. This type of method still fails to uniformly consider the dynamic characteristics and constraints of the actuator, and in practical applications, the pressure adjustment may be too fast or too slow. When the aircraft landing gear contains multiple independent wheels, the method lacks a global coordination and optimization mechanism, making it difficult to achieve the optimal distribution of braking force across multiple wheels, thus affecting the overall braking performance.

[0030] Therefore, this application provides a model-predictive-based aircraft anti-skid braking control method to address the above-mentioned problems. This method mainly solves the following technical problems: 1) Precise control of slip ratio and improvement of braking performance under complex pavement conditions How to achieve precise control of aircraft slip ratio under different runway friction conditions such as dry and wet conditions, thereby effectively shortening the braking distance and comprehensively improving the safety margin of the braking process; 2) High real-time anti-slip control design under actuator dynamic constraints How to systematically incorporate the dynamic characteristics and physical constraints (such as pressure build-up rate, torque saturation, etc.) of hydraulic brake actuators into the controller design while meeting the real-time response requirements of the system, so as to suppress control oscillations and performance degradation caused by actuator saturation; 3) Coordinated optimization of multi-wheel braking and heading stability In a landing gear system with multiple independent braking structures, how can we achieve dynamic coordination and global optimization of the braking force of each tire to ensure the aircraft's runway balance and directional stability while braking efficiently?

[0031] To facilitate understanding of this invention, the abbreviations and key terms involved are defined as follows: Model Predictive Control (MPC) is a control method that uses a predictive model of the controlled object to perform rolling optimization to obtain a control sequence within a finite prediction time domain, and applies only the first control variable at each sampling time.

[0032] Prediction Time Domain: The discrete step count used in MPC for state and output prediction.

[0033] Objective function: The optimization objective is to sum the weighted values ​​of tracking error, control increment, and constraint violation in the prediction time domain.

[0034] Weight matrix: The weight coefficient matrix of each term in the cost function, used to balance tracking performance and control smoothness.

[0035] Constraints: Boundary restrictions on state / output / control variables and their rates of change, including hard constraints (which cannot be violated) and soft constraints (which allow minor violations at a penalty).

[0036] Quadratic programming: An optimization problem with a quadratic objective function and linear constraints, it is a commonly used solution form for implementing MPC.

[0037] Robustness: The ability of a controller to maintain stability and performance in the presence of model uncertainty, external disturbances, and measurement noise.

[0038] Optimal slip ratio: The slip ratio at which the longitudinal friction coefficient between the tire and the track reaches its peak.

[0039] Runway friction coefficient: The dimensionless friction coefficient between the tire and the runway, reflecting the level of available braking force.

[0040] Braking torque: The braking torque applied to the wheels.

[0041] Ground speed / Ground speed: The actual speed of the aircraft relative to the ground, used to calculate the slip ratio and braking performance.

[0042] In one embodiment, refer to Figure 1 To address the aforementioned technical problems, the model prediction-based aircraft anti-skid braking control method of the present invention is described in detail. This method specifically includes the following steps: When the aircraft is determined to be in the landing touchdown state, the control parameters are initialized; Real-time acquisition of key signals required for braking control, and preprocessing of the acquired key signals; Based on the preprocessed key signals, the real-time slip ratio, instantaneous friction coefficient and optimal slip ratio are calculated, and the runway operating conditions are identified based on the instantaneous friction coefficient. Construct predictive models, including constructing a hydraulic brake actuator model and a sliding motion mechanics model; Based on the prediction model and the optimal slip ratio, a multi-objective weighted optimization objective function is constructed, and a set of constraints for the optimization objective function is set. Based on real-time slip ratio, instantaneous friction coefficient and runway conditions, the control mode is adaptively selected, and the weights of each objective in the objective function are dynamically adjusted and optimized according to the selected control mode. The optimized objective function and constraint set after weight adjustment are transformed into a standard quadratic programming problem, and optimized to obtain the absolute pressure command for controlling the execution of braking pressure. The absolute pressure command is updated to the hydraulic brake actuator model, and the real-time state parameters are updated to the sliding motion mechanics model to provide the initial state for the rolling optimization of the next cycle. When the braking termination condition is met, the braking process ends, the slip ratio-based active control exits, and the system switches to low-speed parking or ground coasting control, and data is recorded.

[0043] In this embodiment, by establishing a discrete prediction model of tire-track contact and brake actuator dynamics, the braking command is optimized in the rolling time domain to keep the slip ratio in the optimal adhesion range, thereby achieving shorter skid distance, smaller pressure oscillation and better brake thermal management under various track conditions.

[0044] Specifically, the model-predictive anti-skid braking control method for aircraft in this embodiment has significant advantages over traditional anti-skid methods based on threshold proportional-integral (PI) control and fuzzy logic control methods. First, by introducing model predictive control, this method can achieve rolling optimization of the control sequence within a finite prediction time domain, thereby more accurately predicting future states and adjusting braking pressure in advance to effectively prevent tire slippage. Second, this method explicitly considers physical constraints such as the pressure build-up rate and maximum braking torque of the hydraulic brakes, as well as the coordination mechanism between multiple wheels, ensuring control stability even when the actuators are close to saturation, avoiding control oscillations and periodic fluctuations in braking pressure. Furthermore, in runway conditions where the friction coefficients of the left and right wheels are inconsistent, this method can adaptively adjust the braking pressure of each wheel to achieve optimal braking force distribution, effectively preventing aircraft yaw. Finally, this method has strong robustness, maintaining stability and performance even with model uncertainties, external disturbances, and measurement noise, ensuring safe braking of the aircraft under various complex operating conditions.

[0045] In one specific embodiment, refer to Figure 2 The control architecture of the present invention includes: 1) Sensing and estimation layer: Collects data from wheel speed sensors, ground speed signals, landing gear wheel load signals, brake pressure, tire temperature, etc. 2) Predictive control layer: Construct an integrated discrete predictive model of roller slip, actuator, and constraint; form a rolling time-domain optimizer; 3) Monitoring and switching layer: Identify which braking mode the aircraft is in (such as normal landing, aborted takeoff, etc.) and switch the corresponding control strategy. When the speed is low or the sensor fails, activate the backup control logic to prevent dangerous situations such as wheel lock-up. 4) Execution layer: Receives pressure or torque commands, drives hydraulic valves or motors to execute them precisely, and monitors the execution effect in a closed loop to ensure that the commands are accurately implemented.

[0046] Furthermore, the key signals include wheel speed, wheel brake pressure, hydraulic system oil temperature, aircraft ground speed, wheel load, and wheel turning angle.

[0047] In one embodiment, the preprocessing of the acquired key signals includes: Based on a unified clock, time synchronization and interpolation resampling are performed on each key signal, and then normalization is performed. The rotational speed and wheel load of each turbine are filtered using a combination of band-limited low-pass filtering and median pulse removal. The components containing power frequency interference are superimposed with notch filters; First-order hysteresis correction and temperature compensation are introduced for the braking pressure of each wheel and the oil temperature of the hydraulic system.

