A method and system for spot braking control

By combining pavement optimization with a local MPC planning controller, the problem of the aircraft anti-skid braking system automatically planning the taxiing in different environments was solved, achieving safe and economical fixed-point braking, and improving braking efficiency and passenger comfort.

CN118323435BActive Publication Date: 2025-10-17BEIHANG UNIV +1
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Patent Information

Application Number
CN202410282385.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-03-12
Publication Date
2025-10-17
Estimated Expiration
2044-03-12

AI Technical Summary

Technical Problem

Existing aircraft anti-skid braking systems are unable to automatically plan the taxiing process under different take-off and landing environments and runway conditions. They have poor adaptability and are affected by internal and external disturbances of the system, making it difficult to achieve safe and economical fixed-point braking.

Method used

A fixed-point braking control method is adopted to obtain the optimal deceleration state through road surface optimization. Combined with the local MPC planning controller and the lower-layer slip state controller, the aircraft slip state is adjusted in real time to resist disturbances, achieve closed-loop control, and ensure safety and economy.

Benefits of technology

It realizes automatic planning of the taxiing process under different runway conditions, resists internal and external disturbances of the system, ensures that the aircraft completes fixed-point braking safely and economically, and improves braking efficiency and passenger comfort.

✦ Generated by Eureka AI based on patent content.

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Abstract

The application discloses a kind of fixed point brake control method and system, the method includes S1, obtains the initial position of aircraft and initial speed of aircraft;S2, the optimal deceleration state corresponding to the deceleration profile and deceleration rate range of aircraft position, aircraft speed is obtained by pavement optimization;S3, real-time acquisition aircraft current position and aircraft current speed;S4, local MPC planning is carried out to obtain target deceleration rate and target slip rate;S5, determine wheel target brake torque according to target deceleration rate and target slip rate, and brake according to wheel target brake torque;S6, repeat steps S3 to S5 until aircraft fixed point brake is completed.The application can be safe and economic as principle, while obtaining more optimal deceleration rate as possible, target speed and target position are planned, while resisting from system inside and outside, headwind and adverse wind, brake disc torque system change etc. disturbance, finally realize fixed point brake.
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Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of aircraft brake systems, in particular to a fixed-point brake control method and system. BACKGROUND

[0002] The aircraft take-off and landing phase is an important phase related to flight safety in the flight process. The aircraft anti-skid brake system is a typical nonlinear system, and its working environment is affected by many factors such as aircraft speed change, ground friction, and runway environment conditions. In order to ensure the safety of the aircraft in harsh working conditions, reduce the time cost, and improve the economic efficiency of the take-off and landing peak time period, the aircraft needs to be able to reduce to the target speed when driving into and out of the runway and smoothly leave, so as to reduce the runway occupation time while ensuring the safety of the brake process.

[0003] The anti-skid brake system of the modern aircraft provides a strong guarantee for the safe landing of the aircraft. In the deceleration phase after the aircraft lands, the kinetic energy of the aircraft body is consumed, and at the same time of completing the braking process, the aircraft wheel lock is prevented and excessive wear is avoided. In addition, the aircraft anti-skid brake system also needs to cooperate with the front wheel and other systems to realize the functions of aircraft turning, parking, etc., which is crucial to the safety of aircraft take-off and landing.

[0004] In the case that the aircraft wheel does not appear deep skidding or locking, the aircraft anti-skid brake system controls the brake torque to improve the utilization rate of the ground adhesion coefficient as much as possible, so as to improve the brake efficiency and make the aircraft reduce to a certain speed or stop in the shortest distance possible. Brake efficiency is a key indicator of brake performance, which is specifically defined as the ratio of the integral of the actual adhesion coefficient used in the braking process to the integral of the ideal adhesion coefficient envelope.

[0005] The design of the anti-skid control algorithm is usually related to the hardware structure of the system. The common modulation control method is to adjust the brake pressure according to the wheel slip state, so that the wheel slip state can be kept in a state with higher brake efficiency as much as possible.

[0006] Among them, the brake control method based on the deceleration rate calculates the wheel deceleration rate according to the feedback signal of the wheel speed sensor and the brake pressure signal, compares it with the preset deceleration rate value to obtain the control signal, that is, generates a target deceleration rate, and then adjusts the brake pressure output according to the control signal by the electro-hydraulic servo valve.

