Distributed active fault-tolerant control method for four-wheel steer-by-wire system

Abstract

The distributed active fault-tolerant control method of four-wheel steer-by-wire system relates to the field of four-wheel steer-by-wire system control of automobile, which determines the ideal automobile yaw angular velocity and mass center side slip angle of four wheels through a reference model; determines the real-time yaw angular velocity and mass center side slip angle of four wheels through a four-wheel yaw angular velocity and mass center side slip angle calculation module; determines the weighted adjacent matrix, degree matrix and Laplace matrix of four wheels through a four-wheel intelligent agent information exchange topological structure module; solves out the four-wheel steering angle of automobile under the condition of known / unknown actuator fault through a distributed active fault-tolerant control module of four-wheel steer-by-wire system; realizes the yaw stability control of automobile through a CarSim automobile model, and outputs the real-time motion state information of automobile. The application effectively balances the calculation efficiency and vehicle stability performance, and improves the safety and stability of four-wheel steer-by-wire system under the condition of actuator gain variation fault, constant deviation fault and stuck fault.

Description

Technical Field

[0001] This invention relates to the field of automotive four-wheel steer-by-wire system control, and mainly to an adaptive distributed fault-tolerant control method for a four-wheel steer-by-wire system. Background Technology

[0002] With the continuous development of automotive electronics technology and the integration of automotive systems, four-wheel steering (4WS) based on steer-by-wire technology will become an important component of the vehicle's active chassis control. It eliminates the traditional mechanical steering system; steering signals are transmitted to the electronic control unit (ECU) via sensors, and after analysis and processing by the ECU, control signals are transmitted to the steering motor. The steering motor then generates the required steering torque based on the control signals, thereby realizing the driver's steering intention. Four-wheel steer-by-wire vehicles rely on flexible control strategies for all four wheels, enabling smaller turning radii and more flexible driving directions. This allows for free steering under extreme conditions and diagonal straight-line driving, ensuring vehicle stability in extreme environments. However, the introduction of electronic components such as sensors, controllers, and steering motors increases the probability of system failures. Depending on the location of the failure, it can be categorized as sensor failure, ECU failure, communication bus failure, and actuator failure. In particular, when the actuators in the control loop that execute control commands experience gain variation, constant deviation, or jamming failures and cannot correctly execute control commands, the vehicle may completely lose its steering ability. Road surface excitation can then cause the front wheels to passively steer, easily leading to vehicle instability.

[0003] Reference 1 [Zhang Shenpeng, Zhang Dengfeng, Li Jun, et al. Fault-Tolerant Method for Four-Wheel Steering Vehicle Based on Control Allocation [J]. Control Engineering, 2019, 26(06): 1035-1041] addresses the potential gain-type abnormal faults in the vehicle steering mechanism by converting them into perturbations of the system's time-varying parameters. A robust fault-tolerant control allocation method capable of suppressing these perturbations is presented, thus ensuring the stability of vehicle handling and good fault-tolerant performance under fault conditions. Reference 2 [Wang Zhimin. Research on Fault-Tolerant Control of Four-Wheel Independent Drive Electric Vehicle Steer-by-Wire System [D]. Jiangsu University, 2023] designs fault-tolerant control for steer-by-wire systems based on hardware redundancy and software fault tolerance for various fault types. Considering the complexity of the fault-tolerant control system model, a data-driven model-free adaptive sliding mode control algorithm is designed to derive the compensated yaw moment and differential steering moment. Reference 3 [Huang Chao, Huang Hailong, Naghdy Fazel, Du Haiping, Ma Dazhong, Actuator fault-tolerant control for steer-by-wire systems, International Journal of Control, Vol 94(11):3123-3134] proposes a two-stage Kalman filter algorithm to detect actuator faults in the fault detection and isolation module. The outputs of fault detection and isolation are used to update fault information, and a model predictive control method is proposed to maintain the handling stability of the steer-by-wire system. The overdrive configuration of four-wheel steer-by-wire systems provides the possibility for controller reconfiguration under fault conditions and improves vehicle driving safety. However, the overdrive configuration of four-wheel steer-by-wire systems also increases model complexity, which poses a greater challenge to the design of fault-tolerant control laws.

