A fuzzy dynamic terminal sliding mode based four-wheel drive vehicle yaw control method

Abstract

The present application belongs to the field of vehicle driving system simulation, and particularly relates to a four-wheel drive vehicle yaw control method based on fuzzy dynamic terminal sliding mode, comprising the following steps: step 1, establishing a vehicle dynamics model and a reference state model, and obtaining a whole vehicle state signal; step 2, according to the whole vehicle state signal and a target reference signal, calculating an expected direct yaw moment through a fuzzy fast dynamic terminal sliding mode controller; step 3, according to the expected direct yaw moment, calculating final motor torque instructions of four wheels through a dynamic weighted minimum energy distribution strategy, and outputting to the wheel hub motor. The method effectively suppresses the integral saturation phenomenon under the condition of continuous disturbance or actuator saturation by introducing a dynamic forgetting integral term in the sliding mode surface, improves the transient control performance, and avoids the control divergence caused by error accumulation.

Description

Technical Field

[0001] This invention relates to the field of vehicle stability control technology, specifically to a direct yaw moment control method applicable to four-wheel independent drive (4WID) electric vehicles, and in particular to a hierarchical lateral stability control strategy based on fuzzy logic, fast dynamic terminal sliding mode control, and dynamic weighted energy distribution. Background Technology

[0002] Against the backdrop of global climate change and carbon neutrality, electric vehicles are reshaping the automotive industry with their energy efficiency and intelligent control advantages. Among them, four-wheel independent drive (4WID) electric vehicles, equipped with independent in-wheel motors, can precisely and rapidly modulate the torque of individual wheels, providing an ideal hardware platform for advanced chassis control systems. However, due to the lack of mechanical differential restraint, wheels are prone to slippage or sideslip on low-friction surfaces or under high-speed extreme conditions. Direct yaw moment control (DYC) has become the mainstream method for maintaining vehicle lateral stability.

[0003] Currently, sliding mode control (SMC) based DYC is widely used in existing technologies. However, traditional first-order SMC has significant drawbacks: its discontinuous switching law can induce high-frequency chattering, potentially triggering unmodeled dynamics; simultaneously, its linear sliding surface can only guarantee asymptotic convergence, limiting tracking accuracy under severe steering conditions. To address this issue, existing technologies have proposed terminal sliding mode control (TSMC) to introduce nonlinear terms to achieve finite-time convergence, and integral sliding mode control (ISMC) to eliminate steady-state errors. However, the integral term in existing ISMC is prone to "integral saturation" under continuous disturbances or actuator saturation, leading to a decline in transient performance. Although some studies have introduced dynamic forgetting mechanisms to suppress integral accumulation, existing methods often rely on fixed controller parameters or assumed known upper limits of disturbances, resulting in insufficient adaptability when the road adhesion coefficient changes rapidly.

[0004] Furthermore, in terms of underlying torque distribution, existing technologies typically map the required yaw moment to the torque of each wheel and establish it as a constrained optimization problem, solving it using numerical methods such as weighted least squares or quadratic programming. However, this iterative numerical calculation process introduces computational delays, which are particularly noticeable under extreme operating conditions with strongly activated constraints. Simultaneously, static weight allocation strategies cannot capture the real-time changes in dynamic vertical load transfer and adhesion margin, often leading to premature saturation of the tire friction circle, thereby reducing the vehicle's stability margin. Summary of the Invention

[0005] To address the problems of integral saturation, poor parameter adaptability, and low-level torque distribution calculation delay in the existing technologies, this invention proposes a yaw control method for four-wheel drive vehicles based on fuzzy dynamic terminal sliding mode, in order to improve the stability and safety of vehicles driving on low-adhesion road surfaces.

[0006] The technical solution of this invention is to propose a yaw control method for four-wheel drive vehicles based on fuzzy dynamic terminal sliding mode, characterized by the following steps:

[0007] Step 1: Establish a seven-degree-of-freedom nonlinear vehicle dynamics model that includes longitudinal, lateral, and yaw motions of the vehicle body and independent rotational motions of the four wheels, and establish a two-degree-of-freedom linear vehicle reference model; calculate the longitudinal and lateral forces of each tire based on the PAC2002 tire model using the magic formula, and calculate the vertical load on the tires in conjunction with dynamic load transfer; calculate the equivalent steering angles of the left and right front wheels based on the Ackerman steering characteristics according to the steering wheel angle input; acquire the vehicle's longitudinal acceleration, lateral acceleration, yaw rate, longitudinal velocity, and wheel speed signals in real time as vehicle state signals, and calculate the target yaw rate and target centroid sideslip angle as target reference signals based on the two-degree-of-freedom linear vehicle reference model combined with the road adhesion coefficient and real-time vehicle speed;

[0008] Step 2: Define the yaw rate tracking error and the center of gravity sideslip angle tracking error based on the vehicle state signal and the target reference signal; construct a combined fast terminal sliding surface with a dynamic forgetting integral term, which is used to suppress integral saturation under continuous disturbance or actuator saturation; introduce a fuzzy logic system, with the road adhesion coefficient and the absolute value of the steering wheel angle as inputs, and the terminal gain parameter as the output for adaptive adjustment; differentiate the sliding surface based on the zero-order hold assumption, design a composite reaching law containing an exponential reaching law and a saturation function, construct the control law for the direct yaw moment, and verify the asymptotic stability of the closed-loop system through Lyapunov stability analysis, and output the desired direct yaw moment;

