Integrated optimization control method for multi-axle vehicle under hub motor failure and failure

Abstract

This invention discloses an integrated optimization control method for multi-axle vehicles under hub motor failure and in-wheel motor malfunction, belonging to the field of multi-axle vehicle multi-wheel independent drive lateral dynamics control technology. First, an ideal dynamic model and reference behavior of the multi-axle vehicle are established. Then, based on the uncertainty of the vehicle dynamics system caused by tire cornering stiffness changes due to tire nonlinearity, the dynamics system of the multi-axle vehicle is rewritten to obtain an uncertain system. Next, based on the uncertain system, top-level and bottom-level controller designs are performed for the multi-axle vehicle under hub motor failure and in-wheel motor malfunction, realizing the yaw moment reconstruction and allocation constraints for each wheel, thus obtaining the optimal control method for the multi-axle vehicle under hub motor failure and in-wheel motor malfunction. This invention achieves optimal tracking performance under hub motor failure, realizing driving safety and energy efficiency for multi-axle vehicles.

Description

Technical Field

[0001] This invention belongs to the field of lateral dynamics control technology for multi-axle vehicles with independent multi-wheel drive, specifically involving an integrated optimization control method for multi-axle vehicles under hub motor failure and inertia. Background Technology

[0002] With increasing environmental pollution and energy issues, the traditional automotive industry has been severely impacted. While traditional cars bring convenience, they also bring many problems, such as traffic accidents and exhaust emissions. For safety and energy conservation reasons, distributed wheel drive vehicles have attracted attention in recent years, becoming a hot topic. In fact, thanks to the tireless efforts of researchers, distributed wheel drive vehicles, characterized by steering redundancy and rapid motor response, are often more maneuverable than ordinary cars. In driving, control flexibility is crucial, and few other vehicles can rival distributed wheel drive vehicles. The in-wheel motors can independently control each wheel, thus quickly and accurately distributing yaw torque. Overall, this technology is an effective way to alleviate energy shortages, and many academic researchers are still exploring its further potential.

[0003] Since the advent of the first automobile, traffic accidents have been a major headache, and vehicle safety must be given sufficient attention. For distributed hub-and-spoke vehicles, there are two main methods to improve handling stability: steering and motor system control. Relying solely on the former can easily lead to loss of control in extreme situations. The latter typically employs a hierarchical control structure to reduce drive redundancy, consisting of top-level and bottom-level controllers.

[0004] In recent years, research on top-level controllers has been established, and many effective algorithms have been proposed. Commonly used algorithms include fuzzy control, optimal control, sliding mode control, and adaptive algorithms. Considering the uncertainties of multi-axle vehicles, the desired yaw moment is calculated based on sliding mode control (SMC). It is well known that SMC is an effective method for handling uncertain nonlinear problems, but when using saturation functions to eliminate chattering, it affects the robustness of the control system. On the other hand, optimal control strategies can reduce control input, but the control effect may decrease due to uncertainties and modeling errors. To overcome the shortcomings of optimal control and sliding mode control, a robust optimal control strategy combining an optimal tracking controller with a sliding mode control law is proposed. The optimal controller is obtained based on a linear nominal model, and the sliding mode control law is derived from a defined integral sliding manifold, maintaining control effectiveness even in the presence of nonlinear modeling and environmental uncertainties. However, the unavoidable chattering problem is neglected and remains unresolved.

[0005] For the lower-level controller, yaw moment distribution should be performed while meeting the requirements of the upper-level controller. Generally, existing yaw moment vector control algorithms fall into two categories. One is a distribution algorithm that follows predetermined rules, typically considering vehicle and tire information. The other method for torque distribution is to solve an optimization problem that includes stability or other metrics. However, existing techniques only focus on how to coordinate the relationship between optimization objectives by treating the four wheels as a whole, rather than setting coordination coefficients for individual actuators. Since the number of actuators in the lower-level controller is greater than the number of system degrees of freedom, it is more reasonable to consider the weight adjustment of different actuators. Summary of the Invention

[0006] To address the issues of chattering in the top-level controller and unreasonable adjustment coefficients in the bottom-level controller in existing technologies, this invention provides an integrated optimization control method for multi-axle vehicles under hub motor faults and failures, considering both stability and economy. This invention designs a yaw moment distribution strategy under hub motor faults and a yaw moment reconstruction distribution strategy under hub motor failures. Furthermore, it utilizes high-order sliding mode control algorithms and optimal control algorithms to achieve integrated optimization control of multi-axle vehicles under hub motor faults and failures.

