A vehicle stability control method based on fuzzy adaptive second-order sliding mode

Abstract

The application discloses a vehicle stability control method based on fuzzy adaptive second-order sliding mode, and relates to the field of direct yaw moment control of electric vehicles. A second-order sliding mode controller is designed by combining backstepping method and Lyapunov theory, so that an additional yaw moment is obtained, and the influence of lateral and yaw disturbances and uncertainty on the vehicle system is inhibited by designing a fuzzy adaptive law, and the value of the disturbance boundary does not need to be determined. Step 1, an ideal linear two-degree-of-freedom model of a vehicle is established; step 2, a first-order sliding mode controller is designed; step 3, a second-order sliding mode controller is designed on the basis of step 2; step 4, an adaptive fuzzy second-order sliding mode controller is designed on the basis of step 3; and step 5, the calculated additional yaw moment is distributed to each wheel to realize vehicle stability control. The method has better control performance, can keep the vehicle stable under extreme working conditions, can converge within a limited time, and can inhibit the chattering phenomenon.

Description

Technical Field

[0001] This invention relates to the field of direct yaw moment control for electric vehicles, and in particular to a vehicle stability control method based on fuzzy adaptive second-order sliding mode. Background Technology

[0002] In recent years, the demand for vehicle yaw stability control has led to the development of direct yaw moment control technology. Simultaneously, direct yaw moment distribution control technology has also received considerable attention. However, commonly used two-degree-of-freedom vehicle models differ significantly from actual models, failing to fully consider the impact of parameter uncertainties and external disturbances on the vehicle. Furthermore, traditional sliding mode control struggles to effectively suppress chattering while maintaining good robustness and approach rate. Summary of the Invention

[0003] To address the above problems, this invention proposes a vehicle stability control method based on fuzzy adaptive second-order sliding mode. It combines backstepping and Lyapunov theory to design a second-order sliding mode controller, thereby obtaining additional yaw moment. Furthermore, it uses fuzzy adaptive laws to suppress the effects of lateral and yaw disturbances and uncertainties on the vehicle system.

[0004] The technical solution of the present invention includes the following steps:

[0005] Step 1: Establish an ideal linear two-degree-of-freedom model of the vehicle and obtain reference values ​​for yaw rate and sideslip angle.

[0006] Define the vehicle state vector as x = [βω] T The ideal linear two-degree-of-freedom model for a vehicle is:

[0007]

[0008] in, ω and β are the yaw rate and sideslip angle, respectively, and A is the system state matrix, containing the element: a 11 a 12 a 21 a 22 B is the input matrix, containing the element: b 11 b 21 ;K f K r These represent the lateral stiffness of the front and rear tires, respectively. a and b represent the distances from the front and rear axles to the vehicle's center of gravity, respectively. z δ is the moment of inertia of the vehicle's center of mass about the z-axis. m is the total mass of the vehicle. f It is the steering angle of the vehicle's front wheels, and δ f =δ sw / i, δ sw It is the steering wheel angle, i is the gear ratio, and vx It is the longitudinal velocity at the vehicle's center of gravity;

[0009] The reference value for yaw rate derived from the ideal vehicle model is:

[0010]

[0011] Where L is the wheelbase between the front and rear axles of the vehicle; As a stability factor;

[0012] The ideal yaw rate is limited by the road surface adhesion coefficient μ, and the lateral acceleration a y Need to satisfy: |a y |≤μg, therefore, in order to meet the complex road conditions and minimize the sideslip angle, the reference values ​​for yaw rate and sideslip angle are:

[0013]

[0014] In actual operation, when the distributed drive system is subjected to external disturbances, the vehicle stability is easily affected; the vehicle lateral and yaw dynamic equations considering continuous bounded disturbances are as follows:

[0015]

[0016] Among them, D y and D z This consists of continuous bounded lateral interference and yaw interference;

[0017]

[0018] Step 2: Design a first-order sliding mode controller;

[0019] The sliding surface selection for a first-order sliding mode controller is as follows:

[0020] s=ω-ω d +ρ(β-β d (6)

[0021] ρ is a weighting factor; the larger its value, the greater the influence of the centroid sideslip angle.