[0009] Step 3: Establish an objective function with the goal of minimizing the weighted sum of squares of the longitudinal forces of each wheel. The weighting coefficients are dynamically adjusted based on the wheel vertical load, front wheel steering angle, and vehicle speed. Construct constraints including longitudinal force balance equations, yaw moment balance equations, tire friction circle constraints, and motor output torque constraints. Transform the inequality constraints into dynamic penalty terms in the objective function to correct the weighting coefficients online. Construct a Lagrange function based on the Lagrange multiplier method and calculate the partial derivatives with respect to the longitudinal forces of each wheel to obtain auxiliary decoupling variables. Construct a second-order linear equation system based on the auxiliary decoupling variables, and use Cramer's rule to directly obtain the analytical solution of the Lagrange multipliers. Calculate the optimal expected longitudinal forces of the four wheels and multiply them by the tire rolling radius to generate the final torque command for each wheel hub motor, which is then output to the wheel hub motor.

[0010] Furthermore, in step 1: establish the differential equation of wheel rotation motion, and determine the dynamic response of the wheel based on the wheel speed signal and motor torque signal of each wheel.

[0011] Further, in step 1: establish a tire kinematic model, and calculate the longitudinal velocity, lateral velocity, wheel slip angle, and longitudinal slip ratio at the center of each wheel based on the vehicle's motion state.

[0012] Further, in step 1: establish the PAC2002 tire model using the magic formula, calculate the longitudinal and lateral forces of each tire, and calculate the vertical load of the tire by combining real-time dynamic load transfer.

[0013] Furthermore, in step 2: a combined fast terminal sliding surface is constructed that incorporates a dynamic forgetting integral term, and a dynamic forgetting integral term is introduced to suppress integral saturation.

[0014] Furthermore, in step 3:

[0015] To achieve the vehicle's target motion, the control distribution must satisfy two equality constraints: longitudinal force balance and yaw moment balance.

[0016] ;

[0017] ;

[0018] in: , , , These represent the longitudinal tire forces of the four wheels: left front, right front, left rear, and right rear, respectively. B is the equivalent front wheel steering angle of the vehicle; F is the vehicle track width; x,total The total longitudinal force for the driver's target. This is the desired yaw torque output by the upper-level controller.

[0019] The beneficial effects of this invention are as follows:

[0020] (1) By introducing a dynamic forgetting integral term into the sliding surface, the integral saturation phenomenon that occurs under continuous disturbance or actuator saturation is effectively suppressed, the transient control performance is improved, and control divergence caused by error accumulation is avoided.

[0021] (2) It has high robustness and adaptability. The terminal sliding mode gain is adjusted online by using a fuzzy inference system, so that the controller can still maintain excellent stability margin when the road adhesion coefficient and steering input change drastically, effectively adapting to complex and ever-changing driving environments.

[0022] (3) The lower-level distributor uses an analytical solution based on the Lagrange multiplier method to replace the traditional numerical iterative calculation, which completely eliminates the calculation delay caused by constraint allocation and greatly improves the real-time response capability of the lower-level control system under extreme driving conditions, thereby ensuring the rapid adjustment of the vehicle's lateral stability. Attached Figure Description

[0023] Figure 1 is a schematic diagram of the structure of the 7-DOF vehicle nonlinear dynamics model provided in an embodiment of the present invention.

[0024] Figure 2 is an overall flowchart of the hierarchical control architecture provided in an embodiment of the present invention.

[0025] Figure 3 is a schematic diagram of the input membership function of the fuzzy inference system in an embodiment of the present invention.

[0026] Figure 4 is a comparison of simulation test results of the embodiment of the present invention under sinusoidal steering conditions.

[0027] Figure 5 is a comparison of simulation test results of the embodiment of the present invention under the dual-line obstacle avoidance condition. Detailed Implementation

[0028] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Those skilled in the art should understand that the following embodiments are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Modifications or substitutions to the details and form of the technical solutions of the present invention can be made without departing from the spirit and scope of the present invention, but all such modifications and substitutions fall within the protection scope of the present invention.

[0029] This embodiment provides a yaw control method for a four-wheel drive vehicle based on fuzzy dynamic terminal sliding mode, and the complete implementation details of each step are as follows:

[0030] Step 1: Establish a seven-degree-of-freedom nonlinear vehicle dynamics model that includes longitudinal, lateral, and yaw motions of the vehicle body and independent rotational motions of the four wheels, and establish a two-degree-of-freedom linear vehicle reference model; calculate the longitudinal and lateral forces of each tire based on the PAC2002 tire model using the magic formula, and calculate the vertical load on the tires in conjunction with dynamic load transfer; calculate the equivalent steering angles of the left and right front wheels based on the Ackerman steering characteristics according to the steering wheel angle input; acquire the vehicle's longitudinal acceleration, lateral acceleration, yaw rate, longitudinal velocity, and wheel speed signals in real time as vehicle state signals, and calculate the target yaw rate and target centroid sideslip angle as target reference signals based on the two-degree-of-freedom linear vehicle reference model combined with the road adhesion coefficient and real-time vehicle speed;

[0031] As shown in Figure 1, this 7-DOF model includes the vehicle's body motion in the longitudinal, lateral, and yaw directions, as well as the independent rotational motion of the four wheels.