[0007] The problem of maintaining the slip state involves the identification of the slip state. The runway optimization method relies on establishing a mathematical model of different runways, identifying the degree of slip of the aircraft wheels according to the model, and providing a basis for the design of an efficient anti-skid brake control law. The slip ratio is usually used to represent the relative motion state of the wheel and the ground, and the optimal slip ratio corresponds to the wheel-ground bonding force close to the maximum bonding force that the runway can provide. The optimal slip ratio is not the same under different runway conditions, but the trend of the slip ratio with the slip speed is similar. The runway optimization method controls the wheel operating point in a range close to the optimal slip ratio in real time by finding the optimal slip ratio corresponding to different runways, thereby improving the brake efficiency.

[0008] The pressure bias module (PBM) is a widely used brake control method based on deceleration rate. Its principle is to generate a reference speed instead of the speed of the aircraft, to establish different pressure rise coefficients by using different slip thresholds generated by the difference between the reference speed and the wheel speed, and to ensure that the wheel slip state remains near the optimal operating point by designing different rules and thresholds.

[0009] For the existing automatic brake system, the optimal deceleration rate supported by different take-off and landing environments and slip runways is unknown, and the aircraft is also subject to various disturbances from inside and outside the system, including external head and tail winds, brake disc torque system changes and other disturbances. It cannot automatically plan the aircraft slip process, and the pilot needs to judge the current state of the aircraft after landing according to experience, and then select the corresponding aircraft deceleration rate, which has poor adaptability to runway state changes. SUMMARY

[0010] The purpose of the present application is to provide a fixed-point brake control method and system to solve the problems in the prior art. It can automatically plan the aircraft runway slip process according to the position, speed and runway conditions of the aircraft on the runway, obtain the optimal deceleration rate as much as possible, plan the target speed and target position, resist disturbances such as head and tail winds from inside and outside the system, brake disc torque system changes and other disturbances, and finally realize fixed-point braking while ensuring the safety, comfort and sufficient economic benefits of the braking process.

[0011] The present application provides a fixed-point brake control method, comprising the following steps:

[0012] S1, obtaining the initial position and initial speed of the aircraft;

[0013] S2, obtaining the deceleration profile and deceleration rate range of the aircraft position and aircraft speed corresponding to the optimal deceleration state supported by the runway through runway optimization;

[0014] S3, obtaining the current position and current speed of the aircraft in real time;

[0015] S4, performing local MPC planning to obtain a target deceleration rate and a target slip rate;

[0016] S5, determining a target wheel brake torque according to the target deceleration rate and the target slip rate, and braking according to the target wheel brake torque;

[0017] S6, repeating steps S3 to S5 until the airplane is parked.

[0018] The method for controlling the airplane to park as described above, wherein, optionally, in step S4, the local MPC planning is performed by inputting the results obtained in steps S1-S3 into a pre-configured local optimization model.

[0019] The method for controlling the airplane to park as described above, wherein, optionally, in the local optimization model, the target evaluation function is:

[0020]

[0021] wherein N p is a prediction step, N c is a control step, y ref is a full-range position-velocity reference value obtained by a road planning module, Δu(k+i)=u(k+i)-u(k) is a control output increment, Q a is a weight coefficient matrix of system output, R1 is a weight coefficient matrix of system control, and R2 is a weight coefficient matrix of control increment.

[0022] The method for controlling the airplane to park as described above, wherein, optionally, in each control cycle, the local optimization problem is:

[0023]

[0024] s.t.x a (k+1)=A a x a (k)+B a u(k)

[0025] 0≤|u a (k+i)|≤u amax ;

[0026] wherein u amax is a maximum deceleration rate supported by the road surface, A a and B a are state matrices.

[0027] The method for controlling the airplane to park as described above, wherein, optionally, the maximum deceleration rate supported by the road surface is calculated from the deceleration rate obtained by optimization, and the formula is:

[0028]

[0029] wherein, σ asafe <1, safety margin of aircraft deceleration rate, r is the optimal aircraft wheel deceleration rate, w r is the wheel radius.

[0030] The fixed-point braking control method as described above, wherein, optionally, in step S4, the highest ground adhesion utilization rate and braking efficiency are obtained under the optimal state constraint.