[0007] An integrated optimization control method for multi-axle vehicles under hub motor failure and in-wheel motor malfunction includes the following steps:

[0008] Step 1: Establish the dynamic model and reference behavior of the multi-axle vehicle;

[0009] In the aforementioned dynamic model, the longitudinal, lateral, and yaw motions, as well as wheel rotation, are described as follows:

[0010]

[0011]

[0012]

[0013]

[0014] Where m is the total mass of the vehicle; I z This refers to the yaw moment of inertia; J w It represents the moment of inertia of the wheels and motor; δ represents the front wheel steering angle; v x and v y These represent longitudinal and lateral velocities, respectively; w represents yaw rate, β represents sideslip angle; l f and l r d and R represent the distances from the center of gravity to the front and rear axles, respectively; d and R represent the truck width and rolling radius. F xi and F yi These represent the longitudinal and lateral forces on the tire, respectively.i T represents the wheel speed. i This represents the output torque of the electric motor. i = fl, fr, rl, rr, representing the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. D d It is an intermediate variable.

[0015] Treating the relationship between tire lateral force and slip angle as linear, therefore the tire lateral force F of the front and rear wheel sets... yf and F yr The calculations are as follows:

[0016]

[0017] Where C f and C r These represent the cornering stiffness of the front and rear wheels, respectively. α f and α r These are the slip angles of the front and rear wheels, calculated as follows:

[0018]

[0019] Where Δδ represents the additional front wheel angle.

[0020] To obtain the additional front wheel angle Δδ and yaw moment ΔM z The control input is selected as u = [ΔδΔM] z ] T Therefore, the state-space equation is expressed as:

[0021]

[0022] in,

[0023] Based on the vehicle dynamics model under steady-state conditions, the reference yaw rate is derived.

[0024]

[0025] in, It is the gradient coefficient that manipulates the failure, C f0 and C ro This represents the average ideal cornering stiffness coefficient of the front and rear wheels.

[0026] Considering the friction limitations between the tires and the road, the ideal yaw rate is changed to

[0027]

[0028] Where c is the safety factor, μ is the tire-road friction coefficient, g is the gravity coefficient, and sign() is the sign function.

[0029] Treating the reference sideslip angle as zero, establish the vehicle's reference behavior x. d =[β d w d ] T ,β d This is the ideal sideslip angle.

[0030] Step 2: Based on the uncertainty of the vehicle dynamics system caused by the change in tire cornering stiffness due to tire nonlinearity, the dynamics system of the multi-axle vehicle is rewritten to obtain an uncertain system.

[0031] The cornering stiffness of the front and rear wheel sets are described as follows:

[0032]

[0033] The state-space equations were further rewritten as follows:

[0034]

[0035] Where ΔA, ΔB, and ΔE are bounded uncertainty terms. A0, B0, and E0 represent the nominal portion of the system with uncertainty, where...

[0036] Step 3: Based on the dynamics system of multi-axle vehicles, design the top-level controller for in-wheel motor failure and hub motor inertia.

[0037] The top-level controller includes a speed tracking controller and a Robust Optimal (RO) controller. The RO controller combines LQR control and sliding mode control to provide active front wheel steering (AFS) and direct yaw moment (DYC) commands for multi-axle vehicle systems. The specific design method is as follows:

[0038] Step 301: Design LQR control based on the nominal model;

[0039] Ignoring hub motor faults and hub motor failures, the nominal state-space equation is expressed as:

[0040]

[0041] Meanwhile, based on the vehicle's reference behavior x d Assume the reference value satisfies the following expression

[0042]

[0043] This represents an unknown error term.