[0004] Multi-agent systems achieve complex intelligence through the cooperation of various agents, reducing system modeling complexity while improving system robustness, reliability, and flexibility. They have been widely applied in fields such as aircraft formation, sensor networks, data fusion, parallel computing, and traffic vehicle control. Therefore, this invention introduces vector transformation and multi-agent methods to improve the safety of four-wheel steer-by-wire systems in the event of actuator failure. Summary of the Invention

[0005] To improve the safety and stability of four-wheel steer-by-wire systems under conditions of actuator gain variation faults, constant deviation faults, and jamming faults, this invention proposes an adaptive distributed fault-tolerant control method for four-wheel steer-by-wire systems to address the uncertainty of system modeling parameters.

[0006] The technical solution adopted by this invention to solve the technical problem is as follows:

[0007] The distributed active fault-tolerant control method for a four-wheel steer-by-wire system includes the following steps:

[0008] Step 1: Based on the steering wheel angle given by the driver and the real-time speed of the car output by the CarSim car model, determine the ideal yaw rate and center of gravity sideslip angle of the four wheels through the reference model.

[0009] Step 2: Based on the real-time motion state information of the car output by the CarSim car model, use the four-wheel yaw rate and center of gravity sideslip angle calculation module to obtain the real-time yaw rate and center of gravity sideslip angle of the four wheels.

[0010] Step 3: Based on the hardware connection structure and internal communication of the four-wheel independent steering vehicle, determine the topology of the four wheel steering agents, and obtain the weighted adjacency matrix, degree matrix and Laplace matrix for information exchange between the four wheel steering agents based on graph theory.

[0011] Step 4: Based on the real-time yaw rate and sideslip angle of the four wheels obtained in Step 2, the ideal yaw rate and sideslip angle of the four wheels obtained in Step 1, the weighted adjacency matrix, degree matrix and Laplace matrix used for information exchange between the four wheel steering agents obtained in Step 3, and the real-time motion state information of the vehicle, the steering angles of the four wheels of the vehicle are solved using the distributed active fault-tolerant control module of the four-wheel steer-by-wire system.

[0012] Step 5: Based on the four wheel rotation angles obtained in Step 4, use the CarSim car model to implement yaw stability control of the car and output the real-time motion state information of the car, including the real-time speed, real-time yaw rate, real-time center of gravity sideslip angle and real-time road adhesion coefficient.

[0013] The beneficial effects of this invention are as follows:

[0014] 1) A dynamic model of four wheel steering subsystems with two degrees of freedom and single input was established based on vector transformation. The hardware connection structure and internal communication of the four-wheel steering vehicle were used to treat the deviation equations of the yaw rate, the center of gravity sideslip angle and the ideal value of each wheel steering subsystem as an independent steering agent. The weighted adjacency matrix, degree matrix and Laplace matrix between the four wheel steering agents were obtained based on graph theory, so as to achieve model decoupling.

[0015] 2) Considering the uncertainty of the modeling process of the i-th agent in the case of known actuator failure, an adaptive estimation of the uncertainty term based on the sliding surface function is proposed. Based on this, a distributed active fault-tolerant control method for a four-wheel steer-by-wire system based on multiple agents is proposed to simplify the algorithm structure and solution process.

[0016] 3) For cases where actuator failure is unknown, a sliding mode extended state observer with sliding surface function as state variable is proposed. Based on this, a distributed active fault-tolerant control method for a four-wheel drive-by-wire system based on the state observer is proposed, which simplifies the algorithm structure and solution process.

[0017] 4) This method provides a new design approach for collaborative fault-tolerant control of other heterogeneous multi-agent systems;

[0018] 5) The method of the present invention is simple and easy to implement, has a wide range of applications, and is suitable for widespread promotion and application. Attached Figure Description

[0019] Figure 1 This is a schematic diagram illustrating the principle of the distributed active fault-tolerant control method for the four-wheel steer-by-wire system of the present invention.