[0048] In this embodiment, data preprocessing effectively filters out noise and interference components from the original signal, improving data quality and providing a reliable basis for subsequent slip ratio calculation, operating condition identification, and control decisions. For example, time synchronization and interpolation resampling ensure that signals collected by different sensors are strictly aligned on the time axis, avoiding calculation errors caused by time deviations; normalization eliminates numerical differences between signals of different dimensions, facilitating unified analysis and processing. A combined band-limited low-pass and median pulse removal filtering method is used for the wheel speed and wheel load signals to effectively suppress high-frequency noise and pulse interference, retaining useful signal components; superimposed notch filtering is applied to components with power frequency interference to further eliminate interference signals at specific frequencies, improving signal purity; and first-order hysteresis correction and temperature compensation are introduced for the wheel brake pressure and hydraulic system oil temperature to compensate for the impact of sensor dynamic response characteristics and temperature changes on measurement results, ensuring the accuracy and stability of measurement data.

[0049] In one embodiment, the calculation of real-time slip ratio, instantaneous friction coefficient, and optimal slip ratio, and the identification of runway operating conditions based on the instantaneous friction coefficient, includes: Calculate the real-time slip ratio based on the aircraft's ground speed and wheel speed; Calculate the instantaneous friction coefficient based on the current wheel brake pressure and wheel load; Based on historical data pairs of slip ratio and friction coefficient, a dynamic adaptive sliding window combined with the least squares method is used to fit and calculate the parameters of the Burckhardt model, thereby obtaining the Burckhardt model expression. The dynamic adaptive sliding window adaptively adjusts the sampling period according to the drastic change in friction coefficient and the variance of slip ratio fluctuation. The window slides successively with the sampling period. When the drastic change in friction coefficient is detected to be greater than the first preset threshold, the window is immediately reset, historical data is cleared, and new data with the minimum window length is re-collected to ensure that the fitting parameters quickly adapt to the new working conditions. Based on the Burckhardt model expression, the optimal slip ratio and its corresponding peak friction coefficient are calculated. Based on the instantaneous friction coefficient, calculate whether the difference between the average friction coefficients of the left and right wheels or the front and rear wheels in the runway area is greater than or equal to the second preset threshold. If so, determine that the current runway condition is the μ-split condition.

[0050] In practice, the dynamically adaptive sliding window is adjusted according to different working conditions, including the following: Steady-state condition (Δμ_rate≤0.02 and σ_λ) 2 ≤0.001, Δμ_rate represents the degree of drastic change in the coefficient of friction, σ_λ 2For the slip variance: N_max = 80 sampling periods (N_max is the maximum window length, corresponding to 0.8s, sampling period Ts = 0.01s), the window contains 80 sets (λ) i (j),μ i When the data pairs are fitted with the parameters c1, c2, and c3 of the Burckhardt model using the least squares method, the sensor noise can be effectively smoothed, and the λ-μ curve fitting error can be ≤5%.

[0051] Moderately variable operating conditions (0.02 < Δμ_rate ≤ 0.05 or 0.001 < σ_λ) 2 ≤0.003): Using N_base=50 sampling periods (N_base is the basic window length, corresponding to 0.5s), a balance is achieved between fitting accuracy (error ≤8%) and real-time performance (parameter update delay 0.5s), which is suitable for the transition scenario of aircraft gradually moving from dry runway to wet runway.

[0052] Drastic operating conditions (Δμ_rate>0.05 or σ_λ) 2 >0.003): Using N_min=20 sampling periods (N_min is the minimum window length, corresponding to 0.2s), the window data update speed is improved by 60%, and it can capture sudden drops in the friction coefficient (such as from 0.8 to 0.3) within 0.2s. The fitting parameters c1, c2, and c3 are quickly adjusted to avoid the deviation of the optimal slip ratio calculation exceeding 0.05 (the deviation of traditional fixed window can reach 0.12).

[0053] The update mechanism for dynamically adaptive sliding windows includes: The method combines "sliding update + trigger reset": Under normal operating conditions, the window slides sequentially with the sampling period, removing the earliest data and adding the latest data; when Δμ_rate>0.08 (extreme operating condition change) is detected, the window is immediately reset, historical data is cleared and N_min new data are collected again to ensure that the fitting parameters quickly adapt to the new operating conditions.

[0054] In this embodiment, the Burckhardt model parameters are dynamically updated: the λ-μ curve is fitted in real time using the least squares method, solving the problem that traditional fixed models cannot adapt to varying runway conditions, improving the tracking accuracy of the optimal slip ratio, and enhancing braking efficiency. Experimental results show that real-time dynamic fitting of the λ-μ model is suitable for various runway conditions such as dry, wet, and icy conditions, reducing braking distance by 5%-18% and improving runway utilization. Furthermore, the identification of the μ-split condition provides an accurate basis for subsequent differentiated braking control. When there is a significant difference in the friction coefficients of the left and right wheels, timely identification of this condition allows the control method to adjust the braking pressure of each wheel accordingly, avoiding aircraft yaw caused by differences in friction coefficients and ensuring the aircraft's taxiing balance and directional stability. For example, when a μ-split condition is identified, the control method dynamically coordinates the braking force of each tire based on the different friction coefficients of the left and right wheels, making the braking force distribution more reasonable. While achieving efficient braking, it effectively prevents yaw caused by uneven braking force between the left and right wheels, greatly improving the safety and stability of aircraft braking under complex runway conditions.

[0055] In one embodiment, the expression for the hydraulic brake actuator model is: u i (k+1)=(1-T s / τ)·u i (k)+(T s / τ)·y i (kd)+w i (k), Among them, u i (k) represents the braking pressure at time k, u i (k+1) represents the braking pressure at time k+1, T s The sampling period is τ, the actuator time constant is y i (kd) is the output of the hydraulic brake controller command at time kd, where d is the lag step number, and w i (k) represents the random disturbance term.

[0056] Furthermore, the construction of the sliding motion mechanical model includes: Based on the discretization of the angular momentum balance equation, the wheel speed prediction formula is obtained: ω i (k+1)=ω i (k)+(T s / I)·(μ i (k)Fz i (k)r-Ku i (k)r), Where, ω i (k) represents the rotational speed of the turbine wheel at time k, ω i(k+1) represents the wheel speed at time k+1, I represents the tire moment of inertia, and μ i (k) is the friction coefficient at time k, Fz i (k) represents the wheel load at time k, r is the effective rolling radius of the tire, and μ i (k)Fz i (k)r represents the ground friction torque, K is the pressure-force conversion coefficient of the braking system, and Ku i (k)r represents the braking torque, T s / I represents the first time coefficient after discretization; Based on the discretization of the longitudinal force balance equation, the ground speed prediction formula is obtained: v(k+1)=v(k)-(T s / m)·∑ i μ i (k)Fz i (k), Where v(k) is the aircraft ground speed at time k, v(k+1) is the aircraft ground speed at time k+1, m is the aircraft mass, and ∑ i μ i (k)Fz i (k) represents the resultant force of all wheels' ground friction, T s / m is the second time coefficient after discretization; Based on the wheel speed prediction formula and the ground speed prediction formula, the sliding motion mechanical model is obtained. The expression of the sliding motion mechanical model is: λ i (k+1)=[v(k+1)-ω i (k+1)r] / max(v(k+1),ε), Where, λ i (k+1) represents the slip ratio at time k+1, and ε is the minimum value.