[0044] The tracking error is defined as e = [β] d -βw d -w]T Its derivative is written as

[0045]

[0046] Next, the objective function to be optimized will be chosen as

[0047]

[0048] in It is a positive semi-definite matrix. It is a positive definite matrix that avoids high control inputs, where t is time.

[0049] According to the LQR control strategy, the optimal control law of the nominal model is calculated as follows:

[0050]

[0051] The matrix P can be solved by... It is derived from Riccati matrix algebraic equations.

[0052] Substituting the LQR control law (16) into the nominal tracking error model (14), we obtain

[0053]

[0054] A multi-axle vehicle system under in-wheel motor failure and hub motor malfunction is modeled. Considering the hub motor failure, the actual tracking error model is reconstructed as follows:

[0055]

[0056] in, These are parameters indicating a fault in the hub motor, and they are bounded.

[0057] Step 302: Sliding mode control (SMC) is used to help LQR control maintain optimal performance, resolve the negative impact of hub motor failure, and further obtain the RO controller for the uncertain system.

[0058] The control law of the RO controller is defined as the sum of the LQR control law u1 and the SMC control law u2, i.e., u3 = u1 + u2.

[0059] When the uncertain system operates on the following integral sliding surface, the tracking trajectory will remain on the same ideal trajectory as the closed-loop dynamic system:

[0060]

[0061] s is the sliding mode variable, H is a constant matrix, and Ξ is a nonlinear function.

[0062] In order to reduce the inevitable chattering in SMC, a nonsingular terminal sliding mode surface is proposed

[0063]

[0064] where λ > 0 is a positive constant, and 1 < a / b < 2. In particular, both a and b are specific odd numbers.

[0065] Through calculation, the SMC control law is obtained as

[0066]

[0067] where ψ(t) is a nonlinear function ε and γ represent positive coefficients, and sgn() is the sign function.

[0068] By adopting the control law of the RO controller u3 = u1 + u2, the vehicle system can overcome the influence of hub motor faults and stabilize within a finite time.

[0069] Step 303: Design a speed tracking controller to provide driving force for the multi-axis vehicle.

[0070] Introduce the tracking error The calculation formula for the driving force provided by the speed tracking controller is

[0071]

[0072] where k p , k i and k d are the weight coefficients of the proportional part, integral part and differential part respectively.

[0073] Step 304: Through the speed tracking controller and RO controller designed above, provide AFS and DYC commands for the multi-axis vehicle system;

[0074] From the perspective of the actual vehicle system, a set of two brushless motors is used to move the bracket assembly, and the driver's angle input is directly corrected according to the command of the additional steering wheel angle, and the response time of vehicle movement is negligible. Therefore, the additional front wheel angle is directly added to the steering wheel angle.

[0075] Step Four: Further design the bottom layer controller based on the results of the top layer controller design to obtain the optimization objective function for each wheel;

[0076] The virtual control signal U = [F x ΔM z T ​Used as an output constraint, this enables the underlying controller to employ different switching strategies for different operating conditions, thereby allocating the drive or braking torque to each wheel and further achieving different control or energy-saving focuses. The specific steps are as follows:

[0077] Step 401: Calculate the optimization objective function for the tire and motor;

[0078] The objective function is optimized by using road surface utilization to constrain actual tire force. The maximum adhesion limit of the tire is:

[0079]

[0080] The first optimization objective function is

[0081]

[0082] Where μ i F represents the proportional weight of each wheel. zi G represents the measurable vertical load on the wheel. xi It is a nonlinear function.

[0083] The in-wheel motor efficiency η is obtained based on motor speed and torque. i For each hub motor, power loss arises from positive drive and negative regenerative braking. The total power loss of the four-wheel motors is expressed as follows:

[0084]

[0085] Therefore, another optimization objective function is:

[0086]

[0087] Among them, P max =T max w max It is the product of the maximum motor torque and the maximum wheel speed, G pi It is a nonlinear function.