[0031] The present application also provides a fixed-point braking control system, comprising a road planning module, a local MPC planning controller and a lower-layer slip state controller.

[0032] The road planning module is used to obtain the initial position and the initial speed of the aircraft, and to perform road planning to obtain the deceleration profile and the deceleration rate range of the aircraft position and speed corresponding to the optimal deceleration state that the road surface can support.

[0033] The local MPC planning controller is used to obtain the calculation results of the road planning module in real time, and to perform local MPC planning to obtain the target deceleration rate and the target slip rate.

[0034] The lower-layer slip state controller is used to obtain the output results of the local MPC planning in real time, and to calculate the target brake torque of the aircraft wheel to control the braking system to brake according to the target brake torque of the aircraft wheel; the lower-layer slip state controller is also used to obtain the output signal of the control system to realize closed-loop control.

[0035] The fixed-point braking control system as described above, wherein, optionally, the local MPC planning controller obtains the current position, the current speed and the current deceleration rate of the aircraft in real time to realize closed-loop control through the local MPC planning controller.

[0036] The fixed-point braking control system as described above, wherein, optionally, the local MPC planning controller generates the target slip state in accordance with the optimal state constraint according to the actual state of the aircraft fed back in real time, so as to realize closed-loop control of the slip state of the aircraft wheel by the lower-layer slip controller.

[0037] The fixed-point braking control system as described above, wherein, optionally, the road planning module comprises a road surface optimization unit.

[0038] Compared with the prior art, the fixed-point brake control method provided by the application takes safety and economy as principles, automatically plans the runway sliding process of the airplane according to the position, speed and runway condition of the airplane on the runway, plans the target speed and target position while obtaining a more optimal deceleration rate as much as possible, resists the disturbance from the system inside and outside, such as headwind, tailwind and brake disc torque system change, and finally realizes the fixed-point brake and ensures the safety, comfort and sufficient economic benefits of the brake process. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 is a step flow chart of the method provided by the first embodiment of the application;

[0040] Figure 2 is a brake control response schematic diagram;

[0041] Figure 3 is a brake deceleration rate tracking schematic diagram.

[0042] Figure 4 is a structural block diagram of the system provided by the second embodiment of the application. DETAILED DESCRIPTION

[0043] The embodiments described below with reference to the drawings are exemplary and are only used to explain the application and cannot be explained as the limitation of the application.

[0044] In order to solve the problems proposed in the background art, the following embodiments are proposed by the application to solve the problems.

[0045] Embodiment one

[0046] In this embodiment, in the initial stage of the airplane after landing without braking, the runway optimization technology is used for road planning, the runway safety threshold is found, the optimal deceleration state supported by the runway is obtained, and then the basic deceleration relationship about the position and speed of the airplane is obtained through optimization.

[0047] The obtained brake process speed and position relationship and optimal state constraint are taken as target inputs, the local MPC planning controller adjusts the current sliding state to the target sliding state according to the current feedback state. The target sliding state output by the local MPC planning controller enters the lower sliding state controller, realizes the closed-loop control of the wheel brake system, completes the antiskid brake process with a faster response speed, realizes the fixed-point brake, and ensures the safety of the brake process.

[0048] Specifically, please refer to Figure 1 The embodiment provides a fixed-point brake control method, which comprises the following steps.

[0049] S1, obtaining the initial position X0 of the airplane and the initial speed v of the airplane p0In specific implementation, the initial position X0 and the initial speed v of the aircraft p0 It can be measured by a sensor or calculated from other physical quantities. This is a conventional technical means in the prior art and can be obtained by those skilled in the art, so it will not be described in detail here.

[0050] S2, through the road surface optimization to obtain the aircraft position, aircraft speed deceleration profile and deceleration rate range corresponding to the optimal deceleration state that the road surface can support; during the braking process, the aircraft state is estimated, and the relationship between the current speed and current position of the aircraft is obtained by the road surface optimization technology, and the optimal state constraint is generated as the control input of the local MPC planning controller. In the specific implementation, the road surface optimization is achieved through the slip factor dF f / dλ, the gradient change of wheel friction with respect to slip rate can be used to characterize the nonlinear characteristics of the pavement. In specific implementation, the purpose of pavement optimization is to obtain the aircraft position X corresponding to the optimal deceleration state supported by the pavement conditions. ref and the deceleration profile v of the aircraft speed ref , and the range of deceleration rate (u cmin ,u cmax ). That is, in the initial stage after the aircraft lands and does not brake, the road surface optimization technology is used to plan the road surface, find the road surface safety threshold, obtain the optimal deceleration state that the road surface can support, and then obtain the basic deceleration relationship between the aircraft position and speed through optimization. Among them, u cmin is the minimum value allowed for road planning, u cmax The maximum value allowed for road planning.