[0057] In this embodiment, a discrete prediction model was constructed. This model organically combines the tire-track contact characteristics with the dynamic characteristics of the brake actuator. Through discretized mathematical expressions, it accurately describes the dynamic changes of key state variables such as brake pressure, wheel speed, ground speed, and slip ratio at each sampling moment. Specifically, the hydraulic brake actuator model fully considers factors such as actuator time constant, control command lag, and random disturbances, accurately simulating the dynamic response process of brake pressure. The slip dynamics model, based on the angular momentum balance and longitudinal force balance equations, obtains prediction formulas for wheel speed and ground speed through discretization, and further derives the calculation expression for slip ratio, providing a reliable prediction basis for subsequent rolling time-domain optimization. This method of constructing a discrete prediction model not only improves the model's adaptability to complex working conditions but also lays a solid foundation for the design and implementation of optimized control strategies.

[0058] In one embodiment, the expression for the multi-objective weighted optimization objective function is: J=∑_{i=1}^{N p}[w_λ·(λ i (k+i|k)-λ * (k)) 2 +w a ·(ä_d es -ä act (k+i|k)) 2 +w_Δu·(Δu i (k+i|k)) 2 ], Where J is the objective function, N p For prediction in the time domain, λ i (k+i|k) represents the predicted slip ratio for the i-th prediction step, and w_λ is the slip ratio tracking weight. * (k) represents the optimal slip ratio, ä_d es To decelerate the target, ä act (k+i|k) represents the actual predicted deceleration value for the i-th prediction step, w a For deceleration tracking weights, Δu i (k+i|k) represents the brake pressure increment command for the i-th prediction step, and w_Δu is the weight of the control command change rate. The constraint set includes actuator constraints, overall machine stability constraints, and safety protection constraints. Actuator constraints include brake pressure increment Δu i Meets the acceleration / deceleration rate limit, Δu i ∈[-u down T s ,u up T s ], u up For the maximum boost rate, u down This is the maximum pressure relief rate; Overall machine stability constraints include ensuring the symmetry of the brake pressure difference between the left and right wheels. left -u right |≤Δu sYm u left For the left wheel brake pressure, u right The right wheel brake pressure, Δu sYm The threshold is set to be symmetry-based. Safety protection constraint: when the slip ratio λ i >λ hi At that time, the forced braking pressure increment Δu i ≤0,λ hi This is the high slip ratio threshold.

[0059] In this embodiment, a multi-objective weighted optimization objective function and its constraint set are constructed. This optimization objective function comprehensively considers multiple objectives such as slip ratio tracking, deceleration tracking, and control command change rate, and balances the importance of each objective by setting different weight coefficients w_λ, wa, and w_Δu. Specifically, the slip ratio tracking objective aims to make the predicted slip ratio within the prediction step as close as possible to the optimal slip ratio, ensuring that the aircraft remains in the optimal adhesion range during braking and improving braking efficiency. The deceleration tracking objective focuses on the deviation between the actual deceleration and the target deceleration, optimizing control to enable the aircraft to brake at a predetermined deceleration for a smooth stop. The control command change rate objective limits the amplitude of changes in the brake pressure increment command, avoiding actuator pressure oscillations caused by drastic changes in control commands and improving control stability.

[0060] Meanwhile, the constraint set further ensures the safety and rationality of the control process. Actuator constraints consider the rate of increase and decrease of brake pressure increments, ensuring that the hydraulic brakes operate within their physical limits and preventing damage to the actuators due to excessively rapid pressure changes. Overall aircraft stability constraints limit the brake pressure difference between the left and right wheels, ensuring the aircraft's symmetry during braking and preventing yaw caused by uneven braking forces, thus improving directional stability. Safety protection constraints force the brake pressure increment to zero or negative values ​​under high slip ratio conditions, promptly reducing brake pressure and preventing tire lock-up, ensuring braking safety under various complex conditions. This control strategy, combining multi-objective weighted optimization with constraint sets, can achieve multi-objective optimization of aircraft anti-skid braking control while meeting various physical limitations and safety requirements, effectively improving the aircraft's braking performance and safety.

[0061] In one embodiment, refer to Figure 3 The control modes include torque tracking mode, anti-slip priority mode, and hybrid mode. The method adaptively selects the control mode based on real-time slip ratio, instantaneous friction coefficient, and runway conditions, and dynamically adjusts and optimizes the weights of each objective in the objective function according to the selected control mode, including: When the instantaneous friction coefficient μ i (k)≥μ and the real-time slip ratio is within the normal range λ low <λ i (k)<λ hi When μ is the threshold value of the friction coefficient, λ low To achieve a low slip threshold, torque tracking mode is selected, and the weights of each objective in the optimization objective function are adjusted as follows: w a =0.8, w_λ=0.3, w_Δu=0.1; When the real-time slip ratio λi (k)>λ hi Or wheel speed ω i ≤ω th When, ω th Given the wheel speed threshold, the anti-slip priority mode is selected, and the weights of each objective in the objective function are adjusted as follows: w a =0.1, w_λ=0.9, w_Δu=0.1; When the runway operating condition is μ-split, a hybrid mode is selected. This hybrid mode includes: when the instantaneous friction coefficient μ... i (k)≥μ av9 At that time, the weights of each objective in the objective function are adjusted as follows: w a =0.8, w_λ=0.3, w_Δu=0.1; when the instantaneous friction coefficient μ i (k)<μ av9 At that time, the weights of each objective in the objective function are adjusted as follows: w a =0.1, w_λ=0.9, w_Δu=0.1, μ av9 The average coefficient of friction for the left and right wheels; When switching control modes, the current control mode must be held for a preset time, and the slip ratio must exceed the hysteresis threshold.

[0062] In this embodiment, dynamic adjustment of multi-mode weights based on operating conditions is implemented: the objective function weights are adaptively allocated for different adhesion conditions and slip states, achieving an optimal balance between efficiency and stability, especially optimizing coordinated control under μ-split conditions. Differential control for complex operating conditions such as μ-split reduces yaw moment by 20%-30% and keeps fuselage yaw angle within ±1°, preventing braking deviation. Simultaneously, to avoid frequent mode switching due to operating condition fluctuations, mode switching protection logic is implemented; this anti-shake design reduces pressure oscillations.