[0088] Step 402, further coordinate the weights, optimize the objective function evaluation according to equation (23) and the total power loss function of the four-wheel motors according to equation (25), the following inequalities must hold:

[0089]

[0090] From the actual value x i and y i The distance to the boundary of the circle is derived as follows:

[0091]

[0092] Where, ξ xi ξPi The actual values ​​x are respectively i and y i Distance to the boundary of the circle; sqrt() is the square root function.

[0093] By employing a barrier function, the coordinated weight ψ was obtained. xi and ψ Pi They are respectively:

[0094]

[0095] Step 403: Calculate the constrained optimization objective function using the above-described optimization objective function and weight allocation;

[0096] The yaw moment distribution constraint for each wheel is as follows:

[0097]

[0098] The constrained final optimization objective function is rearranged to reassign the yaw moment, resulting in...

[0099]

[0100] in, B t Let u be the coefficient matrix. t For the yaw moment, u ti Constraints are assigned to distribute the yaw moment of each wheel after reconstruction.

[0101] Step 5: Obtain the optimal solution of the objective function (31) through the Gurobi solver to realize the comprehensive optimal control strategy for the handling performance of multi-axle vehicles under the condition of hub motor failure.

[0102] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0103] (1) This invention overcomes the shortcomings of the average LQR and SMC methods by employing a novel RO control scheme in the top-level controller to achieve optimal tracking performance in the presence of hub motor failures. Furthermore, it demonstrates that the RO controller is chatter-free and that the system can converge to the origin within a finite time, enabling multi-axle vehicles to achieve better performance.

[0104] (2) The underlying controller designed in this invention completes the torque distribution through the optimal torque vector algorithm, and also takes into account stability and economy. It automatically adjusts the weight coefficient of each actuator using the designed limit circle and obstacle function theory, thereby realizing driving safety and energy saving of multi-axle vehicles. Attached Figure Description

[0105] Figure 1This is a schematic diagram of the integrated optimization control method for multi-axle vehicles under hub motor failure and inertia conditions, as proposed in this invention.

[0106] Figure 2 This is a flowchart of the integrated optimization control method for multi-axle vehicles under hub motor failure and malfunction conditions, as described in this invention. Detailed Implementation

[0107] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0108] Conversely, this invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of the invention as defined in the claims. Furthermore, to provide a better understanding of the invention, certain specific details are described in detail below. However, those skilled in the art will fully understand the invention even without these detailed descriptions.

[0109] This invention proposes a Linear Quadratic Regulator (LQR) controller based on a nominal model and ideal motion. For yaw torque distribution under hub motor failure and yaw torque reconstruction under hub motor incompatibility, a novel robust optimal control strategy is further proposed, combining optimal control with high-order sliding mode control to design a top-level controller. Utilizing integrals and terminal sliding surfaces, the resulting robust optimal control method not only achieves better performance but also converges within a finite time without chattering. For the bottom-level controller, an optimization algorithm is developed to dynamically determine the weight of each term in the torque distribution objective function and coordinate the relationship between driving safety and energy efficiency, enabling the hub motor to be switched on and off, i.e., different switching strategies can be used under different operating conditions to achieve different control and energy-saving focuses.

[0110] Figure 1 The control scheme diagram of the present invention specifically includes:

[0111] 1) Modeling the vehicle system under both hub motor failure and hub motor inoperability conditions lays the foundation for the design of the optimal controller. Simultaneously, a reference model is used to provide ideal motion.

[0112] 2) The main task of the top-level controller is to provide virtual AFS and DYC commands for the system under conditions of hub motor failure and hub motor malfunction, based on drive information and ideal motion. The top-level control component consists of a speed tracking controller and a RO controller. The RO controller, by combining LQR control with sliding mode control, can generate appropriate additional front wheel angle and yaw moment commands. Furthermore, to mitigate the effects of longitudinal speed variations, the speed tracking controller can generate the desired driving force.