[0020] Figure 2 This is a schematic diagram of the information exchange topology of the four steering agents of the present invention. Detailed Implementation

[0021] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0022] like Figure 1 As shown, the distributed active fault-tolerant control method for the four-wheel steer-by-wire system of this invention includes a reference model, a four-wheel yaw rate and sideslip angle calculation module, an information exchange topology for four steering agents, a distributed active fault-tolerant control module for the four-wheel steer-by-wire system, and a CarSim vehicle model. The reference model is used to determine the ideal yaw rate and sideslip angle of the four wheels; the four-wheel yaw rate and sideslip angle calculation module is used to determine the real-time yaw rate and sideslip angle of the four wheels; the four-wheel steering agent information exchange topology module is used to determine the weighted adjacency matrix, degree matrix, and Laplace matrix of the four wheels; the distributed active fault-tolerant control module for the four-wheel steer-by-wire system is used to solve for the steering angles of the four wheels of the vehicle under known / unknown actuator fault conditions; the CarSim vehicle model implements yaw stability control of the vehicle and outputs real-time motion state information of the vehicle, including real-time vehicle speed, real-time yaw rate, real-time sideslip angle, real-time road adhesion coefficient, real-time vertical load, and real-time wheel steering angles.

[0023] like Figure 2 As shown, this invention treats four independent wheel steering systems as four heterogeneous intelligent agents. Based on the communication and hardware connection between the four wheel steering systems, a topological structure for information exchange among the four wheel steering subsystems is established. The weighted adjacency matrix, degree matrix, and Laplace matrix among the four wheel steering intelligent agents are obtained based on graph theory.

[0024] The specific implementation steps of the distributed active fault-tolerant control method for the four-wheel steer-by-wire system of the present invention are as follows:

[0025] 1. Reference Model

[0026] (1) Ideal four-wheel steering angle of a four-wheel independent steering system based on Ackermann geometry

[0027] When a car is turning, the wheels can only roll purely, effectively reducing cornering resistance, if the Ackermann geometry principle is satisfied. Therefore, assuming that at a certain moment the steering wheels of a four-wheel independently steering car are rotating around the same instantaneous center o', let δ dr For steering wheel angle, Let k be the ideal wheel angle for the i-th wheel, where i = 1, 2, ..., 4 represent the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. dr This is the gear ratio of the left front wheel steering system. According to Ackermann's principle of geometry, we can obtain:

[0028]

[0029] In the formula, k f For the front wheel lateral stiffness, k r This refers to the rear wheel lateral stiffness. d For wheelbase, l f l r These are the distances from the front and rear axles to the center of mass, respectively. x Let m be the car's speed, m be the car's mass, and K be the coefficient. δ for:

[0030]

[0031] (2) The ideal yaw rate and sideslip angle generated at the center of mass under the action of the lateral force of the i-th wheel alone.

[0032] Maintaining a zero sideslip angle at the vehicle's center of gravity during steering improves handling stability and maneuverability. Four-wheel independent steering vehicles can maintain a zero sideslip angle at the center of gravity over a wide speed range, meaning the ideal sideslip angle for the i-th wheel is achieved.

[0033] To reduce abrupt changes in the driver's steering input, an ideal yaw rate can be generated at the center of gravity when the forces of the four wheels act independently. Introducing a first-order inertial element

[0034]

[0035] In the formula, k γi τ is the steady-state gain of the ideal yaw rate. γiThe time constant for the ideal yaw rate response.

[0036]

[0037] In the formula, η1=l f η2=l f η3=-l r η4=-l r k1, k2, k3, and k4 represent the lateral stiffness of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. z Let θ be the moment of inertia of the car. kγi and θ τγi These are design parameters for improving the dynamic characteristics of the system.

[0038] 2. Yaw velocity and sideslip angle calculation module

[0039] According to Newton's laws, the differential equations of motion for a linear two-degree-of-freedom car model can be described as follows:

[0040]

[0041] In the formula, γ and β represent the yaw rate and sideslip angle at the vehicle's center of gravity, respectively, when the lateral forces of the four wheels act together. yi Let be the lateral force of the i-th wheel.

[0042] Let γ i β i Let be the yaw rate and sideslip angle at the vehicle's center of gravity when the lateral force of the i-th wheel acts alone, respectively, satisfying:

[0043] γ=γ1+γ2+γ3+γ4, β=β1+β2+β3+β4

[0044] make η1=l f η2=l f η3=-l r η4=-l r Therefore, the differential equation of motion (3) of the linear two-degree-of-freedom car model can be rewritten in the following form:

[0045]

[0046] The slip angle of each wheel can be calculated from the equations of motion and corresponding geometric relationships of the linear two-degree-of-freedom car model, as follows:

[0047]

[0048] In the formula, δ i Let α be the wheel angle of the i-th wheel.i Let be the sideslip angle of the i-th wheel, where i = 1, 2, ..., 4.