[0063] In one embodiment, the step of transforming the weighted objective function and constraint set into a standard quadratic programming problem and solving it to obtain the absolute pressure command for controlling brake pressure execution includes: The weighted objective function and constraint set are transformed into a standard quadratic programming problem. The interior point method is used to optimize and solve the standard quadratic programming problem to obtain the pressure increment command for each turbine. The pressure increment command of each wheel is converted into an absolute pressure command to control the brake pressure, and the absolute pressure command is ensured to comply with the actuator constraint by limiting the amplitude.

[0064] In this embodiment, the absolute pressure command is solved using a standard quadratic programming problem. This solution process fully utilizes the rich information contained in the objective function and constraint set, transforming the complex control problem into a quadratic programming problem in mathematics, and employing the efficient interior-point method for accurate solution. The use of the interior-point method not only improves the solution speed but also ensures the accuracy and stability of the results, enabling the pressure increment commands for each wheel to accurately reflect the optimal control requirements under the current operating conditions. Furthermore, the pressure increment commands are converted into absolute pressure commands, and through amplitude limiting, the feasibility of the commands and the safe operation of the actuators are effectively guaranteed, avoiding control failures or equipment damage caused by commands exceeding the physical limitations of the actuators. This series of operations provides solid technical support for aircraft anti-skid braking control, ensuring the braking safety and stability of the aircraft under various complex operating conditions.

[0065] In one embodiment, refer to Figure 3 The method further includes: When an abnormal situation occurs during the optimization process, a safety degradation mode is immediately triggered, and the braking pressure is forcibly adjusted according to preset rules. The forced adjustment of the braking pressure according to preset rules includes: When it is λ i (k)>λ hi In overslip scenarios, a pressure relief strategy proportional to the degree of overslip is adopted, as shown in the formula: Δu i =-α·(λ i (k)-λ hi )·T s , Wherein, α is the pressure relief gain; When it is v(k) <v min In vulgar scenes, v min To achieve the minimum ground speed for the aircraft, low-speed safety pressure control is employed, using the following formula: u i (k)=min(u i (k-1)+β·T s ,u low ), Where β is the low-speed boost rate, u low This represents the maximum braking pressure at low speeds.

[0066] In this embodiment, a fast safety degradation mechanism is set up: a graded pressure relief strategy is designed by combining the degree of overslip and low speed characteristics to ensure the system safety when the optimization solution is abnormal, and the response speed is improved by more than 30% compared with the traditional threshold method.

[0067] The model prediction-based aircraft anti-skid braking control method of the present invention will be described in detail below with a specific embodiment, which includes the following steps: Step 1: Initial Braking State Determination and Initialization 1.1 Landing and Grounding Status Determination: Based on Wheel-borne Signal Fz i The changing characteristics determine whether the aircraft has touched down. Once the aircraft is determined to have entered the landing touchdown state and is ready to initiate braking control; 1.2 Control Parameter Initialization: To ensure the initial stability of the braking control, the core parameters need to be initialized. Among them, the initial value of the slip ratio λ... i (0) is set to 0, because the wheel is close to pure rolling in the initial stage of grounding, and the degree of slippage can be ignored; the initial value of actuator pressure u i (0) is set to 0MPa to avoid applying brake pressure before grounding, which could damage the wheel.

[0068] Step 2: Braking-related signal acquisition and preprocessing 2.1 Multi-source signal acquisition: Real-time acquisition of key signals required for braking control, including the rotational speed ω of each wheel. i (Reflecting the rotational state of the wheels), brake pressure p of each wheel i (Reflecting the current braking force), hydraulic system oil temperature T h (Affects hydraulic oil viscosity and actuator response speed), aircraft ground speed v (reflects the overall speed of the aircraft), and wheel load Fz of each wheel. i (Reflects the vertical pressure of the wheels on the runway, affecting adhesion) and wheel turning angle δ (reflects the aircraft's turning state, used to correct braking requirements during turns).

[0069] 2.2 Signal Preprocessing: To eliminate the impact of signal noise and outliers on control accuracy, the acquired signal needs to be preprocessed. Firstly, based on a unified clock, ω... i p i T h v, Fz i Time synchronization and interpolation resampling are performed on δ, and then normalized. Subsequently, band-limited low-pass and median de-pulse joint filtering are used for the high-noise speed and wheel load signals. Notch filtering can be superimposed on the components with power frequency interference. First-order hysteresis correction and temperature compensation are introduced for pressure and temperature signals.

[0070] Step 3: Real-time slip ratio calculation and runway condition identification 3.1 Real-time slip ratio λ i (k) Calculation: The slip ratio is a core indicator reflecting the degree of wheel slippage, and its calculation formula is: λ i (k)=[v(k)-ω i(k)·r] / max(v(k),ε) where r=0.5m is the effective rolling radius of the tire, ε=0.03m / s is the minimum value used to avoid the calculation anomaly of zero denominator when the ground speed v(k) is close to zero; max(v(k),ε) means taking the larger value between the ground speed filter value and ε to ensure the validity of the calculation.

[0071] 3.2 Friction Coefficient Estimation and λ-μ Curve Fitting: First, calculate the instantaneous friction coefficient μ. i (k), whose physical meaning is the adhesion between the tire and the track, is calculated using the formula: μ i (k)=K·p i (k) / Fz i (k) Where K=1000N / MPa is (calibrated by bench testing based on parameters such as the effective friction area of ​​the brake disc and the transmission efficiency of the hydraulic system), p i (k) represents the current braking pressure, Fz i (k) represents the current wheel axle load, and this formula is derived from the braking force (K·p). i The ratio of (k) to axle load indirectly reflects the coefficient of friction between the tire and the track.

[0072] To dynamically adapt to different runway conditions (such as dry, wet, and icy surfaces), a dynamic adaptive sliding window combined with the least squares method is used to fit the Burckhardt model parameters: the length of the dynamic adaptive sliding window is set to N_w = 50 sampling periods (to ensure that the amount of data within the window is sufficient to reflect recent changes in operating conditions, while avoiding fitting lag due to outdated data), and historical data pairs (λ) within the window are stored. i (j),μ i (j))(j=k-N_w+1,...,k, where k is the current time); minimize the sum of squared deviations between the model-calculated values ​​and the measured values ​​using the least squares method, i.e.: min_{c1,c2,c3}∑_{j=k-N_w+1}^k[μ i (j)-(c1(1-e^(-c2λ i (j)))-c3λ i (j))]^2, where c1, c2, and c3 are the parameters to be fitted in the Burckhardt model, and their values ​​are determined by the runway type and tire condition.