[0051] The obtained braking process speed and position relationship and the optimal state constraint are used as the target input. The local MPC planning controller adjusts the current slip state to the target slip state based on the current feedback state. Specifically, the specific process of MPC planning is shown in steps S3 and S4.

[0052] S3, real-time acquisition of the aircraft's current position X and current speed v p In practical applications, according to actual needs, the current deceleration rate of the aircraft can also be obtained. p .

[0053] S4, perform local MPC planning to obtain the target deceleration rate a ref and target slip ratio λ ref During braking, the aircraft's state is estimated, and the relationship between its speed and position is determined using road surface optimization techniques. This generates optimal state constraints, which serve as control inputs for the local MPC planning controller. In this step, the goal is to achieve the highest possible ground engagement and braking efficiency within the optimal state constraints.

[0054] The results obtained in steps S1-S3 are input into the pre-set local optimization model.

[0055] The pre-set local optimization model setting process is as follows:

[0056] The core objective of the fixed-point braking control is not to infinitely approach the optimal braking efficiency, which means that the slip state of the system does not need to approach the maximum coefficient point, but only needs to obtain the highest ground adhesion force utilization rate and braking efficiency under the optimal state constraint. To this end, when the slip state is small, the wheel target deceleration rate The aircraft target deceleration rate a ref It can be considered that the following approximate condition is met:

[0057]

[0058] In the above formula, r W is the wheel radius.

[0059] The deceleration rate-based braking control law is tested on a dry runway, and the wheel deceleration rate value is changed at 15s, 25s and 35s respectively. The test results are shown in FIGS. 15, 25 and 35. Figure 2 and Figure 3

[0060] In addition to the initial stage of braking, the actual deceleration rate a p of the aircraft body can be approximated to a first-order inertia link as the target deceleration rate a ref .

[0061]

[0062] In the formula, K bp is the system gain, τ a is the time constant, and the continuous state equation can be expressed as:

[0063]

[0064] According to the forward Euler method, the discrete system state equation of the system local optimization is obtained as:

[0065] x a (k+1)=A a x a (k)+B a u a (k)

[0066]

[0067] In the formula, T s is the sampling time, and k+1 represents the next sampling time. Since the fixed-point braking requires a specific speed at a specific position, the system output equation is obtained as: ​

[0068] y a (k+1) = C a x a (k), C a = [1 1 0] (3)

[0069] where A a , B a and C a are state matrices, T s is the sampling time, and k is the current sampling time.

[0070] The higher the deceleration rate during braking, the greater the ground adhesion force. In order to ensure the tracking accuracy during control, while reducing the control amount as much as possible, reducing hardware loss such as tire wear and brake disc temperature, and improving the passenger's ride experience, the impact of acceleration impact should be minimized. The objective evaluation function defined by the above constraint conditions is:

[0071]

[0072] where N p is the prediction step, N c is the control step, y ref is the position-velocity reference value obtained by the road planning module, Δu(k+i) = u(k+i)-u(k) is the control output increment, Q a is the weight coefficient matrix of the system output, R1 is the weight coefficient matrix of the system control variable, and R2 is the weight coefficient matrix of the control increment.

[0073] The constraints on the control variable are mainly obtained by system optimization, so

[0074] 0≤|u a (k+i)|≤u amax (4)

[0075] where u max is the maximum deceleration rate that the road surface can support, which can be obtained from the optimal deceleration rate:

[0076]

[0077] where σ asa f e <1 is the safety margin of the aircraft deceleration rate, and f is the aircraft deceleration level. In order to avoid the influence of instantaneous gusts and other disturbances on the aircraft deceleration level, affecting the safety and efficiency of the braking process, a certain margin is designed for the aircraft deceleration level.