[0049] Using the Magic Formula tire model, the formula for calculating the lateral force of the i-th wheel is as follows:

[0050] F yi =D fi ·sin(C fi arctan(B) fi ·x yi -E fi (B fi ·x fi -arctan(B fi ·x fi ))))+S vi (6)

[0051] In the formula:

[0052]

[0053] In the formula, B of the i-th wheel fi D is the stiffness factor. fi C is the peak factor. fi E is the curve shape factor. fi A is the curvature factor of the curve. Πi For the fitting parameters, Π = 0, 1, 2, ..., 13, A is obtained through experiments. 0i =1.65, A 1i =-34, A 2i =1250, A 3i =3036, A 4i =12.8, A 5i =0, A 6i =0.021, A 7i =0.7739, A 8i =0.0029, A 9i =0.0134, A 10i =0.0037, A 11i =19.1656, A 12i =1.2136, A 13i =6.2621. γ φi F is the camber angle of the i-th wheel; zi Let be the vertical load on the i-th wheel, where i = 1, 2, ..., 4.

[0054] Substituting the slip angle (5) of each wheel into equation (6) yields the lateral forces of the four wheels. Then, substituting these forces into the motion differential equation (4) of the linear two-degree-of-freedom car model, and integrating, yields the yaw rate γ generated at the vehicle's center of gravity under the action of the lateral force of the i-th wheel alone.i And the centroid side slip angle β i

[0055]

[0056] 3. Information exchange topology of four-wheel steering agents

[0057] (1) Dynamic model of the i-th wheel steering subsystem

[0058] When the lateral acceleration of the car is within 0.4g, the tire lateral stiffness is within the linear range, and the slip angle is small, the change in tire lateral stiffness Δk is considered. i and the residual lateral force ΔF of the tire yi The lateral force F of the i-th wheel in equation (4) yi Write it in the following form

[0059] F yi =(k i +Δk i )α i +ΔF yi (9)

[0060] In the formula, k i (i = 1, 2, 3, 4) represents the lateral stiffness of the i-th wheel. α i (i = 1, 2, 3, 4) is the sideslip angle of the i-th wheel.

[0061] Substituting γ = γ1 + γ2 + γ3 + γ4 and β = β1 + β2 + β3 + β4 into equation (5), we get the slip angles of each wheel:

[0062]

[0063] In the formula, δ i Let i = 1, 2, ..., 4 be the steering angle of the i-th wheel steering system, and α be the steering angle of the i-th wheel steering system. i Let w be the slip angle of the i-th wheel. αi This refers to the impact of other steering subsystems on this system.

[0064] w α1 =-(β2+β3+β4)-l f (γ2+γ3+γ4) / v x

[0065] w α2 =-(β1+β3+β4)-l f (γ1+γ3+γ4) / v x

[0066] w α3 =-(β2+β1+β4)+l r(γ2+γ1+γ4) / v x

[0067] w α4 =-(β2+β3+β1)+l r (γ2+γ3+γ1) / v x

[0068] Let w i =Δk i α i +ΔF yi +(k i +Δk i )w αi , representing the modeling error of the linear model of the i-th tire force, substituting equation (4) into equation (3), we get:

[0069] F yi =k i δ i -k i β i -k i η i γ i / v x +w i (11)

[0070] Substituting equation (10) into equation (9), we obtain the dynamic model of the i-th wheel steering subsystem:

[0071]

[0072] It can be seen that, through vector transformation, the 2-DOF 4-input vehicle dynamics model (1) is written as a coordinated form of 4 2-DOF single-input steering subsystem dynamics models (12).

[0073] (2) Ideal dynamic model of the i-th wheel steering subsystem

[0074] Under the ideal four-wheel steering angle of a four-wheel independent steering system obtained based on Ackermann geometry, the ideal lateral force of the i-th wheel can be obtained as follows:

[0075]

[0076] In the formula, w i * This represents the impact of other wheel steering subsystems under ideal conditions on this system. δ i * (i = 1, 2, 3, 4) represents the ideal turning angle of the i-th wheel.