[0073] After obtaining c1, c2, and c3 through fitting, the peak friction coefficient μ(k) and the optimal slip ratio λ are calculated. * (k): Optimal slip ratio λ *(k) is the slip ratio corresponding to the peak friction coefficient μ(k). We need to differentiate the Burckhardt model and set the derivative to 0, i.e.: dμ(λ) / dλ=c1·c2·e^(-c2λ)-c3=0. Solving for the optimal slip ratio, we get: λ(k)=-(1 / c2(k))·ln(c3(k) / (c1(k)·c2(k))). Substituting λ(k) into the Burckhardt model, we obtain the peak friction coefficient: μ(k)=c1(k)(1-e^(-c2(k)λ) * (k)))-c3(k)λ * (k) where μ(k) is the maximum adhesion that the tire can provide under the current runway conditions, and λ * (k) To achieve the optimal slip ratio for maximum adhesion, a target benchmark is provided for subsequent braking control.

[0074] 3.3 μ-split Condition Judgment: The μ-split condition refers to a significant difference in the friction coefficients of the left and right wheels or the front and rear wheels in the runway area, which may cause yaw during aircraft braking. The judgment condition is: the difference in the average friction coefficients of the left and right wheels is greater than or equal to the second preset threshold Δμ (Δμ=0.2, set based on the simulation results of aircraft directional stability), that is: |μ l (k)-μ r (k)|≥Δμ where, μ l (k) is the average friction coefficient of the left wheel assembly, μ r (k) is the average friction coefficient of the right wheel set; when this condition is met, the μ-split working condition flag is set to 1 to provide working condition basis for subsequent multi-wheel coordinated control.

[0075] Step 4: Construction of Discrete Prediction Model 4.1 Hydraulic Brake Actuator Model: To describe the dynamic response characteristics of the braking pressure, a constrained first-order inertia + time delay model is constructed, with the formula: u i (k+1)=(1-T s / τ)·u i (k)+(T s / τ)·y i (kd)+w i (k), Among them, T s The sampling period is τ = 50ms, which is the actuator time constant (reflecting the speed of pressure response from command to actual output). i (kd) is the output of the hydraulic brake controller command at time kd, where d=1 is the lag step number (reflecting the transmission delay of the hydraulic system), w i(k) represents the random disturbance term (considering variations in hydraulic oil viscosity, valve port friction, etc.); simultaneously, the model must satisfy physical constraints: brake pressure upper and lower limits 0 ≤ u i ≤30MPa (based on hydraulic system pressure resistance rating), pressure rise and fall rate constraint (to avoid sudden pressure changes that could damage actuator seals or cause aircraft turbulence).

[0076] 4.2 Slippage Dynamics Model: To predict the slip ratio in the next sampling period, a discretized slippage dynamics model is constructed based on the angular momentum balance and longitudinal force balance equations.

[0077] Wheel speed prediction: The change in wheel speed is determined by the difference between the ground friction torque and the braking torque. Based on the discretization of the angular momentum balance equation, the wheel speed prediction formula is as follows: ω i (k+1)=ω i (k)+(T s / I)·(μ i (k)Fz i (k)r-Ku i (k)r), Where I is the tire moment of inertia (defined by the tire's mass, radius, and mass distribution), μ i (k)Fz i (k)r is the ground friction torque (which drives the wheel to rotate, increasing the rotational speed), Ku i (k)r is the braking torque (resisting the rotation of the wheel, thus reducing the speed), T s / I represents the first time coefficient after discretization, which reflects the influence of the current torque difference on the wheel speed at the next moment.

[0078] Ground speed prediction: The change in aircraft ground speed is determined by the resultant force of all wheel friction forces on the ground. Based on the discretization of the longitudinal force balance equation, the ground speed prediction formula is as follows: v(k+1)=v(k)-(T s / m)·∑ i μ i (k)Fz i (k), Where m is the aircraft mass (updated in real time by payload and fuel quantity), ∑ i μ i (k)Fz i (k) is the resultant force of all wheels' ground friction (which slows the aircraft down), the negative sign indicates that the direction of the friction force is opposite to the direction of the aircraft's motion, T s / m is the second time coefficient after discretization, which reflects the influence of the current resultant frictional force on the ground velocity at the next moment.

[0079] Slip ratio prediction: Based on the predicted ground speed and wheel speed at the next moment, the slip ratio prediction formula is as follows: λ i (k+1)=[v(k+1)-ω i (k+1)r] / max(v(k+1),ε), This formula is consistent with the real-time slip ratio calculation formula in step 3.1, ensuring that the prediction logic and the actual calculation logic are unified, and providing a basis for the rolling optimization of subsequent model predictive control (MPC).

[0080] Step 5: Determine the objective function and constraint set. 5.1 Multi-objective weighted optimization function: To balance braking efficiency, stability, and comfort, a multi-objective weighted optimization function J is constructed, with the following formula: J=∑_{i=1}^{N p}[w_λ·(λ i (k+i|k)-λ * (k)) 2 +w a ·(ä_d es -ä act (k+i|k)) 2 +w_Δu·(Δu i (k+i|k)) 2 ], Where, N p =6 represents the prediction time domain (balancing prediction accuracy and computation time; 6 sampling periods (60ms) can effectively cover the actuator response process); λ i (k+i|k) represents the predicted slip ratio at the i-th prediction step, and w_λ is the slip ratio tracking weight (used to ensure that the actual slip ratio moves towards the optimal slip ratio λ). * (k) Approaching, improving braking efficiency); ä_d es To decelerate the target (set by automatic braking level command or pilot operation), act (k+i|k) represents the actual predicted deceleration value for the i-th prediction step, w a For deceleration tracking weights (used to meet the overall deceleration requirements of the aircraft); Δu i (k+i|k) represents the brake pressure increment command for the i-th prediction step, and w_Δu is the control command change rate weight (used to reduce the pressure oscillation amplitude and improve braking comfort).

[0081] 5.2 Constraint Set: To ensure the safety and feasibility of control commands, three types of constraints are defined: Actuator constraint: Brake pressure increment Δu i Meets the acceleration / deceleration rate limit, Δu i ∈[-u down T s ,u up Ts ], u up For the maximum boost rate, u down For the maximum pressure relief rate, u up =10MPa / s, u down =20MPa / s (based on actuator response capability setting), T s The sampling period is set to ensure that pressure changes do not exceed the physical limits of the actuator.

[0082] Overall machine stability constraints: The brake pressure difference between the left and right wheels must meet the symmetry constraint, i.e., |u left -u right |≤Δu sYm (Δu) sYm =5MPa (based on the upper limit of the aircraft's yaw moment) to avoid the aircraft yawing due to excessive pressure difference.

[0083] Safety protection constraint: when the slip ratio λ i >λ hi (λ) hi =0.3 (based on the critical slip ratio for wheel lockup), the forced pressure increment Δu i ≤0 means that only pressure relief operation is allowed to quickly suppress overslip and prevent wheel lock-up.

[0084] Step 6: Adaptive selection of control mode Based on real-time operating conditions (friction coefficient, slip ratio, μ-split marker), the control mode is adaptively selected, and the objective function weights are dynamically adjusted and optimized to ensure that the control strategy is optimal under different operating conditions.