[0078] The principle of the local MPC planning controller is to minimize the evaluation function defined by equation (6) under the conditions of equation (4), equation (5) and equation (7). In each control cycle, the optimization problem can be defined as follows:

[0079]

[0080] s.t.x a (k+1)=A a x a (k)+B a u(k)

[0081] 0≤|u a (k+i)|≤u amax (6)

[0082] where y is the current aircraft position, and u(k) is the deceleration rate control input.

[0083] To calculate the optimization problem represented by equation (9) on an embedded system, it can be converted into a standard quadratic programming problem, and the conversion process is very mature.

[0084] After the local MPC planning controller generates the target slip state that meets the optimal state constraint according to the current feedback of the actual state of the aircraft, the lower slip controller takes this as the target to realize closed-loop control of the aircraft wheel slip state, and finally completes the fixed-point braking process.

[0085] In actual work, local MPC planning is a cyclic process, and different planning cycles correspond to different sampling times. The target slip state output by the local MPC planning controller enters the lower slip state controller to realize closed-loop control of the aircraft wheel braking system, complete the anti-skid braking process with faster response speed, realize fixed-point braking, and ensure the safety of the braking process.

[0086] S5, determine the target wheel braking torque according to the target deceleration rate and the target slip rate, and brake according to the target wheel braking torque. In specific implementation, this step can be realized by the lower slip state controller through closed-loop control.

[0087] S6, repeat steps S3 to S5 until the fixed-point braking of the aircraft is completed.

[0088] Embodiment Two

[0089] This embodiment is a specific implementation of the method described in Embodiment One. The same parts will not be repeated, and only the different parts will be described below.

[0090] During the braking process after the aircraft landing, the optimal deceleration state that can be supported by the runway is obtained by using the runway optimization technology for road planning, and then the target control output of the local MPC planning controller is entered into the lower slip state controller to realize closed-loop control of the aircraft wheel braking system, complete the antiskid braking process with faster response speed, realize the fixed-point braking, and ensure the safety of the braking process.

[0091] The aircraft wheel dynamics and disturbance observation belong to the lower slip state controller. The aircraft wheel dynamics are used to represent the motion characteristics of the aircraft wheel during the braking process, and based on the motion characteristics, the braking torque corresponding to the target slip speed and target deceleration rate can be obtained. Disturbance observation: there are many uncertain factors in the braking control system, such as the nonlinear change of the brake disc torque coefficient, random environmental factors, etc. In order to reduce the interference of these factors on the braking as much as possible, some sensors are usually used to observe and estimate different disturbances. The aircraft and wheel dynamics system includes the dynamic characteristics of the aircraft and the wheel during the braking process. The braking torque is input into the aircraft and wheel dynamics system, which can further calculate the position, speed, wheel angular velocity and other important parameters of the aircraft.

[0092] Specifically, please refer to Figure 4 The embodiment provides a fixed-point braking control system, which comprises a road planning module, a local MPC planning controller and a lower slip state controller.

[0093] The road planning module is used for acquiring an initial position and an initial speed of the aircraft, and performing road planning to obtain a deceleration profile and a deceleration rate range of the aircraft position and speed corresponding to the optimal deceleration state that can be supported by the runway. The road planning module is used for runway optimization and state estimation, that is, the state of the aircraft is estimated during the braking process, and in the initial stage of the aircraft landing without braking, the runway optimization technology is used for road planning, the runway safety threshold is searched, the optimal deceleration state that can be supported by the runway is obtained, and then the basic deceleration relationship about the position and speed of the aircraft is obtained by optimization.

[0094] The local MPC planning controller obtains the calculation result of the road planning module in real time, and performs local MPC planning to obtain a target deceleration rate and a target slip rate. The MPC planning controller is provided with a longitudinal kinematics model and a speed-position evaluation function. The local MPC planning controller adjusts the current slip state to the target slip state according to the current feedback state.

[0095] The lower layer slip state controller acquires the output result of the local MPC planning in real time, and calculates the wheel target brake torque to control the brake system to brake according to the wheel target brake torque; the lower layer slip state controller is also used to acquire the output signal of the control system to realize closed-loop control. That is, the target slip state output by the local MPC planning controller enters the lower layer slip state controller, and the closed-loop control is realized for the wheel brake system to complete the anti-skid braking process with faster response speed, realize the fixed-point braking, and ensure the safety of the braking process. Specifically, the local MPC planning controller acquires the current position of the aircraft, the current speed of the aircraft, and the current deceleration of the aircraft in real time, so as to realize the closed-loop control through the local MPC planning controller.