[0077] w1 * =-(β2) * +β3* +β4 * )-l f (γ2 * +γ3 * +γ4 * ) / v x

[0078] w2 * =-(β1) * +β3 * +β4 * )-l f (γ1 * +γ3 * +γ4 * ) / v x

[0079] w3 * =-(β2) * +β1 * +β4 * )+l r (γ2 * +γ1 * +γ4 * ) / v x

[0080] w4 * =-(β2) * +β3 * +β1 * )+l r (γ2 * +γ3 * +γ1 * ) / v x

[0081] According to equation (9), the ideal lateral force of the i-th wheel is obtained as follows:

[0082] F yi * =k i α i * (14)

[0083] Based on equations (4), (13), and (14), the ideal dynamic model of the i-th wheel steering subsystem is established as follows:

[0084]

[0085] (3) Deviation equation

[0086] Define Δγ i =γ i -γ i * Δβi =β i -β i * ,Δδ i =δ i -δ i * , Δw i =w i -w i * According to equations (12) and (15), the deviation equations of the yaw rate and sideslip angle of the i-th wheel steering subsystem from the ideal values ​​can be obtained as follows:

[0087]

[0088] (4) Graph-based information exchange topology of four steering agents

[0089] The deviation equation of each wheel steering subsystem is treated as a steering agent. Based on the communication and hardware connection between the four wheel steering subsystems, an auxiliary system is established. Figure 2 The topology of information exchange between the four wheel steering subsystems is shown.

[0090] The weighted adjacency matrix, degree matrix, and Laplace matrix among the four steering agents are obtained using graph theory. Let V = {1, 2, ..., N} be a non-empty subset associated with the N steering agents, where N is the number of steering agents, and N = 4. Let a be the boundary of a set of N steering agents, and let a be the connection weight between the i-th steering agent and the j-th steering agent. ij When (i,j)∈ε, a ij >0. The weighted adjacency matrix of N turning agents is defined as A = [a ij ]∈R N×N The degree matrix of N turning agents is defined as D = diag{d1,d2,...,d...} N},in The Laplace matrix is ​​defined as L∈R N×N The condition L = DA is satisfied. According to the appendix... Figure 2 From the structure, we can obtain the weighted adjacency matrix, degree matrix, and Laplace matrix for information exchange among the four steering agents:

[0091]

[0092] 4. Distributed active fault-tolerant control for four-wheel drive electric vehicles

[0093] (1) Distributed active fault-tolerant control of four-wheel steer-by-wire system under known actuator failure conditions

[0094] Considering the three typical types of actuator faults in a four-wheel steer-by-wire system: gain variation fault (multiplicative fault), constant deviation fault (additive fault, here referring to a fixed value), and jamming fault (constant actuator output). The actuator output under different fault conditions is uniformly described by the following formula:

[0095] u fi =(1-ξ i )u i +r i (18)

[0096] Where, ξ i r represents the actuator gain variation coefficient. i The value u represents the value indicating whether the actuator has a constant deviation fault or a jamming fault. i This represents the actuator output under normal operating conditions. Based on the actuator fault characteristics, the normal state is: ξ i =0, r i =0; Gain variation fault: 0 < ξ i <1, r i =0; Constant deviation fault: ξ i =0, r i ≠0; Fault causing a jam: ξ i =1, r i ≠0.

[0097] make:

[0098] u fi =Δδ i

[0099] Equation (16) can be rearranged into the following form:

[0100]

[0101] make For B i The pseudo-inverse matrix satisfies Design a pseudo-inverse matrix It is in the following form:

[0102]

[0103] Multiply both sides of equation (19) We can obtain:

[0104]

[0105] make ε i =∑a ij (e i -e j )+b i ei Select a non-singular terminal sliding surface:

[0106]

[0107] In the formula, 1 < q / p < 2, and q and p are odd numbers.

[0108] Design the actuator output u under known fault conditions. i :

[0109]

[0110] In the formula, k s >0, For Δw i The estimated value is obtained online using the following adaptive law. i The estimated value

[0111]

[0112] By designing the non-singular terminal sliding surface (22) of the i-th wheel steering agent, the output of the actuator (23) and The adaptive rate (24) enables the vehicle's center of gravity sideslip angle and yaw rate to quickly follow the ideal value when the actuator failure is known.

[0113] (2) Distributed active fault-tolerant control of four-wheel steer-by-wire system based on fault state observer

[0114] When the actuator fault parameter ξ i r i In the case of unknown faults, in order to isolate the faulty items, the actuator output (18) under the faulty condition is transformed as follows:

[0115] u fi =u i +(-ξ i u i +r i (25)

[0116] Let f i If the actuator is faulty, then:

[0117] f i =-ξ i u i +r i (26)

[0118] Equation (21) can be rearranged into the following form:

[0119]

[0120] Design the actuator output u under unknown fault conditions. i :

[0121]

[0122] In the formula, f i Δw i The estimated value is obtained online using the following adaptive law. i The estimated value

[0123]

[0124] In the formula, τ i >0, κ 1i >0.