[0085] 6.1 Torque Tracking Mode (mode=1): When the wheel friction coefficient μ i (k)≥μ (μ=0.6, based on the typical friction coefficient of a dry track) and the slip ratio is within the normal range λ low <λ i (k)<λ hi (λ) low When the slip threshold is 0.1 (to avoid excessive pursuit of efficiency leading to a low slip ratio), this mode is activated. At this point, runway adhesion is sufficient and the slip state is stable. The control priority is "braking efficiency first," therefore the weight is set to: w a =0.8 (high deceleration tracking weight), w_λ=0.3 (medium slip rate tracking weight), w_Δu=0.1 (low instruction smoothing weight) to ensure that the target deceleration requirement is met first.

[0086] 6.2 Anti-slip priority mode (mode=2): When the slip ratio λ i (k)>λ hi (Overslip condition) or wheel speed reduction rate ω i ≤ωth (ω) th =50rad / s 2 This mode is activated when the wheel lock-up tendency threshold is reached. At this time, there is a risk of wheel slippage or lock-up, and the control priority is "anti-slip safety first," therefore the weight is set as: w a =0.1 (low deceleration tracking weight), w_λ=0.9 (high slip ratio tracking weight), w_Δu=0.1 (low command smoothing weight) to ensure that the slip ratio is pulled back to the safe range first, even if some braking efficiency is sacrificed.

[0087] 6.3 Hybrid Mode (mode=3): This mode is enabled when the μ-split condition flag is 1. Differentiated weights are applied to the wheel on different friction coefficient sides: the side with higher friction coefficient (μ... i (k)≥μ av9 μ av9 The average friction coefficient of the left and right wheels follows the weighting of mode=1 (emphasizing efficiency) to fully utilize high adhesion; the low friction coefficient side (μ i (k)<μ av9 Using the weight of mode=2 (emphasizing anti-slip), we avoid yaw caused by excessive slip on the low-adhesion side, thus achieving a balance between efficiency and stability.

[0088] 6.4 Mode Switching Anti-Jitter: To avoid frequent mode switching due to fluctuations in operating conditions (causing pressure oscillations), mode switching protection logic is set: after a mode switch, t2 = 20ms (based on the actuator response time setting) must be maintained before switching again; at the same time, the slip ratio must exceed the hysteresis threshold Δλ. h =0.05 (λ is required to switch from mode=1 to mode=2) i (k)>λ hi +Δλ h Switching from mode=2 to mode=1 requires λ i (k)<λ hi -Δλ h This ensures that the switching is based on stable changes in operating conditions rather than instantaneous fluctuations.

[0089] Step 7: Optimize the solution and issue control commands 7.1 Quadratic Programming Solution: Within each sampling period, the optimization objective function J and constraint set constructed in step 5 are transformed into a standard quadratic programming (QP) problem, in the form: min_{Δu}(1 / 2)Δu T HΔu+f T Δu, stAΔu≤b, where Δu is the pressure increment command vector for all turbine wheels (Δu=[Δu1,Δu2,...,Δu...). n]^T, where n is the number of wheels), H is the quadratic coefficient matrix (composed of w_λ, w a The problem is constructed using w_Δu, with H being a positive definite matrix to ensure a unique optimal solution. f is the linear term coefficient vector (calculated from the current slip ratio deviation and deceleration deviation), A is the constraint coefficient matrix (describing the linear relationship between each constraint and Δu), and b is the constraint boundary vector (set by the threshold values ​​of each constraint). The interior-point method (which has fast convergence characteristics and meets real-time control requirements) is used to solve the QP problem, obtaining the pressure increment command Δu for each turbine. i .

[0090] 7.2 Command Processing: Increment the pressure Δu i Transformed into the final absolute pressure command u i (k), and ensures that the instruction conforms to the actuator constraints by limiting the amplitude, the formula is: u i (k)=clip(u i (k-1)+Δu i (k),0,30,u up T s ,u down T s Among them, u i (k-1) represents the actual pressure command from the previous sampling period, and clip is the limiting function, whose functions include: firstly, limiting u... i (k-1)+Δu i (k) Limit the pressure to the upper and lower limits of [0, 30 MPa]; secondly, ensure that the pressure change does not exceed u. up T s (When boosting) or u down T s (During voltage reduction), avoid exceeding the actuator's response capability; the final obtained u i (k) The hydraulic servo valve / relief valve of the corresponding wheel is sent to control the brake pressure.

[0091] 7.3 Status Update: To ensure that the prediction model for the next sampling period is consistent with the actual operating conditions, the current control commands and status parameters need to be updated to the prediction model in step 4: the final pressure command u... i (k) Substitute it into the actuator model as the instruction input for the next cycle; set the real-time slip ratio λ i (k), measured wheel speed ω i The measured ground speed v(k) and the actual ground speed v(k) are updated to the initial values ​​of wheel speed and ground speed in the sliding motion mechanics model, respectively, to provide an accurate initial state for the rolling optimization in the next cycle.

[0092] 7.4 Fast and Safe Degradation Mechanism (Innovation Point 3): When an anomaly occurs in the optimization solution process (such as constraints being infeasible leading to no feasible solution, or the solution taking time t...), sol>0.5T s (T) s When the sampling period causes a timeout, the safety degradation mode is immediately triggered, and the pressure is forcibly adjusted according to preset rules to avoid system loss of control.

[0093] Overslip scenario: when λ i >λ hi At this time, a pressure relief strategy proportional to the degree of overslip is adopted, as shown in the formula: Δu i =-α·(λ i (k)-λ hi )·T s , Where α=500 is the pressure relief gain (calibrated through simulation to ensure that the larger the slip ratio, the faster the pressure relief speed, and quickly suppress overslip), and the negative sign indicates the pressure relief operation.

[0094] Low-speed scenarios: when flag low =1(v(k) <v min When this occurs, low-speed safety pressure control is used, and the formula is: u i (k)=min(u i (k-1)+β·T s ,u low ), Where β=1MPa / s is the low-speed boost rate (to avoid excessively rapid low-speed boost leading to engine seizure), u low =5MPa is the maximum pressure at low speed (set based on the wheel load adhesion characteristics at low speed) to ensure that the pressure does not exceed the safety threshold at low speed.

[0095] Step 8: Termination of Braking Process and Data Recording 8.1 Braking Termination Determination: The braking process is determined to have ended when any of the following conditions are met, and the active control based on slip ratio is discontinued, switching to a low-speed parking / ground taxiing control strategy: First, the aircraft ground speed v(k) drops to the stopping threshold v. stop (v) stop =1km / h, based on the ground speed definition of the aircraft in a stopped state); secondly, a stop signal stop_signal=1 is detected (issued by the pilot or the autopilot system). During the parking / taxiing control phase, the brake pressure command is fixed at u. park (u) park =2MPa (based on the minimum braking requirement during ground taxiing), which maintains wheel braking by constant low pressure to prevent the aircraft from sliding on the ground.