[0113] 3) Torque distribution, along with the required longitudinal force and additional yaw moment signal, is achieved by solving an optimization problem in the underlying controller. The weights are dynamically determined based on the defined limit circle and barrier function.

[0114] Integrated optimization control methods for multi-axle vehicles under hub motor faults and failures, such as Figure 2 As shown, the specific implementation method is as follows:

[0115] 1) Establishment of vehicle model and reference behavior. First, a vehicle dynamics model was established, whose longitudinal, lateral, and yaw motions, as well as wheel rotation, can be described as follows:

[0116]

[0117]

[0118]

[0119]

[0120] Where m is the total mass of the vehicle; I z This refers to the yaw moment of inertia; J w It represents the moment of inertia of the wheels and motor; δ represents the front wheel steering angle; v x and v y These represent longitudinal and lateral velocities, respectively; w represents yaw rate, β represents sideslip angle; l f and l r d and R represent the distances from the center of gravity to the front and rear axles, respectively; d and R represent the truck width and rolling radius. F xi and F yi These represent the longitudinal and lateral forces on the tire, respectively. i T represents the wheel speed. i This represents the output torque of the electric motor. i = fl, fr, rl, rr, representing the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. D d It is an intermediate variable.

[0121] The relationship between tire lateral force and slip angle is considered to be linear, therefore

[0122]

[0123] Where C f and C r This indicates the cornering stiffness of the front and rear wheels. α f and α r It is the slip angle of the front and rear wheels, which can be calculated as follows:

[0124]

[0125] Where Δδ represents the additional front wheel angle. To obtain the required additional front wheel angle and yaw moment, the control input is selected as u = [ΔδΔM]. z ] T Therefore, the state-space equation is expressed as:

[0126]

[0127] in,

[0128] The reference yaw rate can be derived from the vehicle dynamics model under steady-state conditions.

[0129]

[0130] in, It is the gradient coefficient that caused the manipulation failure. C f0 and C ro This represents the average ideal cornering stiffness coefficient of the front and rear wheels.

[0131] Considering the friction limitations between the tire and the road, the ideal yaw rate is changed to

[0132]

[0133] Where c is the safety factor, μ is the tire-road friction coefficient, g is the gravity coefficient, and sign() is the sign function.

[0134] The sideslip angle should be as small as possible; here, the reference sideslip angle is considered to be zero. Therefore, a reference behavior x is established. d =[β d w d ] T .

[0135] 2) In fact, vehicle dynamics systems are characterized by uncertainty. Apart from speed disturbances caused by hub motor failures, the uncertainty of parameters mainly comes from changes in tire cornering stiffness caused by tire nonlinearity.

[0136] The front and rear wheel cornering stiffness is described as follows:

[0137]

[0138] The state-space equations were further rewritten as follows:

[0139]

[0140] Where ΔA, ΔB, and ΔE are bounded uncertainty terms. A0, B0, and E0 represent the nominal portion of the system with uncertainty, where...

[0141] 3) Design the top-level controller based on the hub motor faults and failures in step 2).

[0142] This can be achieved through the following steps:

[0143] 3.1) LQR Control Design Based on Nominal Model: By ignoring hub motor faults and hub motor failures, the nominal state-space equation can be expressed as:

[0144]

[0145] Meanwhile, assume the reference value satisfies the following expression

[0146]

[0147] The tracking error is defined as e = [β] d -βw d -w] T Its derivative can be written as

[0148]

[0149] Next, the objective function to be optimized will be chosen as

[0150]

[0151] According to the LQR control strategy, the optimal control law of the nominal model can be calculated as follows:

[0152]

[0153] Substituting the LQR control law (16) into the nominal tracking error model (14), we obtain

[0154]

[0155] Taking into account the failure of the hub motor, the actual tracking error model was reconstructed as follows:

[0156]

[0157] in, The problem is with the hub motor, and it is bounded.