[0022] Differentiating formula (6) and substituting it into formula (1), we get:

[0023]

[0024] in, Known and It is bounded, so we can find a constant such that Then, the expression for the first-order sliding mode controller is derived from formula (7);

[0025] The expression for the first-order sliding mode controller is given by formula (8). When σ0>0, the sliding surface s can converge to the origin in a finite time.

[0026]

[0027] Where, ΔM z To add yaw moment;

[0028] Step 3: Design a second-order sliding mode controller based on Step 2;

[0029] Taking the derivative of formula (7) further, we obtain the second derivative of s:

[0030]

[0031] in:

[0032]

[0033] make Therefore, formula (12) can be written in the following form:

[0034]

[0035] Where ψ(t,ω) characterizes the disturbance, including system uncertainty and external disturbance;

[0036] When the DYC top-level controller is designed as Equation (14), then the sliding variable s and It converges to the origin within a finite time.

[0037]

[0038] Where d, k1, and c1 are all control parameters;

[0039] Step 4: Based on Step 3, design an adaptive fuzzy second-order sliding mode controller;

[0040] When formulas (33), (34), and (35) are the top-level controller of DYC, the sliding variable s and It converges to the origin within a finite time.

[0041]

[0042] in, For control functions, For the adaptive law of the design parameters;

[0043] Step 5: Distribute the calculated additional yaw moment to each wheel to achieve vehicle stability control;

[0044] The vehicle state variables, along with the ideal values ​​of yaw rate and sideslip angle, are input into the top-level controller, specifically into the adaptive fuzzy second-order sliding mode controller established in step 4, to obtain the desired additional yaw moment ΔM. z Finally, the average torque distribution in the underlying controller determines the driving torque on each wheel. It should be explained that determining the driving torque on each wheel through torque distribution is a conventional technical method in the prior art, and will not be elaborated on in this case.

[0045] Derive the first-order sliding mode controller established in step 2 using the following steps:

[0046] Define the Lyapunov function V0 = 1 / 2s 2 Differentiating it and substituting it into formula (7), we get:

[0047]

[0048] This can be further written as:

[0049]

[0050] According to Lyapunov's stability theory, s will converge to the origin in a finite amount of time.

[0051] Derive the second-order sliding mode controller established in step 3 using the following steps:

[0052] Let z1 = s, Formula (13) can be written in the following form:

[0053]

[0054] In practical applications, ψ(t,ω) is bounded: Define the target value of z1 as z 1d e1 is the control error of z1:

[0055] e1 = z1 - z 1d (16)

[0056]

[0057] Define a new Lyapunov function V1 and find its derivative:

[0058]

[0059] Depend on From the expression, we can see that when And when c1 is a positive real number, The condition is semi-negative definite, where z1 approaches 0 in a finite amount of time. Then, an intermediate variable e2 is introduced:

[0060]

[0061] Substituting formula (21) into formula (17) yields

[0062]

[0063] At this point, combining formulas (22) and (23):

[0064]

[0065] To make both e1 and e2 approach 0, we introduce a variable τ and take its derivative:

[0066] τ=k1e1+e2,k1>0 (25)

[0067] Substituting formula (23) into formula (25) yields:

[0068]

[0069] It is easy to see that when τ = 0, both e1 and e2 can approach 0 in a finite time. At this time, the Lyapunov function V2 is defined as follows:

[0070]

[0071] Taking the derivative of V2 and substituting the derivative of formula (25) into the equation, we get:

[0072]

[0073] Combining formula (14) and letting z1, we obtain the target value z. 1d =0, therefore:

[0074]

[0075] Define the Q matrix as follows:

[0076]

[0077] Let E = [e1 e2] T It can be deduced that:

[0078]

[0079] Therefore, when Q is a positive definite matrix:

[0080]

[0081] To keep Q a positive definite matrix, let |Q| = d(k1+c1)-1 / 4 > 0, thus we have According to Lyapunov's stability theorem and LaSalle's invariance principle, it is possible to achieve z1→z in a finite time. 1d as well as If at this time Then s→0 and

[0082] Derive the adaptive fuzzy second-order sliding mode controller established in step 4 using the following steps:

[0083] The control function fuzzifies the sliding mode variables using a Gaussian membership function.