[0032] In a preferred embodiment, a nonlinear tire model (Magic Formula PAC2002) and a steering system kinematic model are introduced to fully describe the nonlinear coupled dynamics of the vehicle under complex driving conditions. Specifically, step 1 includes the following sub-steps:

[0033] Step 1.1: Establish a 7-DOF nonlinear vehicle dynamics model and acquire the vehicle's longitudinal acceleration, lateral acceleration, yaw rate, longitudinal velocity, and wheel speed signals of each wheel in real time.

[0034] Based on Newton's second law, the differential equations of motion of the vehicle in the longitudinal, lateral, and yaw directions are constructed as follows:

[0035] 1. Differential equation of longitudinal motion of the vehicle:

[0036]

[0037] Where: m is the total vehicle mass; The longitudinal acceleration of the vehicle; γ is the lateral velocity at the vehicle's center of gravity; γ is the yaw rate; F x,ij and F y,ij These represent the longitudinal tire force and lateral tire force of each wheel (subscripts ij and ij represent fl (left front), fr (right front), rl (left rear), and rr (right rear), respectively); δ f This is the equivalent front wheel steering angle; F res This represents the resistance during travel.

[0038] 2. Differential equations of vehicle lateral motion:

[0039] ;

[0040] in: It is lateral acceleration; γ is the longitudinal velocity at the vehicle's center of gravity; γ is the yaw rate; F x,ij and F y,ij These represent the longitudinal tire force and lateral tire force of each wheel (subscripts ij represent fl (left front), fr (right front), rl (left rear), and rr (right rear), respectively); δ f This is the equivalent front wheel steering angle.

[0041] 3. Differential equation of vehicle yaw motion:

[0042] ;

[0043] Among them: I z Let be the yaw moment of inertia about the Z-axis; Let L be the yaw acceleration. f L r These are the distances from the center of gravity to the front and rear axles, respectively; B is the track width; F x,ij and F y,ij These represent the longitudinal tire force and lateral tire force of each wheel (subscripts ij and ij represent fl (left front), fr (right front), rl (left rear), and rr (right rear), respectively); δ f This is the equivalent front wheel steering angle.

[0044] Step 1.2: Establish the differential equation of wheel rotation motion, and determine the dynamic response of the wheel based on the wheel speed signal and motor torque signal of each wheel.

[0045] The rotational dynamics equations for each wheel are expressed as follows:

[0046] ;

[0047] In the formula: I w The moment of inertia of the wheel; T represents the angular acceleration of each wheel (i.e., the derivative of the wheel's angular velocity with respect to time). ij F represents the output torque of each hub motor. x,ij Here, f represents the longitudinal tire force of each wheel, f is the rolling resistance coefficient, and R is the effective rolling radius of the tire.

[0048] Step 1.3: Establish a tire kinematic model, and calculate the longitudinal velocity, lateral velocity, wheel slip angle, and longitudinal slip ratio at the wheel center of each wheel based on the vehicle's motion state; based on the vehicle's motion state, the longitudinal velocity v at the wheel center of each wheel... x,ij Lateral velocity v y,ij and resultant velocity v ij The longitudinal velocities of each wheel center are calculated as follows:

[0049] ;

[0050] Lateral velocity of each wheel center:

[0051] ;

[0052] in: The longitudinal velocity at the vehicle's center of gravity; The lateral velocity at the vehicle's center of gravity; This refers to the yaw rate; The wheelbase of the vehicle; and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. , , , These represent the longitudinal velocities at the center of the left front, right front, left rear, and right rear wheels, respectively. , , , These represent the lateral velocities at the center of the left front, right front, left rear, and right rear wheels, respectively.

[0053] Further, calculate the slip angle α of each wheel. ij With longitudinal slip ratio λ ij The formula is:

[0054] Wheel slip angle:

[0055] ;

[0056] ;

[0057] Slip ratio:

[0058] ;

[0059] in, For the equivalent front wheel steering angle, R represents the angular velocity of each wheel (the subscripts ij and ij represent fl (left front), fr (right front), rl (left rear), and rr (right rear), respectively); R is the effective rolling radius of the tire. , , , These represent the slip angles of the left front, right front, left rear, and right rear wheels, respectively. The longitudinal slip ratio of each wheel; This represents the longitudinal velocity at the center of each wheel; This represents the lateral velocity at the center of each wheel. At that time, it indicated that the wheel was slipping. This indicates that the wheel has slipped.

[0060] Step 1.4: Establish the PAC2002 tire model using the magic formula, calculate the longitudinal and lateral forces of each tire, and calculate the vertical load of the tire by combining the real-time dynamic load transfer.

[0061] This embodiment uses the Magic Formula tire model to calculate the nonlinear forces of the tire under pure longitudinal slip, pure sideslip, and combined conditions. The basic expression is:

[0062] y (x) = D sin {C arctan [B1x - E(B1x - arctan(B1x))]};

[0063] In the formula, y is the output force, either longitudinal or lateral; x is the input variable, which is the slip ratio λ under longitudinal slip conditions and the slip angle α under lateral slip conditions; B1 is the stiffness factor, used to determine the slope at the origin of the curve; C is the shape factor, which determines the effective range of the sine function; D is the peak factor, which determines the maximum value that the curve can reach; and E is the curvature factor, used to adjust the shape near the peak of the curve.