[0125] For actuator failure f i For unknown situations, a sliding mode expansion state observer with sliding mode surface functions as observer state variables is proposed to realize the observation of unknown actuator faults f. i Observations f i The observer design is as follows:

[0126]

[0127] In the formula, and s i and f i The estimated value, k 1i >0, k 2i >0. And the design parameter k s k 2i κ 2i κ 1i ρ, p, and q satisfy

[0128]

[0129] In the formula, κ 1i >0, κ 2i >0, |Δf i | up For Δf i The upper bound of the absolute value.

[0130] For a four-wheel steer-by-wire system with unknown actuator failure, a non-singular terminal sliding surface (22) for the i-th steering agent and an actuator output (28) under unknown failure conditions are designed. Adaptive rate (29), actuator failure f iWith the observer (30) and the constraint (31), the actual yaw rate and the center of gravity sideslip angle of the vehicle can be quickly followed to their ideal values ​​when the actuator failure is unknown.

Claims

1. A distributed active fault-tolerant control method for a four-wheel steer-by-wire system, characterized in that, The method includes the following steps: Step 1: Based on the steering wheel angle given by the driver and the real-time speed of the car output by the CarSim car model, determine the ideal yaw rate and center of gravity sideslip angle of the four wheels through the reference model. Step 2: Based on the real-time motion state information of the car output by the CarSim car model, use the four-wheel yaw rate and center of gravity sideslip angle calculation module to obtain the real-time yaw rate and center of gravity sideslip angle of the four wheels. Step 3: Based on the hardware connection structure and internal communication of the four-wheel independent steering vehicle, determine the topology of the four wheel steering agents, and obtain the weighted adjacency matrix, degree matrix and Laplace matrix for information exchange between the four wheel steering agents based on graph theory. Step 4: Based on the real-time yaw rate and sideslip angle of the four wheels obtained in Step 2, the ideal yaw rate and sideslip angle of the four wheels obtained in Step 1, the weighted adjacency matrix, degree matrix, and Laplace matrix used for information exchange between the four wheel steering agents obtained in Step 3, and the real-time motion state information of the vehicle, the steering angles of the four wheels of the vehicle are solved using the distributed active fault-tolerant control module of the four-wheel steer-by-wire system. The calculation process is as follows: (1) Distributed active fault-tolerant control of four-wheel steer-by-wire system under known actuator failure conditions The actuator output of the four-wheel steer-by-wire system under different types of fault conditions is uniformly described by the following formula: (18) in, This represents the actuator gain variation coefficient. The value indicates whether the actuator has experienced a constant deviation fault or a jamming fault. This indicates the actuator output under normal operating conditions. These represent the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively; according to the actuator fault characteristics, the normal state is: =0、 =0; Gain variation fault: , =0; Constant deviation fault: =0、 ;Stuck fault: =1、 ; make: ， ， ， In the formula, , , ; , These are the yaw rate and sideslip angle at the center of gravity of the vehicle when the lateral force of the i-th wheel acts alone. Let be the lateral stiffness of the i-th wheel. For the rotational inertia of the car, For car speed, For the quality of the car, , , , ; , These are the distances from the front and rear axles to the center of mass, respectively. , These are the ideal yaw rate and ideal sideslip angle at the vehicle's center of gravity when the lateral force of the i-th wheel acts alone. Let i be the wheel angle of the i-th wheel. The ideal wheel angle for the i-th wheel; The first The deviation equations of the yaw rate and the center-of-gravity sideslip angle of the individual wheel steering subsystem from the ideal values ​​can be summarized as follows: (19) In the formula, , This represents the modeling error of the linear force model for the i-th tire. The impact of other wheel steering subsystems on this system under ideal conditions; make for The pseudo-inverse matrix satisfies Design a pseudo-inverse matrix It is in the following form: (20) Multiply both sides of equation (19) We can obtain: (21) make , In the formula, Let the connection weights of the i-th and j-th steering agents be... Let N be a non-empty subset associated with N turning agents, where N is the number of turning agents. , Let N be the boundary of the set of turning agents, when hour, ; This represents the information connection weight between the i-th turning agent and the virtual reference node. Select a non-singular terminal sliding surface: (22) In the formula, q and p are odd numbers; Design parameters for non-singular terminal sliding surfaces. ; Design the actuator output under known fault conditions. : (23) In the formula, , for The estimated value is obtained online by designing the following adaptive law. The estimated value : (24) In the formula, ; By designing the non-singular terminal sliding surface (22) of the i-th wheel steering agent, the output of the actuator (23) and The adaptive rate (24) enables the vehicle's center of gravity sideslip angle and yaw rate to quickly follow the ideal value when the actuator failure is known. (2) Distributed active fault-tolerant control of four-wheel steer-by-wire system based on fault state observer When the actuator fault parameters , In the case of unknown faults, in order to isolate the faulty items, the actuator output (18) under the faulty condition is transformed as follows: (25) make If the actuator is faulty, then: (26) Equation (21) can be rearranged into the following form: (27) Design actuator output under unknown fault conditions : (28) In the formula, , They are respectively , The estimated value is obtained online by designing the following adaptive law. The estimated value : (29) In the formula, , , for The estimated value; For actuator failure For unknown situations, a sliding mode expansion state observer with sliding mode surface functions as observer state variables is proposed to realize the observation of unknown actuator faults. Observations ; The observer design is as follows: (30) In the formula, for The estimated value, , And design parameters , , , , , and satisfy ， ， (31) In the formula, , , , for Upper bound of absolute value; For a four-wheel steer-by-wire system with unknown actuator failure, a non-singular terminal sliding surface (22) for the i-th steering agent and an actuator output (28) under unknown failure conditions are designed. Adaptive rate (29), actuator failure With the observer (30) and the constraint (31), the actual yaw rate and the center of gravity sideslip angle of the whole vehicle can be quickly followed to their ideal values ​​when the actuator failure is unknown. Step 5: Based on the four wheel rotation angles obtained in Step 4, use the CarSim car model to implement yaw stability control of the car and output the real-time motion state information of the car, including the real-time speed, real-time yaw rate, real-time center of gravity sideslip angle and real-time road adhesion coefficient.