[0096] In the implementation, the local MPC planning controller generates the target slip state conforming to the optimal state constraint according to the current feedback of the actual state of the aircraft, so as to realize the closed-loop control of the slip state of the aircraft wheel by the lower layer slip controller.

[0097] In Figure 4 , the aircraft and wheel dynamics system is used to represent the brake system, and in the actual application, the aircraft can be braked by the brake system according to the corresponding torque, the current position X of the aircraft, and the current speed v p and the current deceleration a p of the aircraft can be obtained through sensors or calculation.

[0098] The above detailed description of the structure, features and effects of the application is based on the embodiments shown in the drawings, and the above description is only the preferred embodiment of the application, but the application is not limited by the drawings. Any change or modification made according to the concept of the application, or equivalent embodiment with equivalent changes, as long as it does not exceed the spirit of the specification and drawings, shall be within the protection scope of the application.

Claims

1. A fixed-point braking control method, characterized in that: The following steps are involved: S1, obtain the initial position and initial speed of the aircraft; S2, through pavement optimization, obtains the aircraft position, aircraft speed deceleration profile, and deceleration rate range corresponding to the optimal deceleration state that the pavement can support; S3, real-time acquisition of the aircraft's current position and speed; S4, perform local MPC planning to obtain the target deceleration rate and target slip rate; S5, determining a target wheel braking torque according to the target deceleration rate and the target slip rate, and braking according to the target wheel braking torque; S6, repeating steps S3 to S5 until the aircraft's fixed-point braking is completed; In step S4, local MPC planning is performed by inputting the results obtained in steps S1-S3 into a pre-set local optimization model; In the local optimization model, the objective evaluation function is: ; in, is the prediction step length, To control the step size, is the full-distance position-speed reference value obtained by the road planning module, To control the output increment, is the weight coefficient matrix of the system output, is the weight coefficient matrix of the system control quantity, is the weight coefficient matrix for controlling the increment; In each control cycle, the local optimization problem is: ; in, is the maximum deceleration rate that the road surface can support, and are all state matrices.

2. The fixed-point braking control method according to claim 1, characterized in that: The maximum deceleration rate that the road surface can support is calculated from the deceleration rate obtained by optimization, and the formula is: ; in, , is the safety margin of the aircraft deceleration rate, The wheel deceleration rate obtained by searching for the optimal value is: is the wheel radius.

3. The fixed-point braking control method according to claim 1, characterized in that: In step S4, the goal is to obtain the highest possible ground engagement force utilization and braking efficiency under optimal state constraints.

4. A fixed-point brake control system using the fixed-point brake control method according to any one of claims 1 to 3, characterized in that: It includes a road planning module, a local MPC planning controller and a lower-layer slip state controller; The path planning module is used to obtain the initial position and initial speed of the aircraft and perform path planning to obtain the aircraft position, aircraft speed deceleration profile and deceleration rate range corresponding to the optimal deceleration state that the road surface can support; The local MPC planning controller obtains the calculation results of the road planning module in real time and performs local MPC planning to obtain a target deceleration rate and a target slip rate; The lower-layer slip state controller obtains the output results of the local MPC planning in real time and calculates the target wheel braking torque to control the braking system to brake according to the target wheel braking torque; the lower-layer slip state controller is also used to obtain the output signal of the control system to achieve closed-loop control.

5. The fixed-point brake control system according to claim 4, characterized in that: The local MPC planning controller obtains the current position, current speed and current deceleration rate of the aircraft in real time, so as to realize closed-loop control through the local MPC planning controller.

6. The fixed-point brake control system according to claim 5, characterized in that: The local MPC planning controller generates a target slip state that meets the optimal state constraint based on the current feedback of the actual state of the aircraft, so that the lower-level slip controller can use this as a target to achieve closed-loop control of the aircraft wheel slip state.

7. The fixed-point brake control system according to claim 4, characterized in that: The road planning module includes a road surface optimization unit.

Citation Information

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