[0064] Under combined working conditions, the longitudinal force and lateral force are expressed as follows:

[0065] Longitudinal force: ;

[0066] Lateral force: ;

[0067] In the formula, F x0 and F y0 These represent tire forces under pure longitudinal slip and pure lateral slip conditions, respectively; G xα and G yα This is a weighting function under combined operating conditions, used to reflect the longitudinal slip-lateral coupling effect; S yα This represents the curve drift. This refers to the camber angle of the wheel.

[0068] Meanwhile, the tire vertical load F z,ij Both longitudinal and lateral load transfer need to be considered; taking the left front wheel as an example:

[0069] ;

[0070] Where m is the vehicle mass; B is the track width; g is the acceleration due to gravity; h g L is the vehicle's center of gravity height; L is the wheelbase, L = L f + L r L f L r , a, are the distances from the center of mass to the front and rear axes, respectively. x and a y These are the vehicle's longitudinal acceleration and lateral acceleration, respectively. .

[0071] Step 1.5: Establish a kinematic model of the steering system. Based on the driver's steering wheel angle input, calculate the equivalent steering angles of the left and right front wheels based on the Ackermann steering angle characteristics.

[0072] In a preferred embodiment, front wheel steering employs a kinematic model conforming to Ackermann's steering angle characteristics. Its input is the steering wheel angle δ. sw The output is the equivalent steering angle δ of the left and right front wheels. fl and δfr Because there is a transmission ratio i between the steering wheel and the front wheels. sw The actual equivalent front wheel steering angle is:

[0073] The precise turning angles of the left and right wheels are determined based on Ackermann geometry.

[0074] Step 1.6: Establish a 2-DOF linear vehicle reference model, and calculate the target yaw rate and target centroid sideslip angle as the target reference signal by combining the road surface adhesion coefficient and real-time vehicle speed.

[0075] The target yaw rate γ was calculated using a 2-DOF linear vehicle dynamics model. d And the target centroid sideslip angle β d As shown in Figure 2.

[0076] The vehicle dynamics equations for this 2-DOF model are as follows:

[0077] ;

[0078] Where: m is the vehicle mass; B is the track width; k1 is the front axle equivalent lateral stiffness, and k2 is the rear axle equivalent lateral stiffness; I is the longitudinal velocity at the vehicle's center of gravity. z Let be the yaw moment of inertia about the Z-axis; The sideslip angle is the angle of the centroid. Let be the sideslip angular velocity of the vehicle's center of gravity. Let γ be the yaw acceleration and γ be the yaw velocity. and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively.

[0079] Based on the road surface adhesion limit, the following target reference signal is constructed, where the vehicle stability factor K is defined as follows:

[0080] ;

[0081] Where: K is the vehicle stability factor, used to quantify the understeer gradient during steady-state steering; m is the vehicle mass; k1 is the front axle equivalent lateral stiffness, and k2 is the rear axle equivalent lateral stiffness; and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively.

[0082] The obtained reference yaw rate γ d And the reference centroid side slip angle β d This will be used as input to the sliding mode controller in subsequent steps to calculate the tracking error.

[0083] The specific constraints are as follows:

[0084] ;

[0085] ;

[0086] in: For reference yaw rate; The reference centroid sideslip angle; µ is the road adhesion coefficient; Let m be the standard symbolic function, and m be the vehicle mass. The longitudinal velocity at the vehicle's center of gravity; The real-time sideslip angle of the vehicle's center of gravity. and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively; L is the wheelbase, L = L f + L r K is the vehicle stability factor, used to quantify the understeer gradient during steady-state steering; k1 is the front axle equivalent lateral stiffness; k2 is the rear axle equivalent lateral stiffness.

[0087] Step 2: Define the yaw rate tracking error and the center of gravity sideslip angle tracking error based on the vehicle state signal and the target reference signal; construct a combined fast terminal sliding surface containing a dynamic forgetting integral term, which is used to suppress integral saturation under continuous disturbance or actuator saturation; introduce a fuzzy logic system, with the road adhesion coefficient and the absolute value of the steering wheel angle as inputs, and the terminal gain parameter as the output for adaptive adjustment; differentiate the sliding surface based on the zero-order hold assumption, design a composite reaching law containing an exponential reaching law and a saturation function, construct the control law for the direct yaw moment, and verify the asymptotic stability of the closed-loop system through Lyapunov stability analysis, outputting the desired direct yaw moment.

[0088] As shown in Figure 2, the control system designed in this invention adopts a two-layer hierarchical architecture. In the control flow shown in the figure, the upper-layer FFDTSMC controller, on the one hand, combines the fuzzy inference system shown in Figure 3 to dynamically adjust the control gain, and on the other hand, receives feedback signals from the reference model and the 7-DOF vehicle model, and finally calculates the desired additional yaw moment. The output is then distributed to the lower-level allocation module. This includes the following sub-steps:

[0089] Step 2.1: Based on the current vehicle status signal and the target reference signal, define the yaw rate tracking error and the center of gravity sideslip angle tracking error:

[0090] To achieve accurate tracking of the target trajectory, the error must first be calculated before designing the control law:

[0091] ;

[0092] in, and These are the vehicle's real-time center of gravity sideslip angle tracking error and yaw rate tracking error, respectively. These errors will be used as the direct inputs to the sliding mode controller. For reference yaw rate; For reference centroid sideslip angle; γ is the sideslip angle of the center of mass, and γ is the yaw rate.