2. The distributed active fault-tolerant control method for a four-wheel steer-by-wire system as described in claim 1, characterized in that, Step one, which involves determining the ideal yaw rate and sideslip angle of the four wheels based on the steering wheel angle given by the driver and the real-time speed of the car output by the CarSim car model, includes the following steps: (1) Ideal four-wheel steering angle of a four-wheel independent steering system based on Ackermann geometry Suppose that at a certain moment, the steering wheels of a four-wheel independent steering car are rotating around the same instantaneous center o', let For steering wheel angle, For the ideal wheel angle of the i-th wheel, These represent the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively; let This is the gear ratio of the left front wheel steering system. According to Ackermann's principle of geometry, we can obtain: ， ， In the formula, For the front wheel lateral stiffness, Rear wheel lateral stiffness; Wheelbase , These are the distances from the front and rear axles to the center of mass, respectively. For car speed, For vehicle mass, coefficient for: (2) The ideal yaw rate and sideslip angle generated at the center of mass under the action of the lateral force of the i-th wheel alone. During steering, maintain the vehicle's center of gravity sideslip angle at zero, i.e., the ideal center of gravity sideslip angle for the i-th wheel. , ; When the forces of the four wheels act individually, the ideal yaw rate generated at the center of mass is... Introducing a first-order inertial element (1) In the formula, The steady-state gain for the ideal yaw rate; Let be the ideal yaw rate response time constant; ∠ is the complex frequency domain variable in the Laplace transform; ， (2) In the formula, , , , ; , The lateral stiffness of the left front wheel, right front wheel, left rear wheel, and right rear wheel are respectively. The moment of inertia of the car; and These are design parameters for improving the dynamic characteristics of the system.