[0158] 3.2) RO Controller Design for Uncertain Systems: To address the negative impacts caused by hub motor failures, the SMC method is adopted to assist the LQR control in maintaining optimal performance. The RO control law is defined as u3 = u1 + u2, which is equal to the sum of the LQR control law u1 and the SOSM control law u2.

[0159] When the uncertain system operates on the following integral sliding mode surface, the tracking trajectory will remain on the same ideal trajectory as the closed-loop dynamic system.

[0160]

[0161] To reduce the inevitable chattering in SMC, a non-singular terminal sliding mode surface is proposed.

[0162]

[0163] where λ > 0 and 1 < a / b < 2. In particular, both a and b are specific odd numbers.

[0164] By introducing the RO control law, the first derivative of the ISM surface is reformulated as

[0165]

[0166] Through calculation, the control law can be obtained as

[0167]

[0168] where

[0169] By adopting the RO control input u3 = u1 + u2, the system can overcome the influence of hub motor failures and stabilize within a finite time.

[0170] 3.3) Speed Tracking Controller Design: The main function of the speed tracking controller is to reduce the difference between the actual vehicle speed and the target vehicle speed by providing the correct driving force. The tracking error is introduced. The calculation formula is

[0171]

[0172] where k p , k i and k d are the weight coefficients of the proportional part, integral part, and differential part.

[0173] From the perspective of a practical vehicle system, a set of two brushless motors is used to move the support assembly to directly correct the driver's angle input based on commands for additional steering wheel angle, where the response time is negligible when it comes to vehicle movement. Therefore, the additional front wheel angle is directly added to the steering wheel angle.

[0174] 4) Based on the results of the top-level controller design in step 3), further design the bottom-level controller, and calculate the virtual control signal U = [F] by the top-level controller. x ΔM z ] T Used as an output constraint, different switching strategies can be used for different operating conditions to allocate the driving or braking torque of each wheel, and further realize different control or energy-saving focuses, which can be achieved through the following steps.

[0175] 4.1) Optimization of the objective function evaluation: Road surface utilization rate is used to constrain actual tire force. Maximum adhesion limit is considered.

[0176]

[0177] To achieve appropriate attachment utilization and maintain stability, the first optimization objective function was chosen as follows:

[0178]

[0179] Where μ i F represents the proportional weight of each wheel. zi This indicates the measurable vertical load on the wheel.

[0180] Besides stability, economic efficiency should also be considered, primarily focusing on the power consumption of the in-wheel motors. Motor efficiency is derived by treating motor speed as a constant. In reality, when a vehicle turns, the motor speeds of the four wheels become unequal and fluctuate dramatically. This invention obtains the in-wheel motor efficiency η based on motor speed and torque. i For each hub motor, power loss arises from positive drive and negative regenerative braking. The total power loss of the four-wheel motors is expressed as follows:

[0181]

[0182] Therefore, another optimization objective function is derived from

[0183]

[0184] Among them, P max =T max w max It is the product of the maximum motor torque and speed.

[0185] 4.2) Further coordinate the weights, optimize the objective function evaluation according to equation (23) and the total power loss function of the four-wheel motor according to equation (25), and the following inequalities must hold.

[0186]

[0187] From the actual value x i and y i The distance to the boundary of the circle is derived as follows:

[0188]

[0189] By employing a barrier function, coordinated weights were obtained.

[0190]

[0191] 4.3) Constrained Optimization Objective Function: The motor output should not only comply with the constraints of the actuator but also take into account the tire friction ring constraints. Therefore, the yaw moment distribution constraint for each wheel can be derived as follows:

[0192]

[0193] By rearranging the constrained final optimization objective function and reconfiguring the yaw moment allocation, we can obtain...

[0194]

[0195] in,

[0196] 5) The optimization objective function (31) eventually becomes a typical quadratic programming problem, and the optimal solution can be obtained through the Gurobi solver, realizing the comprehensive optimal control strategy for the handling performance of multi-axle vehicles under the condition of hub motor failure and ineffectiveness.