[0093] Step 2.2: Construct a combined fast terminal sliding surface that incorporates a dynamic forgetting integral term. Introduce the dynamic forgetting integral term to suppress integral saturation, and determine the mathematical expression of the sliding surface.

[0094] Referring to the control framework shown in Figure 2, the sliding surface is as follows:

[0095] ;

[0096] Where: s is the defined combined fast-ending sliding surface, and To assign weighting coefficients, satisfying + =1; This refers to the real-time tracking error of the vehicle's center of gravity sideslip angle. This refers to the real-time yaw rate tracking error of the vehicle. and is the independent terminal integration gain; p and q are positive odd numbers satisfying 0 < p / q < 1; This is the dynamic forgetting coefficient; Forgetting factor; is the time integration variable in the integration operation; t is the current running time. In the formula... This refers to the introduction of a dynamic forgetting term, the purpose of which is to use the exponential weighting characteristic to attenuate historical control errors, thereby eliminating integral saturation caused by continuous large disturbances or actuator saturation.

[0097] Step 2.3: Introduce a fuzzy logic system, using the road surface adhesion coefficient and the absolute value of the steering wheel angle as input variables, and outputting terminal gain parameters; through the triangular membership function and the engineering experience fuzzy rule table, use the centroid method to defuzzify and obtain an adaptive terminal gain to adapt to different road surface adhesion conditions.

[0098] To adapt to drastic changes in road surface conditions, this invention introduces a fuzzy inference system based on the construction of the sliding surface. As shown in Figure 3, this fuzzy system uses the road surface adhesion coefficient µ and the absolute value of the steering angle |δf | represents two input variables, and the output is the terminal gain. and .

[0099] Figure 3 The diagram clearly shows the triangular membership function distribution, including three normalized membership intervals: Low, Medium, and High. After logical reasoning using a fuzzy rule table based on engineering experience, defuzzification is performed using the centroid method (COG), ultimately obtaining an adaptive gain output.

[0100] ;

[0101] in, and These are the centroid sideslip angle terminal gain and yaw rate terminal gain output by the fuzzy inference system, respectively; N is the total number of entries in the fuzzy rule table; i is the natural number index of the fuzzy rule; Let be the membership degree at which the i-th rule is activated; δ is the road surface adhesion coefficient; f | represents the absolute value of the equivalent front wheel steering angle; and These are the terminal gain values ​​of the centroid sideslip angle and yaw rate, respectively, for the i-th rule in the fuzzy rule table.

[0102] Step 2.4: Based on the zero-order hold assumption, differentiate the sliding surface to separate the known dynamic terms that are independent of the control input, design a composite reaching law that includes an exponential reaching law and a saturation function, and then construct the control law formula for the direct yaw moment.

[0103] Assuming the fuzzy output remains constant during the control cycle, differentiate with respect to the sliding surface s. To reduce redundancy and complexity in the control law derivation, the derivative of the error is first decomposed into two parts: a known dynamic term independent of the control input. and A reaching law is constructed. By combining the exponential reaching law and the saturation function, chattering is reduced. The final designed direct yaw moment control law is as follows:

[0104] ;

[0105] in: To add the desired yaw moment to the output of the upper-level controller; , To assign weighting coefficients; and The known dynamic values ​​after removing the control terms; d is the control effectiveness coefficient (here d = 1 / Iz); and These are the terminal gains of the centroid sideslip angle and the yaw rate, respectively, output by the fuzzy inference system. For the gain of the switching item; The exponential convergence rate; is a saturation function used to provide smooth switching action inside and outside the boundary layer to suppress chattering; p and q are positive odd numbers that satisfy 0 < p / q < 1; This is the dynamic forgetting coefficient; t is the forgetting factor; t is the current running time; It is a saturation function used to provide smooth switching action inside and outside the boundary layer of the sliding surface, thereby suppressing high-frequency chattering.

[0106] Step 2.5: Construct the Lyapunov function and perform Lyapunov stability analysis on the control law designed in Step 2.4 to verify the asymptotic stability of the closed-loop control system and obtain the reliable desired yaw torque.

[0107] To mathematically guarantee the stable operation of the system under arbitrary initial states, this step employs a rigorous proof using Lyapunov's second method. The Lyapunov function is chosen. Substituting into the approach law and differentiating, we analyze the two cases of the sliding surface inside and outside the boundary layer: outside the boundary layer, it satisfies... The negative definite condition satisfies the semi-negative definite condition within the boundary layer, thus proving that the closed-loop system can achieve asymptotic stability in all states inside and outside the boundary layer, ensuring that the system can effectively converge to the ideal objective.