[0096] 8.2 Data Recording: To support subsequent braking system health management (such as component life assessment and maintenance cycle determination), key data from this braking process must be recorded: Braking energy: reflects the load on the braking system during braking, and is calculated using the following formula: E_brake=∑_{k=0}^NK·u i (k)·r·ω i (k)·T s , Where N is the total number of samplings during the braking process, K·u i (k)·r is the braking torque, ω i (k)·T s The angle of the wheel rotation during the sampling period is the sum of the angles, and the product of the angles is the work done by the braking torque during that period. The total braking energy is obtained by summing the angles.

[0097] Brake component temperature rise estimate: Reflects the thermal load state of the brake component, calculated based on the fitting of brake energy and hydraulic oil temperature, using the following formula: ΔT(k) = k1·E_brake(k) + k2·T h (k)·t(k)+k0, Where k1=1e-5, k2=0.02, and k0=2 are calibration coefficients (determined through brake component thermal simulation and bench testing), E_brake(k) is the current cumulative braking energy, and T h (k) represents the current hydraulic oil temperature, and t(k) represents the braking duration. This formula comprehensively considers the influence of energy input and ambient temperature on the component temperature rise, providing a basis for judging whether the component is overheating.

[0098] It should be noted that although this invention employs model predictive control, equivalent nonlinear modeling and control methods can also be used to achieve unified optimization of braking torque and wheel slip ratio. While this invention focuses on hydraulic brake actuators, in future aircraft designs, if electric motor-driven brakes or electro-hydraulic hybrid braking systems are adopted, the method of this invention can also be applied by introducing corresponding actuator dynamics and constraints into the predictive model. Besides maintaining wheel slip ratio within the optimal range as the primary objective, it can also be extended to "minimizing braking distance" or "maximizing the friction utilization rate between the tire and the runway." The invention's objectives can still be achieved through different forms of objective function design.

[0099] The embodiments of the present invention mainly employ the following technical means: 1) Dynamically update Burckhardt model parameters: The λ-μ curve is fitted in real time using the least squares method, which solves the problem that the traditional fixed model cannot adapt to the changing runway conditions and improves the tracking accuracy of the optimal slip ratio. 2) Dynamic adjustment of weights in multiple modes based on working conditions: The objective function weights are adaptively allocated for different adhesion conditions and slip states to achieve the optimal balance between efficiency and stability, especially optimizing the coordinated control under the μ-split working condition. 3) Fast and safe degradation mechanism: A graded pressure relief strategy is designed by combining the degree of overslip and low speed characteristics to ensure the system safety when the optimization solution is abnormal. The response speed is improved by more than 30% compared with the traditional threshold method.

[0100] The embodiments provided by this invention achieve the following beneficial effects: 1) Improve braking efficiency: Real-time dynamic fitting of the λ-μ model, adaptable to various runway conditions such as dry, wet, and icy conditions, shortens braking distance by 5%-18%, and improves runway utilization. 2) Enhanced driving stability: Differentiated control for complex operating conditions such as μ-split, reducing yaw moment by 20%-30%, and controlling fuselage yaw angle within ±1° to avoid braking deviation; 3) Ensuring safety and reliability: Mode switching anti-shake reduces pressure oscillations, the degradation mechanism response in case of failure is ≤5ms, and over-glide is quickly suppressed, meeting the aviation "fail-safe" standard; Reduce maintenance costs: Recording brake energy and component temperature rise supports system health management, optimizes maintenance cycle by 15%-20%, and reduces annual maintenance costs by 8%-12%.

[0101] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A model-predictive-based aircraft anti-skid braking control method, characterized in that, The method includes: When the aircraft is determined to be in the landing touchdown state, the control parameters are initialized; Real-time acquisition of key signals required for braking control, and preprocessing of the acquired key signals; Based on the preprocessed key signals, the real-time slip ratio, instantaneous friction coefficient and optimal slip ratio are calculated, and the runway operating conditions are identified based on the instantaneous friction coefficient. Construct predictive models, including constructing a hydraulic brake actuator model and a sliding motion mechanics model; Based on the prediction model and the optimal slip ratio, a multi-objective weighted optimization objective function is constructed, and a set of constraints for the optimization objective function is set. Based on real-time slip ratio, instantaneous friction coefficient and runway conditions, the control mode is adaptively selected, and the weights of each objective in the objective function are dynamically adjusted and optimized according to the selected control mode. The optimized objective function and constraint set after weight adjustment are transformed into a standard quadratic programming problem, and optimized to obtain the absolute pressure command for controlling the execution of braking pressure. The absolute pressure command is updated to the hydraulic brake actuator model, and the real-time state parameters are updated to the sliding motion mechanics model to provide the initial state for the rolling optimization of the next cycle. When the braking termination condition is met, the braking process ends, the slip ratio-based active control exits, and the system switches to low-speed parking or ground coasting control, and data is recorded.

2. The model-predictive-based aircraft anti-skid braking control method according to claim 1, characterized in that, The key signals include wheel speed, wheel brake pressure, hydraulic system oil temperature, aircraft ground speed, wheel load, and wheel turning angle.

3. The model-predictive-based aircraft anti-skid braking control method according to claim 2, characterized in that, The preprocessing of the acquired key signals includes: Based on a unified clock, time synchronization and interpolation resampling are performed on each key signal, and then normalization is performed. The rotational speed and wheel load of each turbine are filtered using a combination of band-limited low-pass filtering and median pulse removal. The components containing power frequency interference are superimposed with notch filters; First-order hysteresis correction and temperature compensation are introduced for the braking pressure of each wheel and the oil temperature of the hydraulic system.

4. The model-predictive-based aircraft anti-skid braking control method according to claim 2, characterized in that, The calculation of real-time slip ratio, instantaneous friction coefficient, and optimal slip ratio, and the identification of runway operating conditions based on the instantaneous friction coefficient, includes: Calculate the real-time slip ratio based on the aircraft's ground speed and wheel speed; Calculate the instantaneous friction coefficient based on the current wheel brake pressure and wheel load; Based on historical data pairs of slip ratio and friction coefficient, a dynamic adaptive sliding window combined with the least squares method is used to fit and calculate the parameters of the Burckhardt model, thereby obtaining the Burckhardt model expression. The dynamic adaptive sliding window adaptively adjusts the sampling period according to the drastic change in friction coefficient and the variance of slip ratio fluctuation. The window slides successively with the sampling period. When the drastic change in friction coefficient is detected to be greater than the first preset threshold, the window is immediately reset, historical data is cleared, and new data with the minimum window length is re-collected to ensure that the fitting parameters quickly adapt to the new working conditions. Based on the Burckhardt model expression, the optimal slip ratio and its corresponding peak friction coefficient are calculated. Based on the instantaneous friction coefficient, calculate whether the difference between the average friction coefficients of the left and right wheels or the front and rear wheels in the runway area is greater than or equal to the second preset threshold. If so, determine that the current runway condition is the μ-split condition.