[0084]

[0085] Where μ f,i (τ) is the control function f (AF) The membership function of variable τ, α f,i σ represents the mean of the Gaussian membership function of the variable τ. f,i The variance of the Gaussian membership function representing the variable τ;

[0086] The mean and variance of the membership function in formula (36) have the following design rules:

[0087]

[0088] Control function f (AF) The fuzzy expression is:

[0089]

[0090] Where: θ i (i∈{NB,...,PB}) are the defuzzification parameters, and Π is the normalized fuzzy vector;

[0091]

[0092] According to the fuzzy universal approximation theory, there always exists an ideal defuzzification parameter θ. * This allows the fuzzy function to approximate continuous external disturbances with arbitrary precision. However, ideal parameters are difficult to obtain directly, and designing fixed fuzzy parameters cannot adapt to changes in vehicle speed and environment, thus reducing the control effect. Therefore, an adaptive method is used to design fuzzy parameters so that the control function can not only stabilize the system but also make the control signal smooth.

[0093] Define the adaptive fuzzy parameter vector as follows:

[0094]

[0095] Define the difference between the adaptive defuzzification parameter and the ideal value and find its derivative:

[0096]

[0097] Define Lyapunov functions Differentiating, we get:

[0098]

[0099] Substituting formulas (28), (33), (34), and (41) into formula (42) yields:

[0100]

[0101] Substituting the adaptive law of the design parameters, i.e., formula (35), into formula (43), we get:

[0102]

[0103] Using the universal fuzzy approximation theory, the following conclusion holds true:

[0104] ψ-θ *T Π≤γ1τ γ1≥0 (45)

[0105] Substituting formula (45) into formula (44) yields:

[0106]

[0107] This concludes the derivation.

[0108] Compared with existing technologies, the present invention, employing the above technical solution, has the following technical advantages: This method takes into account the chattering phenomenon of traditional sliding mode control and the disturbance boundary in adaptive control methods. The value of is unknown, requiring continuous debugging and analysis. Therefore, the fuzzy adaptive approximation method is combined to obtain the disturbance boundary, thereby improving the control effect, suppressing disturbances, and reducing chattering.

[0109] This invention designs a top-level controller that combines fuzzy adaptive theory with second-order sliding mode, with lower-level controllers distributing torque. This method offers better control performance, enabling the vehicle to remain stable under extreme conditions, converge within a finite time, and suppressing chattering. Attached Figure Description

[0110] Figure 1 This invention provides a framework for a vehicle stability control strategy based on fuzzy adaptive second-order sliding mode.

[0111] Figure 2 Interference A is designed during the simulation process of this invention;

[0112] Figure 3 This is a comparison chart of the yaw rate at 108 km / h and on a wet, slippery road surface (road adhesion coefficient of 0.3) according to the present invention.

[0113] Figure 4 This is a comparison diagram of the centroid sideslip angle at 108 km / h and on a wet and slippery road surface (road adhesion coefficient of 0.3) according to the present invention.

[0114] Figure 5 This is a data analysis chart of the tracking performance of the present invention under the working conditions of 108km / h and wet and slippery road surface (road surface adhesion coefficient is 0.3);

[0115] Figure 6 This is a comparison chart of the additional yaw moment at 108 km / h and on a wet and slippery road surface (road adhesion coefficient of 0.3) according to the present invention;

[0116] Figure 7 This is a comparison chart of the torque of each wheel at 108 km / h on a wet and slippery road surface (road adhesion coefficient of 0.3). Detailed Implementation

[0117] To clearly illustrate the technical features of this patent, the following detailed description is provided through specific embodiments and in conjunction with the accompanying drawings.

[0118] like Figure 1 As shown, this invention provides a vehicle stability control method based on fuzzy adaptive second-order sliding mode, comprising the following steps:

[0119] Step 1: Establish an ideal linear two-degree-of-freedom model of the vehicle and obtain reference values ​​for yaw rate and sideslip angle.

[0120] Define the vehicle state vector as x = [βω] T The ideal linear two-degree-of-freedom model for a vehicle is:

[0121]

[0122] in, ω and β are the yaw rate and sideslip angle, respectively, and A is the system state matrix, containing the element: a 11 a 12 a 21 a 22 B is the input matrix, containing the element: b 11 b 21 K f K r These represent the lateral stiffness of the front and rear tires, respectively. a and b represent the distances from the front and rear axles to the vehicle's center of gravity, respectively. z δ is the moment of inertia of the vehicle's center of mass about the z-axis. m is the total mass of the vehicle. f It is the steering angle of the vehicle's front wheels, and δ f =δ sw / i, δ swIt is the steering wheel angle, i is the gear ratio, and v x It is the longitudinal velocity at the vehicle's center of gravity.