[0108] Step 3: Establish an objective function with the goal of minimizing the weighted sum of squares of the longitudinal forces of each wheel. The weighting coefficients are dynamically adjusted based on the wheel vertical load, front wheel steering angle, and vehicle speed. Construct constraints including longitudinal force balance equations, yaw moment balance equations, tire friction circle constraints, and motor output torque constraints. Transform the inequality constraints into dynamic penalty terms in the objective function to correct the weighting coefficients online. Construct a Lagrange function based on the Lagrange multiplier method and calculate the partial derivatives with respect to the longitudinal forces of each wheel to obtain auxiliary decoupling variables. Construct a second-order linear equation system based on the auxiliary decoupling variables, and use Cramer's rule to directly obtain the analytical solution of the Lagrange multipliers. Calculate the optimal expected longitudinal forces of the four wheels and multiply them by the tire rolling radius to generate the final torque command for each hub motor, which is then output to the hub motor.

[0109] After obtaining the desired yaw torque output from the upper-level controller, this step performs the lower-level torque allocation, that is, how to reasonably allocate the total demand to the four independent hub motors, as shown in the lower-level control module DWMEA in Figure 2.

[0110] Step 3.1: Determine the minimum energy consumption objective function, with the goal of minimizing the weighted sum of squares of the longitudinal forces of each wheel. The weighting coefficients are dynamically adjusted based on the wheel vertical load, front wheel steering angle, and vehicle speed.

[0111] Based on the desired additional yaw moment provided by the upper-level controller The underlying control and distribution system needs to convert this into driving or braking force for each wheel. This embodiment sets the optimization objective as minimizing the weighted sum of the squares of the longitudinal tire forces of each wheel, in order to reduce energy consumption and maintain lateral force reserves.

[0112] ;

[0113] Where J is the constructed minimum energy consumption objective function value; i is the index of the wheel, with values ​​ranging from fl, fr, rl, rr, corresponding to the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively; ω i The dynamic weighting coefficients for each wheel. Let be the longitudinal tire force of the i-th wheel. This weighting coefficient is not a preset fixed value, but is dynamically adjusted in real time according to the vehicle's driving state. The other parameters are consistent with the definitions in the aforementioned motion equations. The specific adjustment equation is:

[0114] ;

[0115] in, Indicates the vertical load, steering, and speed adjustment coefficients, satisfying... ;F z0 This is the nominal vertical load; Let be the real-time vertical load of the i-th wheel; δ0 be the reference steering angle; v0 be the reference vehicle speed; ε be a small constant to prevent zero singularities; I front (i) is an indicator function representing the difference between the front and rear axles. The value is 1 when i is the front wheel and 0 when i is the rear wheel.

[0116] Step 3.2: Construct system constraints for the objective function, including equality constraints for longitudinal force balance and yaw moment balance, and inequality constraints for tire friction circle and motor output torque; convert the inequality constraints into dynamic penalty terms in the objective function, and correct the dynamic weight coefficients online.

[0117] To achieve the vehicle's target motion, the control distribution must satisfy two equality constraints: longitudinal force balance and yaw moment balance.

[0118] ;

[0119] ;

[0120] in: , , , These represent the longitudinal tire forces of the four wheels: left front, right front, left rear, and right rear, respectively. B is the equivalent front wheel steering angle of the vehicle; F is the vehicle track width; x,total The target total longitudinal force for the driver (derived from the difference between the desired vehicle speed and the current vehicle speed through PI control, which is common knowledge in this field). This is the desired yaw torque output by the upper-level controller.

[0121] Meanwhile, to prevent tire saturation on low-adhesion surfaces or under extreme operating conditions, two types of inequality constraints are introduced: tire adhesion ellipse constraint and motor peak torque constraint.

[0122] ;

[0123] Where: i is the index of the wheel, and the value range is fl, fr, rl, rr, which correspond to the left front wheel, right front wheel, left rear wheel and right rear wheel respectively; F is the absolute value of the longitudinal force on the i-th wheel. z,i The real-time vertical load of the i-th wheel; Let be the real-time lateral force of the i-th wheel; R is the upper limit of the peak output torque of the hub motor; R is the effective rolling radius of the tire.

[0124] In practical solutions, to avoid iteration while ensuring the results do not exceed limits, this embodiment transforms the above inequality constraints into a dynamic penalty term in the objective function, thereby adjusting the original weight ω. i Online corrections are performed. When a tire approaches its adhesion boundary or torque limit, the correction factor increases sharply, thus imposing a strong penalty on the objective function to reduce the longitudinal force requirement of that wheel.

[0125] ;

[0126] in, These are the dynamic weight coefficients after correction for inequality constraints. ζ1 represents the original dynamic weighting coefficients before correction; ζ2 represents the friction circle constraint gain, used to adjust the penalty intensity caused by the friction circle constraint; ζ3 represents the actuator saturation constraint gain, used to adjust the penalty intensity caused by motor torque saturation; F x,i F is the longitudinal tire force of the i-th wheel; y,i F is the real-time lateral force of the i-th wheel; μ is the road adhesion coefficient; F z,i R is the real-time vertical load of the i-th wheel; R is the effective rolling radius of the tire; Tmotor_max This represents the upper limit of the peak output torque of the hub motor. All subsequent derivations are based on the corrected value. For the sake of accuracy and ease of writing, the following text will continue to use the same format. .

[0127] Step 3.3: Based on the Lagrange multiplier method, construct the Lagrange function for the equation constraints of longitudinal force balance and yaw moment balance, and obtain the auxiliary decoupling variables by taking the partial derivative with respect to the longitudinal force of each wheel.