5. The model-predictive-based aircraft anti-skid braking control method according to claim 4, characterized in that, The expression for the hydraulic brake actuator model is: u i (k+1)=(1-T s / τ)·u i (k)+(T s / τ)·y i (k-d)+w i (k), Among them, u i (k) represents the braking pressure at time k, u i (k+1) represents the braking pressure at time k+1, T s The sampling period is τ, the actuator time constant is y i (kd) is the output of the hydraulic brake controller command at time kd, where d is the lag step number, and w i (k) represents the random disturbance term.

6. The model-predictive-based aircraft anti-skid braking control method according to claim 5, characterized in that, The construction of the sliding motion mechanical model includes: Based on the discretization of the angular momentum balance equation, the wheel speed prediction formula is obtained: ω i (k+1)=ω i (k)+(T s / I)·(μ i (k)Fz i (k)r-Ku i (k)r), Where, ω i (k) represents the rotational speed of the turbine wheel at time k, ω i (k+1) represents the wheel speed at time k+1, I represents the tire moment of inertia, and μ i (k) is the friction coefficient at time k, Fz i (k) represents the wheel load at time k, r is the effective rolling radius of the tire, and μ i (k)Fz i (k)r represents the ground friction torque, K is the pressure-force conversion coefficient of the braking system, and Ku i (k)r represents the braking torque, T s / I represents the first time coefficient after discretization; Based on the discretization of the longitudinal force balance equation, the ground speed prediction formula is obtained: v(k+1)=v(k)-(T s / m)·∑ i μ i (k)Fz i (k), Where v(k) is the aircraft ground speed at time k, v(k+1) is the aircraft ground speed at time k+1, m is the aircraft mass, and ∑ i μ i (k)Fz i (k) represents the resultant force of all wheels' ground friction, T s / m is the second time coefficient after discretization; Based on the wheel speed prediction formula and the ground speed prediction formula, the sliding motion mechanical model is obtained. The expression of the sliding motion mechanical model is: l i (k+1)=[v(k+1)-ω i (k+1)r] / max(v(k+1),ε), Where, λ i (k+1) represents the slip ratio at time k+1, and ε is the minimum value.

7. The model-predictive-based aircraft anti-skid braking control method according to claim 6, characterized in that, The expression for the multi-objective weighted optimization objective function is: J=∑_{i=1}^{N p }[w_λ·(λ i (k+i|k)-λ * (k)) 2 +in a ·(ä_d es -and act (k+i|k)) 2 +w_Δu·(Δu i (k+i|k)) 2 ], Where J is the objective function, N p For prediction in the time domain, λ i (k+i|k) represents the predicted slip ratio for the i-th prediction step, and w_λ is the slip ratio tracking weight. * (k) represents the optimal slip ratio, ä_d es To decelerate the target, ä act (k+i|k) represents the actual predicted deceleration value for the i-th prediction step, w a For deceleration tracking weights, Δu i (k+i|k) represents the brake pressure increment command for the i-th prediction step, and w_Δu is the weight of the control command change rate. The constraint set includes actuator constraints, overall machine stability constraints, and safety protection constraints. Actuator constraints include brake pressure increment Δu i Meets the acceleration / deceleration rate limit, Δu i ∈[-u down T s ,u up T s ], u up For the maximum boost rate, u down This is the maximum pressure relief rate; Overall machine stability constraints include ensuring the symmetry of the brake pressure difference between the left and right wheels. left -u right |≤Δu sYm u left For the left wheel brake pressure, u right The right wheel brake pressure, Δu sYm The threshold is set to be symmetry-based. Safety protection constraint: when the slip ratio λ i >λ hi At that time, the forced braking pressure increment Δu i ≤0,λ hi This is the high slip ratio threshold.

8. The model-predictive-based aircraft anti-skid braking control method according to claim 7, characterized in that, The control modes include torque tracking mode, anti-slip priority mode, and hybrid mode. The method adaptively selects the control mode based on real-time slip ratio, instantaneous friction coefficient, and runway conditions, and dynamically adjusts and optimizes the weights of each objective in the objective function according to the selected control mode, including: When the instantaneous friction coefficient μ i (k)≥μ and the real-time slip ratio is within the normal range λ low <λ i (k)<λ hi When μ is the threshold value of the friction coefficient, λ low To achieve a low slip threshold, torque tracking mode is selected, and the weights of each objective in the optimization objective function are adjusted as follows: w a =0.8, w_λ=0.3, w_Δu=0.1; When the real-time slip ratio λ i (k)>λ hi Or wheel speed ω i ≤ω th When, ω th Given the wheel speed threshold, the anti-slip priority mode is selected, and the weights of each objective in the objective function are adjusted as follows: w a =0.1, w_λ=0.9, w_Δu=0.1; When the runway operating condition is μ-split, a hybrid mode is selected. This hybrid mode includes: when the instantaneous friction coefficient μ... i (k)≥μ av9 At that time, the weights of each objective in the objective function are adjusted as follows: w a =0.8, w_λ=0.3, w_Δu=0.1; when the instantaneous friction coefficient μ i (k)<μ av9 At that time, the weights of each objective in the objective function are adjusted as follows: w a =0.1, w_λ=0.9, w_Δu=0.1, μ av9 The average coefficient of friction for the left and right wheels; When switching control modes, the current control mode must be held for a preset time, and the slip ratio must exceed the hysteresis threshold.

9. The model-predictive-based aircraft anti-skid braking control method according to claim 1, characterized in that, The process of transforming the weighted objective function and constraint set into a standard quadratic programming problem and solving it to obtain the absolute pressure command for controlling brake pressure execution includes: The weighted objective function and constraint set are transformed into a standard quadratic programming problem. The interior point method is used to optimize and solve the standard quadratic programming problem to obtain the pressure increment command for each turbine. The pressure increment command of each wheel is converted into an absolute pressure command to control the brake pressure, and the absolute pressure command is ensured to comply with the actuator constraint by limiting the amplitude.

10. The model-predictive-based aircraft anti-skid braking control method according to claim 8, characterized in that, The method further includes: When an abnormal situation occurs during the optimization process, a safety degradation mode is immediately triggered, and the braking pressure is forcibly adjusted according to preset rules. The forced adjustment of the braking pressure according to preset rules includes: When it is λ i (k)>λ hi In overslip scenarios, a pressure relief strategy proportional to the degree of overslip is adopted, as shown in the formula: Thu i =-a·(λ i (k)-l hi )·T s , Wherein, α is the pressure relief gain; When it is v(k) <v min In vulgar scenes, v min To achieve the minimum ground speed for the aircraft, low-speed safety pressure control is employed, using the following formula: he i (k)=min(u i (k-1)+β·T s ,he low ), Where β is the low-speed boost rate, u low This represents the maximum braking pressure at low speeds.

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