[0123] The reference value for yaw rate derived from the ideal vehicle model is:

[0124]

[0125] Where L is the wheelbase between the front and rear axles of the vehicle; This is a stability factor.

[0126] The ideal yaw rate is limited by the road surface adhesion coefficient μ, and the lateral acceleration a y Need to satisfy: |a y |≤μg, therefore, in order to meet the complex road conditions and minimize the sideslip angle, the reference values ​​for yaw rate and sideslip angle are:

[0127]

[0128] In real-world operating conditions, vehicle stability is highly susceptible to disruptions when the distributed drive system is subjected to external disturbances. The lateral and yaw dynamic equations for the vehicle considering continuous bounded disturbances are as follows:

[0129]

[0130] Among them, D y and D z It consists of continuous bounded lateral interference and yaw interference.

[0131]

[0132] Step 2: Design a first-order sliding mode (FOSM) controller;

[0133] The sliding surface selection for a first-order sliding mode controller is as follows:

[0134] s=ω-ω d +ρ(β-β d (6)

[0135] ρ is a weighting factor; the larger its value, the greater the influence of the centroid sideslip angle.

[0136] Differentiating formula (6) and substituting it into formula (1), we get:

[0137]

[0138] in, Known and It is bounded, so we can find a constant such that Then, the expression for the first-order sliding mode controller is derived from formula (7).

[0139] Theorem 1: The expression of the first-order sliding mode controller is given by formula (8). When σ0>0, the sliding surface s can converge to the origin in a finite time.

[0140]

[0141] Where, ΔM z To add yaw moment.

[0142] Proof 1: Define the Lyapunov function V0 = 1 / 2s 2 Differentiating it and substituting it into formula (7), we get:

[0143]

[0144] This can be further written as:

[0145]

[0146] According to Lyapunov's stability theory, s will converge to the origin in a finite time. In Theorem 1, the additional yaw moment includes a perturbation term. To suppress disturbances, but The value of is unknown. In order to satisfy Lyapunov's stability theorem... Using a large value will lead to a serious chattering problem. In order to solve this problem, the following second-order sliding mode controller was designed by combining backstepping and Lyapunov theory.

[0147] Step 3: Design a second-order sliding mode (SOSM) controller based on Step 2;

[0148] A second-order sliding mode controller is designed by combining backstepping and Lyapunov theory, and control output is generated during the design process.

[0149] Taking the derivative of formula (7) further, we obtain the second derivative of s:

[0150]

[0151] in:

[0152]

[0153] make Therefore, formula (12) can be written in the following form:

[0154]

[0155] ψ(t,ω) represents the disturbance, including system uncertainty and external disturbance.

[0156] Theorem 2: When the top-level controller of DYC is designed as formula (14), then the sliding variable s and It converges to the origin within a finite amount of time.

[0157]

[0158] Where d, k1, and c1 are all control parameters.

[0159] Proof 2: The following proves the above theorem using Lyapunov stability theory and backstepping:

[0160] Let z1 = s, Formula (13) can be written in the following form:

[0161]

[0162] In practical applications, ψ(t,ω) is bounded: Define the target value of z1 as z 1d e1 is the control error of z1:

[0163] e1 = z1 - z 1d (16)

[0164]

[0165] Define a new Lyapunov function V1 and find its derivative:

[0166]

[0167] Depend on From the expression, we can see that when And when c1 is a positive real number, The condition is semi-negative definite, where z1 approaches 0 in a finite amount of time. Then, an intermediate variable e2 is introduced:

[0168]

[0169] Substituting formula (21) into formula (17) yields

[0170]

[0171] At this point, combining formulas (22) and (23):

[0172]

[0173] To make both e1 and e2 approach 0, we introduce a variable τ and take its derivative:

[0174] τ=k1e1+e2,k1>0 (25)

[0175] Substituting formula (23) into formula (25) yields:

[0176]

[0177] It is easy to see that when τ = 0, both e1 and e2 can approach 0 in a finite time. At this time, the Lyapunov function V2 is defined as follows:

[0178] Taking the derivative of V2 and substituting the derivative of formula (25) into the equation, we get:

[0179]

[0180] Combining formula (14) and letting z1, we obtain the target value z. 1d =0, therefore:

[0181]

[0182] Define the Q matrix as follows:

[0183]

[0184] Let E = [e1 e2] T It can be deduced that:

[0185]

[0186] Therefore, when Q is a positive definite matrix:

[0187]

[0188] To keep Q a positive definite matrix, let |Q| = d(k1+c1)-1 / 4 > 0, thus we have According to Lyapunov's stability theorem and LaSalle's invariance principle, it is possible to achieve z1→z in a finite time. 1d as well as If at this time Then s→0 and

[0189] As can be seen from the derivation in this section, the range of values ​​for most parameters is clear, but the perturbation boundary... The value is unknown.

[0190] Step 4: Design an adaptive fuzzy second-order sliding mode (AFSOSM) controller;

[0191] This section describes how to design a fuzzy adaptive law to suppress the effects of lateral and yaw disturbances and uncertainties on the vehicle system.

[0192] In step 4, considering the chattering phenomenon of traditional sliding mode control and the disturbance boundary in the adaptive control method, The value of is unknown, requiring continuous debugging and analysis. Therefore, the fuzzy adaptive approximation method is combined to obtain the disturbance boundary, thereby improving the control effect and suppressing disturbances.

[0193] Theorem 3: When formulas (33), (34), and (35) are the top-level controllers of DYC, the sliding variable s and It converges to the origin within a finite amount of time.

[0194]

[0195] in, The control function obtained by substituting the adaptive defuzzification vector formula (40) into formula (38) is... The adaptive law for the designed parameters.

[0196] Proof 3: The fuzzy rules between the control function and the variable τ are shown in the table.

[0197]

[0198]

[0199] In the table, NB represents negative large, NM represents negative medium, NS represents negative small, ZE represents zero, PS represents positive small, PM represents positive medium, and PB represents positive large.

[0200] The control function fuzzifies the sliding mode variables using a Gaussian membership function.

[0201]

[0202] Where μ f,i (τ) is the control function f (AF) The membership function of variable τ, α f,i σ represents the mean of the Gaussian membership function of the variable τ. f,i The variance of the Gaussian membership function for variable τ.

[0203] The mean and variance of the membership function in formula (36) have the following design rules:

[0204]

[0205] Control function f (AF) The fuzzy expression is:

[0206]

[0207] Where: θ i(i∈{NB,...,PB}) are the defuzzification parameters, and Π is the normalized fuzzy vector;

[0208]

[0209] According to the fuzzy universal approximation theory, there always exists an ideal defuzzification parameter θ. * This allows the fuzzy function to approximate continuous external disturbances with arbitrary precision. However, ideal parameters are difficult to obtain directly, and designing fixed fuzzy parameters cannot adapt to changes in vehicle speed and environment, thus reducing the control effect. Therefore, an adaptive method is used to design fuzzy parameters so that the control function can not only stabilize the system but also make the control signal smooth.

[0210] Define the adaptive fuzzy parameter vector as follows:

[0211]

[0212] Define the difference between the adaptive defuzzification parameter and the ideal value and find its derivative:

[0213]

[0214] Define Lyapunov functions Differentiating, we get:

[0215]

[0216] Substituting formulas (28), (33), (34), and (41) into formula (42) yields:

[0217]

[0218] Substituting the adaptive law of the design parameters, i.e., formula (35), into formula (43), we get:

[0219]

[0220] Using the universal fuzzy approximation theory, the following conclusion holds true:

[0221] ψ-θ *T Π≤γ1|τ|γ1≥0 (45)

[0222] Substituting formula (45) into formula (44) yields:

[0223]

[0224] This concludes the proof. The adaptive fuzzy sliding mode control algorithm can asymptotically stabilize the yaw rate and sideslip angle tracking errors of the vehicle's closed-loop control system.

[0225] Step 5: Distribute the calculated additional yaw moment to each wheel to achieve vehicle stability control;

[0226] The vehicle state variables, along with the ideal values ​​of yaw rate and sideslip angle, are input into the top-level controller, specifically into the adaptive fuzzy second-order sliding mode controller established in step 4, to obtain the desired additional yaw moment ΔM. z Finally, the average torque distribution in the underlying controller determines the drive torque on each wheel.