[0128] Ignoring inequality constraints, this embodiment becomes a typical convex optimization problem with equality constraints. Therefore, two Lagrange multipliers, λ1 (corresponding to longitudinal force constraints) and λ2 (corresponding to yaw moment constraints), are introduced. The Lagrange function is constructed as follows:

[0129] ;

[0130] in: and Let be the Lagrange multiplier to be determined, and the other parameters are defined in the aforementioned equations of motion. The Lagrangian function is constructed; F is the dynamic weighting coefficient of the i-th wheel. x,i Let be the longitudinal tire force of the i-th wheel; , , , These represent the longitudinal tire forces of the four wheels: left front, right front, left rear, and right rear; F x,total δ represents the total longitudinal force of the driver target; ΔMz represents the desired additional yaw moment output by the upper-level controller; λ1 and λ2 are the Lagrange multipliers to be determined (where λ1 corresponds to the longitudinal force balance equation constraint, and λ2 corresponds to the yaw moment balance equation constraint); f B is the equivalent front wheel steering angle; B is the vehicle track width.

[0131] Taking the partial derivatives of the Lagrange function with respect to the longitudinal forces of the four wheels, and setting the partial derivatives to zero, yields four sets of algebraic equations:

[0132] ;

[0133] ;

[0134] ;

[0135] ;

[0136] in: , , These are the dynamic weighting coefficients for the four wheels: front left, front right, rear left, and rear right. , , , Let λ1 and λ2 represent the longitudinal tire forces of the four wheels: left front, right front, left rear, and right rear, respectively; λ1 and λ2 are the Lagrange multipliers to be determined; B is the vehicle track width. The Lagrange function is constructed.

[0137] Step 3.4: Based on the auxiliary decoupling variables, construct a 2×2 linear equation system, use Cramer's rule to directly obtain the analytical solution of the Lagrange multiplier, and then directly calculate the optimal expected longitudinal force of the four wheels, and multiply it by the tire rolling radius to generate the final torque command of each wheel hub motor.

[0138] To reduce the coupling dimension of the equation system, this embodiment defines two auxiliary variables. and Substituting the above partial derivative equations into the two equality constraints, we can construct a system of 2 × 2 linear equations:

[0139] ;

[0140] ;

[0141] The coefficients are determined by the following formula:

[0142] ;

[0143] ;

[0144] ;

[0145] ;

[0146] Due to the weighting coefficient ω i > 0 and the front wheel steering angle δf physically satisfies Therefore, the determinant of the coefficient matrix of this 2 × 2 linear system of equations is never zero. This embodiment directly provides the unique analytical solution to this system of equations using Cramer's rule:

[0147] ;

[0148] in, , A is the auxiliary variable after decoupling; 11 A 12 A 21 A 22 The coefficients of the system of equations; , , , F represents the dynamic weighting coefficients for the four wheels: front left, front right, rear left, and rear right. x,total The target longitudinal force for the driver; ΔMz is the desired additional yaw moment output by the upper controller; δ f This is the equivalent front wheel steering angle.

[0149] get , Then, by substituting the partial derivative equations, the expected longitudinal force of the four wheels can be directly calculated:

[0150] ;

[0151] ;

[0152] Finally, the desired longitudinal force is multiplied by the effective rolling radius R of the tire to obtain the final desired torque command for the four hub motors:

[0153] ;

[0154] Where T i For the first i The desired torque command for each wheel. Let be the optimal expected longitudinal force for the i-th wheel.

[0155] This analytical solution process requires no numerical iteration and ensures that the underlying control system completes torque distribution within microseconds, greatly improving the real-time response capability of the control architecture under extreme driving conditions.

[0156] This embodiment performs simulation verification and analysis on the relevant scheme. A MATLAB / Simulink simulation platform is built.

[0157] To verify the beneficial effects of the present invention, two harsh operating conditions were set up:

[0158] Condition 1: Road surface adhesion coefficient µ = 0.3 (icy and snowy road surface), vehicle speed 22 m / s, and a sinusoidal steering excitation with an amplitude of 2 rad is applied. The corresponding simulation results are shown in Figure 4, where (a) is the steering wheel angle input, (b) is the yaw rate tracking curve, (c) is the center of gravity sideslip angle comparison curve, and (d) is the four-wheel torque output curve.

[0159] Figure 4(a) shows the smooth sinusoidal steering wheel input; the curve comparison in Figure 4(b) proves that the proposed solution (FFDTSMC-DWMEA) has minimal phase lag and no overshoot during yaw rate tracking, while the comparative integral terminal sliding mode control (ITSMC) and traditional sliding mode control (SMC) show obvious tracking overshoot and oscillation; in Figure 4(c), the proposed method limits the vehicle's center of gravity sideslip angle to a safe range of ±2°, while the SMC solution achieves a sideslip angle of 6.5°, fully verifying the advantages of the proposed solution in maintaining vehicle stability; Figure 4(d) clearly depicts the four-wheel torque output by the proposed method, and no high-frequency vibration occurred during the entire test.