3. The distributed active fault-tolerant control method for a four-wheel steer-by-wire system as described in claim 2, characterized in that, The calculation methods for the real-time yaw rate and sideslip angle of the four wheels mentioned in step two are as follows: According to Newton's laws, the differential equations of motion for a linear two-degree-of-freedom car model can be described as follows: (3) In the formula, , These are the yaw rate and sideslip angle at the center of gravity of the vehicle when the lateral forces of the four wheels act together. The lateral force of the i-th wheel; make , Let be the yaw rate and sideslip angle at the vehicle's center of gravity when the lateral force of the i-th wheel acts alone, respectively, satisfying: ， make , , , , , , , , , , , Therefore, the differential equation of motion (3) of the linear two-degree-of-freedom car model can be rewritten in the following form: (4) The slip angle of each wheel can be calculated from the equations of motion and corresponding geometric relationships of the linear two-degree-of-freedom car model, as follows: (5) In the formula, Let i be the wheel angle of the i-th wheel. Let be the sideslip angle of the i-th wheel. ; Using the Magic Formula tire model, the formula for calculating the lateral force of the i-th wheel is as follows: (6) In the formula: (7) In the formula, the i-th wheel Stiffness factor As the peak factor, For curve shape factor, For the curvature factor of the curve, For fitting parameters, Obtained through experiments =1.65, =-34, =1250, =3036, =12.8, =0, =0.021, =0.7739, =0.0029, =0.0134, =0.0037, =19.1656, =1.2136, =6.2621; Let θ be the camber angle of the i-th wheel; Let be the vertical load on the i-th wheel. ; Substitute the slip angles of each wheel into equation (6) to obtain the lateral forces of the four wheels. Then, substitute these forces into the differential equation of motion (4) of the linear two-degree-of-freedom car model. After integration, obtain the yaw rate at the center of gravity of the vehicle under the action of the lateral force of the i-th wheel alone. and centroid side slip angle (8)。 4. The distributed active fault-tolerant control method for a four-wheel steer-by-wire system as described in claim 3, characterized in that, Step three includes the following steps: (1) Dynamic model of the i-th wheel steering subsystem When the lateral acceleration of the vehicle is within 0.4g, the tire lateral stiffness is within the linear range, and the slip angle is small, the change in tire lateral stiffness should be considered. and the residual lateral force of the tire The lateral force of the i-th wheel in equation (4) Write it in the following form (9) In the formula, It is the lateral stiffness of the i-th wheel; It is the sideslip angle of the i-th wheel; Will , Substituting into equation (5), the slip angles of each wheel are: (10) In the formula, , Let i be the steering angle of the i-th wheel steering system. Let i be the slip angle of the i-th wheel. The impact of other steering subsystems on this system; make , representing the modeling error of the linear model of the i-th tire force, substituting equation (4) into equation (3), we get: (11) Substituting equation (10) into equation (9), we obtain the dynamic model of the i-th wheel steering subsystem: (12) It can be seen that, through vector transformation, the 2-DOF 4-input vehicle dynamics model is written as a coordinated form of 4 2-DOF single-input steering subsystem dynamics models (12); (2) Ideal dynamic model of the i-th wheel steering subsystem Under the ideal four-wheel steering angle of a four-wheel independent steering system obtained based on Ackermann geometry, the ideal lateral force of the i-th wheel can be obtained as follows: (13) In the formula, The impact of other wheel steering subsystems on this system under ideal conditions; The ideal turning angle for the i-th wheel; According to equation (9), the ideal lateral force of the i-th wheel is obtained as follows: (14) Based on equations (4), (13), and (14), the ideal dynamic model of the i-th wheel steering subsystem is established as follows: (15) (3) Deviation equation definition , , , According to equations (12) and (15), we can obtain the first... The equations for the deviations of the yaw rate and sideslip angle of the individual wheel steering subsystem from the ideal values ​​are as follows: (16) (4) Graph theory-based information exchange topology of four-wheel steering agents The deviation equation of each wheel steering subsystem is regarded as a steering agent. Based on the communication and hardware connection between the four wheel steering subsystems, a topology for information exchange between the four wheel steering subsystems is established. The weighted adjacency matrix, degree matrix, and Laplacian matrix of the four wheel-steering agents are obtained using graph theory methods; let... Let N be a non-empty subset associated with N turning agents, where N is the number of turning agents, and N=4; Let N be the boundary of the set of N steering agents, and let the connection weight between the i-th steering agent and the j-th steering agent be... ,when hour, The weighted adjacency matrix of N turning agents is defined as follows: The degree matrix of N turning agents is defined as follows: ,in The Laplace matrix is ​​defined as follows: ,satisfy ; Based on the topology of information exchange among the four wheel steering subsystems, the weighted adjacency matrix, degree matrix, and Laplace matrix for information exchange among the four wheel steering agents can be obtained: ， ， (17)。

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