Claims

1. An integrated optimization control method for multi-axle vehicles under hub motor faults and failures, firstly establishing an ideal dynamic model and reference behavior for the multi-axle vehicle; then, based on the uncertainty of the vehicle dynamic system caused by tire cornering stiffness changes due to tire nonlinearity, rewriting the dynamic system of the multi-axle vehicle to obtain an uncertain system; characterized in that, Includes the following steps: Step 1: Design the top-level controller for multi-axle vehicles under conditions of hub motor failure and hub motor malfunction. The top-level controller includes a speed tracking controller and a RO controller. The RO controller combines LQR control and sliding mode control to provide active front wheel steering (AFS) and direct yaw moment (DYC) commands for multi-axle vehicle systems. The specific design method is as follows: Step 101: Design LQR control based on the nominal model; Ignoring hub motor faults and hub motor failures, the nominal state-space equation is expressed as: A0, B0, and E0 represent the nominal portion of a system with uncertainty; δ represents the front wheel steering angle; u is the control input; Meanwhile, based on the vehicle's reference behavior x d Assume the reference value satisfies the following expression Indicates an unknown error term; The tracking error is defined as e = [β] d -β w d -w] T Its derivative is written as Where, β d For the ideal sideslip angle, w d The ideal yaw rate is given by w, where w represents the yaw rate and d represents the truck width. Next, the objective function to be optimized will be chosen as in It is a positive semi-definite matrix. It is a positive definite matrix that avoids high control inputs, where t is time; According to the LQR control strategy, the optimal control law of the nominal model is calculated as follows: Where Δδ represents the additional front wheel angle, ΔM z The yaw moment is obtained by solving matrix P. Derived from Riccati matrix algebraic equations; Substituting the LQR control law (16) into the nominal tracking error model (14), we obtain A multi-axle vehicle system under in-wheel motor failure and hub motor malfunction is modeled. Considering the hub motor failure, the actual tracking error model is reconstructed as follows: in, These are the parameters indicating a malfunction in the hub motor; Step 102: Sliding mode control (SMC) is used to help LQR control maintain optimal performance, resolve the negative impact of hub motor failure, and further obtain the RO controller for the uncertain system. When the uncertain system operates on the following integral sliding surface, the tracking trajectory will remain on the same ideal trajectory as the closed-loop dynamic system: s is the sliding mode variable, H is a constant matrix, and Ξ is a nonlinear function; To reduce the unavoidable chattering in SMC, a non-singular terminal sliding surface is proposed. Where λ > 0 is a positive constant, and 1 is a negative constant. Through calculation, the SMC control law is obtained as follows: Then the control rate of the RO controller is u3 = u1 + u2; Where ψ(t) is a nonlinear function, ε and γ represent positive coefficients, and sgn() is the sign function; Step 103: Design a speed tracking controller to provide driving force for multi-axle vehicles; Step 104: Through the speed tracking controller and RO controller designed above, provide AFS and DYC commands to the multi-axle vehicle system; Introducing tracking error The driving force calculation formula provided by the speed tracking controller is as follows: Where, k p k i and k d These are the weighting coefficients for the proportional part, integral part, and differential part, respectively. Step 2: Based on the results of the top-level controller design, further design the bottom-level controller to obtain the optimization objective function for each wheel; Step 201: Calculate the optimization objective function for the tire and motor; The virtual control signal U = [F] calculated by the top-level controller x ΔM z ] T Used as an output constraint, this enables the underlying controller to employ different switching strategies for different operating conditions, thereby allocating the drive or braking torque to each wheel and further achieving different control or energy-saving focuses. The specific steps are as follows: The objective function is optimized by using road surface utilization to constrain actual tire force. The maximum adhesion limit of the tire is: The first optimization objective function is Therefore, another optimization objective function is: Where μ i F represents the proportional weight of each wheel. zi G represents the measurable vertical load on the wheel. xi It is a nonlinear function; T i F represents the output torque of the motor. xi and F yi These represent the longitudinal and lateral forces of the tire, respectively. The in-wheel motor efficiency η is obtained based on motor speed and torque. i The total power loss of the four-wheel motor is expressed as Among them, w i Indicates wheel speed; Step 202, further coordinate the weights, optimize the objective function evaluation according to equation (23) and the total power loss function of the four-wheel motor according to equation (25), the following inequalities must hold: Among them, P max =T max w max It is the product of the maximum motor torque and the maximum wheel speed, G pi It is a nonlinear function; Step 203: Calculate the constrained optimization objective function using the above-described optimization objective function and weight allocation; From the actual value x i and y i The distance to the boundary of the circle is derived as follows: Where, ξ xi ξ Pi The actual values ​​x are respectively i and y i Distance to the boundary of the circle; sqrt() is the square root function; By employing a barrier function, the coordinated weight ψ was obtained. xi and ψ Pi They are respectively: The yaw moment distribution constraint for each wheel is as follows: The constrained final optimization objective function is rearranged to reassign the yaw moment, resulting in... Step 5: Obtain the optimal solution of the objective function (31) through the Gurobi solver, and obtain the comprehensive optimal control strategy for the handling performance of the multi-axle vehicle under the condition of hub motor failure. in, B t Let u be the coefficient matrix. t For the yaw moment, u ti Constraints are assigned to distribute the yaw moment of each wheel after reconstruction. The establishment of the ideal dynamic model and reference behavior for multi-axle vehicles specifically includes:

2. The integrated optimization control method for multi-axle vehicles under hub motor faults and failures as described in claim 1, characterized in that, ​ In the aforementioned dynamic model, the longitudinal, lateral, and yaw motions, as well as wheel rotation, are described as follows: Where m is the total mass of the vehicle; I z This refers to the yaw moment of inertia; J w It represents the moment of inertia of the wheels and motor; δ represents the front wheel steering angle; v x and v y These represent longitudinal and lateral velocities, respectively; w represents yaw rate, β represents sideslip angle; l f and l r d and R represent the distances from the center of gravity to the front and rear axles, respectively; d and R represent the truck width and rolling radius, respectively; F xi and F yi These represent the longitudinal and lateral forces of the tire, respectively; w i T represents the wheel speed. i This represents the output torque of the electric motor; i = fl, fr, rl, rr, representing the left front wheel, right front wheel, left rear wheel, and right rear wheel; D d It is an intermediate variable; Treating the relationship between tire lateral force and slip angle as linear, therefore the tire lateral force F of the front and rear wheel sets... yf and F yr The calculations are as follows: Where C f and C r These represent the cornering stiffness of the front and rear wheels, respectively; α f and α r These are the slip angles of the front and rear wheels, calculated as follows: Where Δδ represents the additional front wheel angle; To obtain the additional front wheel angle Δδ and yaw moment ΔM z The control input is selected as u = [Δδ ΔM] z ] T Therefore, the state-space equation is expressed as: in, Based on the vehicle dynamics model under steady-state conditions, the reference yaw rate is derived. in, It is the gradient coefficient that manipulates the failure, C f0 and C ro This represents the average ideal cornering stiffness coefficient of the front and rear wheels; Considering the friction limitations between the tires and the road, the ideal yaw rate is changed to Where c is the safety factor, μ is the tire-road friction coefficient, g is the gravity coefficient, and sign() is the sign function; Treating the reference sideslip angle as zero, establish the vehicle's reference behavior x. d =[β d w d ] T ,β d This is the ideal sideslip angle.

3. The integrated optimization control method for multi-axle vehicles under hub motor faults and failures as described in claim 2, characterized in that, The cornering stiffness of the front and rear wheels are described as follows: The state-space equations were further rewritten as follows: Where ΔA, ΔB, and ΔE are bounded uncertainties; A0, B0, and E0 represent the nominal components of a system with uncertainty.

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