[0160] Condition 2: With a road surface adhesion coefficient µ = 0.3 and a vehicle speed increased to 33 m / s, a double lane change emergency obstacle avoidance test was conducted. The simulation results are shown in Figure 5, where (a) is the steering wheel angle input, (b) is the yaw rate tracking curve, (c) is the center of gravity sideslip angle comparison curve, and (d) is the four-wheel torque output curve. Figure 5(a) illustrates the intense obstacle avoidance steering operation; Figure 5 (b) and Figure 5 The comparison in (c) in Figure 5 also demonstrates that even under large transient operations, this solution can still accurately track the target yaw rate and effectively suppress the surge in the center of gravity sideslip angle to prevent the vehicle from losing control. The four-wheel torque distribution in (d) in Figure 5 also shows that the DWMEA module can quickly respond to the vehicle's dynamic requirements and maintain good control performance.

[0161] In summary, the hierarchical control method based on fuzzy fast dynamic terminal sliding mode control and dynamic weighted minimum energy allocation provided by this invention can effectively solve the problems of integral saturation, parameter adaptive difference and delay caused by allocation calculation iteration in the prior art, and significantly improve the safety of vehicle driving under low adhesion extreme conditions.

Claims

1. A yaw control method for a four-wheel drive vehicle based on fuzzy dynamic terminal sliding mode, characterized in that, Includes the following steps: Step 1: Establish a seven-degree-of-freedom nonlinear vehicle dynamics model that includes longitudinal, lateral, and yaw vehicle body motion and independent rotational motion of the four wheels, and establish a two-degree-of-freedom linear vehicle reference model; calculate the longitudinal and lateral forces of each tire based on the PAC2002 tire model using the magic formula, and calculate the vertical load of the tire in combination with dynamic load transfer. The equivalent steering angles of the left and right front wheels are calculated based on the steering wheel angle input and the Ackerman steering angle characteristics; the longitudinal acceleration, lateral acceleration, yaw rate, longitudinal speed and wheel speed signals of each wheel of the vehicle are acquired in real time as the vehicle state signals, and the target yaw rate and target centroid sideslip angle are calculated based on the two-degree-of-freedom linear vehicle reference model combined with the road adhesion coefficient and real-time vehicle speed as the target reference signals; Step 2: Define the yaw rate tracking error and the center of gravity sideslip angle tracking error based on the vehicle state signal and the target reference signal; construct a combined fast terminal sliding surface with a dynamic forgetting integral term, which is used to suppress integral saturation under continuous disturbance or actuator saturation; introduce a fuzzy logic system, with the road adhesion coefficient and the absolute value of the steering wheel angle as inputs, and the terminal gain parameter as the output for adaptive adjustment; differentiate the sliding surface based on the zero-order hold assumption, design a composite reaching law containing an exponential reaching law and a saturation function, construct the control law for the direct yaw moment, and verify the asymptotic stability of the closed-loop system through Lyapunov stability analysis, and output the desired direct yaw moment; Step 3: Establish an objective function with the goal of minimizing the weighted sum of squares of the longitudinal forces of each wheel. The weighting coefficients are dynamically adjusted based on the wheel vertical load, front wheel steering angle, and vehicle speed. Construct constraints including longitudinal force balance equations, yaw moment balance equations, tire friction circle constraints, and motor output torque constraints. Transform the inequality constraints into dynamic penalty terms in the objective function to correct the weighting coefficients online. Construct a Lagrange function based on the Lagrange multiplier method and calculate the partial derivatives with respect to the longitudinal forces of each wheel to obtain auxiliary decoupling variables. Construct a second-order linear equation system based on the auxiliary decoupling variables, and use Cramer's rule to directly obtain the analytical solution of the Lagrange multipliers. Calculate the optimal expected longitudinal forces of the four wheels and multiply them by the tire rolling radius to generate the final torque command for each wheel hub motor, which is then output to the wheel hub motor.

2. The yaw control method for a four-wheel drive vehicle based on fuzzy dynamic terminal sliding mode according to claim 1, characterized in that, In step 1: Establish the differential equation of wheel rotation motion, and determine the dynamic response of the wheel based on the wheel speed signal and motor torque signal of each wheel.

3. The yaw control method for a four-wheel drive vehicle based on fuzzy dynamic terminal sliding mode according to claim 1, characterized in that, In step 1: Establish a tire kinematic model and calculate the longitudinal velocity, lateral velocity, wheel slip angle, and longitudinal slip ratio at the center of each wheel based on the vehicle's motion state.

4. The yaw control method for a four-wheel drive vehicle based on fuzzy dynamic terminal sliding mode according to claim 1, characterized in that, In step 1: Establish the PAC2002 tire model using the magic formula, calculate the longitudinal and lateral forces of each tire, and calculate the vertical load of the tire by combining real-time dynamic load transfer.

5. The yaw control method for a four-wheel drive vehicle based on fuzzy dynamic terminal sliding mode according to claim 1, characterized in that, In step 2: Construct a combined fast terminal sliding surface that incorporates a dynamic forgetting integral term, and introduce the dynamic forgetting integral term to suppress integral saturation.

6. The yaw control method for a four-wheel drive vehicle based on fuzzy dynamic terminal sliding mode according to claim 1, characterized in that, In step 3: To achieve the vehicle's target motion, the control distribution must satisfy two equality constraints: longitudinal force balance and yaw moment balance. ； ； in: , , , These represent the longitudinal tire forces of the four wheels: left front, right front, left rear, and right rear, respectively. B is the equivalent front wheel steering angle of the vehicle; F is the vehicle track width; x,total The total longitudinal force for the driver's target. This is the desired yaw torque output by the upper-level controller.

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