[0227] To verify the feasibility and effectiveness of this method, vehicle stability control simulations were performed using this method on the CarSim / Simulink platform, and the simulation results were compared with those of the traditional sliding mode control (OSM) method. Table 1 shows the vehicle parameters, using a double lane change condition, a vehicle speed of 108 km / h, and a road adhesion coefficient of 0.3 for the simulation test.

[0228] parameter value mass m 1270kg Front wheelbase a 1.015m Rear wheelbase b 1.895m <![CDATA[Moment of inertia I z > <![CDATA[1536.7kg·m 2 ]]> <![CDATA[Cornering stiffness K1 of the front wheel]]> -112600N / rad <![CDATA[Lateral stiffness K2 of the rear wheel]]> -89500N / rad Transmission ratio i 17

[0229] Figure 2 Interference A is designed during the simulation process of this invention; Figure 3 This is a comparison chart of the yaw rate at 108 km / h and on a wet, slippery road surface (road adhesion coefficient of 0.3) according to the present invention. Figure 4 This is a comparison diagram of the centroid sideslip angle at 108 km / h and on a wet and slippery road surface (road adhesion coefficient of 0.3) according to the present invention. Figure 5 This is a data analysis chart of the tracking performance of the present invention under the working conditions of 108km / h and wet and slippery road surface (road surface adhesion coefficient is 0.3); Figure 6 This is a comparison chart of the additional yaw moment at 108 km / h and on a wet and slippery road surface (road adhesion coefficient of 0.3) according to the present invention; Figure 7 This is a comparison chart of the torque of each wheel at 108 km / h on a wet and slippery road surface (road adhesion coefficient of 0.3).

[0230] There are many specific ways to implement this invention. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A vehicle stability control method based on fuzzy adaptive second order sliding mode, characterized in that, Comprising the following steps: Step 1, establishing a linear two-degree-of-freedom model of the vehicle, obtaining the reference values of yaw rate and sideslip angle; The vehicle state vector x = [β ω] is defined T The vehicle ideal linear two-degree-of-freedom model is: wherein ω, β are the yaw rate and the sideslip angle of the center of mass, respectively, A is the system state matrix, containing the elements: 11 , a 12 , a 21 , a 22 B is the input matrix, containing the elements: 11 , b 21 ; K f , K r are the front and rear tire cornering stiffness, respectively.a, b are the distances from the front and rear axles to the center of mass of the vehicle.I z is the moment of inertia of the center of mass of the vehicle about the z-axis.m is the total mass of the vehicle.δ f is the steering angle of the front wheels, and δ f = δ sw / i, δ sw is the steering wheel angle, i is the transmission ratio, v x is the longitudinal velocity at the center of mass of the vehicle; The reference value of yaw rate derived from the ideal model of the vehicle is: L is the wheelbase of the vehicle; is a stability factor; The ideal yaw rate is limited by the road adhesion coefficient μ, the lateral acceleration a y The following must be satisfied: |a y |≤ μg, so in order to satisfy the complex road conditions while making the mass side slip angle as small as possible, the reference values of the yaw rate and the mass side slip angle are taken as: In actual working conditions, when the distributed drive system is disturbed by external interference, the stability of the vehicle is easily affected; considering the continuous bounded disturbance, the lateral and yaw dynamics equation of the vehicle is: where D y and D z are continuous bounded lateral and yaw disturbances; Step 2, designing a first-order sliding mode controller; The sliding surface of the first-order sliding mode controller is selected as follows: s = ω - ω d + p(β - β d ) (6) ρ is a weight factor, the greater the value, the greater the influence of the center of mass sideslip angle; Deriving formula (6) and substituting formula (1) can obtain: wherein It is known and is bounded, so that one can find a constant such that Then the expression of the first order sliding mode controller is derived from equation (7); The expression form of the first-order sliding mode controller is formula (8), when σ0>0, the sliding surface s can converge to the origin in finite time; where ΔM z is the additional yaw moment; Step 3, designing a second-order sliding mode controller based on step 2; Further derivation of formula (7) obtains the second derivative of s: Wherein: Let So equation (12) can be written as follows: Wherein ψ(t,ω) represents disturbance, including system uncertainty and external disturbance; When the DYC top-level controller is designed as formula (14), then the sliding variable s and Converge to the origin in finite time; Wherein d, k1, c1 are control parameters; Step 4, designing an adaptive fuzzy second-order sliding mode controller based on step 3; When formula (33), (34), (35) is the top controller of DYC, the sliding variable s and Converge to the origin in finite time; wherein, is a control function, is a designed parameter adaptive law; Step 5, distributing the calculated additional yaw moment to each wheel to realize vehicle stability control; The vehicle state quantity and the ideal values of yaw rate and mass center side slip angle are input into the top layer controller, i.e. into the adaptive fuzzy second order sliding mode controller established in step 4, to obtain the additional yaw moment ΔM desired to be output z Finally, the drive torque on each wheel is determined through the average torque distribution decision in the bottom layer controller.

2. The vehicle stability control method based on fuzzy adaptive second order sliding mode according to claim 1, characterized in that, The first-order sliding mode controller established in step 2 is derived as follows: Define Lyapunov function V0=1 / 2s 2 Taking the derivative of it and substituting into equation (7), we get: Further written as: According to Lyapunov stability theory, s will converge to the origin in finite time.

3. The vehicle stability control method based on fuzzy adaptive second order sliding mode according to claim 1, characterized in that, The second-order sliding mode controller established in step 3 is derived as follows: Let z1 = s, Equation (13) can be written in the following form: In practical applications, ψ(t, ω) is bounded: The target value of z1 is defined as z 1d e1 is the control error of z1: e1 = z1 - z 1d (16) Define a new Lyapunov function V1 and derive it: From the expression of and c1 is a positive real number, and c1 is a positive real number, is semi-negative, in which case z1 tends to 0 in finite time, then introduce the intermediate variable e2: Substituting formula (21) into formula (17) can obtain At this time, combined with formula (22) and formula (23): In order to make e1 and e2 tend to 0, introduce variable τ and derive it: τ=k1e1+e2, k1>0 (25) Substituting formula (23) into formula (25) obtains: It is easy to know that when τ=0, e1 and e2 can tend to 0 in finite time, at this time, define Lyapunov function V2: Derive V2 and substitute the derivative of formula (25) into it: Combining equation (14) and letting z1get the target value z 1d = 0, we get: Define the Q matrix as follows: Take E = [e1 e2] T It can be derived that: Therefore, when Q is a positive definite matrix: To make Q a positive definite matrix, let |Q| = d(k1+ c1)1 / 4> 0, so that According to Lyapunov stability theorem and LaSalle invariance principle, it can be realized that z1→ z 1d and At this time, if then s→ 0 and 4. The vehicle stability control method based on fuzzy adaptive second order sliding mode according to claim 1, characterized in that, The adaptive fuzzy second-order sliding mode controller established in step 4 is derived as follows: The control function is fuzzy by Gaussian membership function to the sliding variable, where μ f,i (τ) is a control function f (AF) a membership function of the variable τ, α f,i denotes a Gaussian-type membership function of the variable τ mean, σ f,i denotes a Gaussian-type membership function of the variable τ variance; The mean and variance of the membership function in formula (36) have the following design rules: Control function f (AF) The fuzzy expression of f is: where: θ i (i∈{NB,...,PB}) is a deblurring parameter, and Π is a normalized blur vector. According to the theory of fuzzy universal approximation, there always exists an ideal deblurring parameter θ * The fuzzy function can approach the continuous external disturbance with arbitrary accuracy, but the ideal parameter is difficult to obtain directly, and the fixed fuzzy parameter design cannot adapt to the change of vehicle speed environment, thus reducing the control effect. Therefore, the adaptive method is used to design the fuzzy parameter, so that the control function can not only stabilize the system, but also make the control signal smooth. Define the adaptive fuzzy parameter vector as: Define the difference between the adaptive de-fuzzification parameter and the ideal value and derive it: Defining a Lyapunov function Taking the derivative gives: Substituting formula (28), (33), (34) and (41) into formula (42) obtains: Then substitute the designed parameter adaptive law, i.e. formula (35) into formula (43) to obtain: Using the universal fuzzy approximation theory, the following conclusions are established: ψ - θ *T Π ≤ γ1τ γ1≥ 0 (45) Substituting formula (45) into formula (44) can obtain: Thus, the derivation is completed.

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