CN105172790B

CN105172790B - A kind of vehicle yaw stability control method based on three-step approach

Info

Publication number: CN105172790B
Application number: CN201510719063.7A
Authority: CN
Inventors: 郭洪艳; 宋林桓; 马骉; 陈虹; 于树友
Original assignee: Jilin University
Current assignee: Jilin University
Priority date: 2015-10-30
Filing date: 2015-10-30
Publication date: 2017-09-12
Anticipated expiration: 2035-10-30
Also published as: CN105172790A

Abstract

The invention discloses a kind of vehicle yaw stability control method based on three-step approach, using the strategy of hierarchical control, front wheel angle and additional yaw moment are obtained using three-step approach, and additional yaw moment is allocated from the optimization method of quadratic programming, additional yaw moment is assigned as Braking on four wheels in vehicle.Step 1: setting up simplified vehicle dynamic model：The relation between the control stability of vehicle and the lateral movement and weaving of vehicle is characterized with two-freedom model；Step 2: design three-step approach controller, it will it is expected that yaw velocity information is input to three-step approach controller, according to the value and the vehicle side acceleration of Real-time Feedback of expecting yaw velocity, actual yaw velocity, actual side slip angle and longitudinal speed, with three-step approach algorithm flow, decision-making goes out additional yaw moment and front wheel angle；Step 3: carrying out vehicle yaw stability control based on the three-step approach controller that step 2 is designed.

Description

vehicle yaw stability control method based on three-step method

Technical Field

The invention relates to a vehicle active safety control method, in particular to a vehicle yaw stability control method based on a three-step method.

Background

Vehicle stability control is an automobile electronic control technology emerging from abroad, which is developed on the basis of the research on brake anti-lock systems and drive anti-skid systems. The stability control concept originates from the idea of using the two systems mentioned above to solve the stability problem, but researchers have begun to focus on algorithmic improvements, so that only part of the stability problem can be addressed. The system does not have deep theoretical analysis and matched hardware equipment, so the system cannot be called a real stability control system. By the beginning of the nineties of the twentieth century, researchers have broken through theoretical research, and have proposed a new idea of Direct Control adjustment (DYC) for Yaw motion, which indicates theoretically the direction of research in this field. The intention of steering to a driver is introduced into the idea, and direct control and adjustment are performed according to the yaw movement, so that the automobile is guaranteed to run in a stable area. This new idea represents a real formation of the concept of stability control.

The three-step method is an algorithm process based on a model and is mainly applied to the tracking control problem of a system. The design idea is derived from a control structure of 'feedforward + PID feedback' frequently adopted in engineering. The basic structure of the three-step method is 'steady-state control-feedforward control-error feedback control', each step has a corresponding control purpose, each part contains state information of a system or working condition information, and the updating result of each time of the information enables the gain of the controller to achieve the self-adjusting effect. The three steps are related to each other step by step, and the three steps cannot be reversed in sequence, so the method is called as a three-step method.

Disclosure of Invention

The invention provides a vehicle yaw stability control method based on a three-step method, which adopts a layered control strategy, obtains a front wheel corner and an additional yaw moment by applying the three-step method, distributes the additional yaw moment by selecting an optimization method of quadratic programming, and distributes the additional yaw moment into braking forces on four wheels to act on a vehicle.

The invention is realized by the following technical scheme:

step one, establishing a simplified vehicle dynamics model: representing the relationship between the steering stability of the vehicle and the lateral motion and the yaw motion of the vehicle by using a two-degree-of-freedom model;

step two, three-step method controller design: designing a three-step controller based on the simplified vehicle dynamics model established in the first step, inputting expected yaw velocity information into the three-step controller, and deciding an additional yaw moment and a front wheel corner by using a three-step algorithm process (steady state control, feedforward control and error feedback control) according to the value of the expected yaw velocity, the vehicle lateral acceleration fed back in real time, the actual yaw velocity, the actual mass center lateral deviation angle and the longitudinal vehicle speed;

and step three, carrying out vehicle yaw stability control by a three-step controller designed based on the step two: and (3) inputting the front wheel turning angle information and the additional yaw moment information into an additional yaw moment distribution module, converting the additional yaw moment distribution problem into a constrained quadratic programming optimization problem, distributing the additional yaw moment into braking forces on four wheels and outputting the braking forces to a braking system, and outputting the front wheel turning angle obtained in the step two to a steering system, wherein the braking forces and the steering system act on a vehicle system together to enable the vehicle to keep a yaw stable state.

The invention has the beneficial effects that:

1. the three-step method controller has a standard and clear structure, each step has an actual design purpose, and the three-step method controller is convenient for practical application in engineering.

2. The invention converts the additional yaw moment distribution module into a quadratic programming method, and considers the strategy of braking force wheel distribution, the limitation of the braking force, and the like, thereby obtaining the optimal solution.

3. According to the invention, the front wheel steering angle information and the differential braking information are taken into consideration in the stability control analysis, so that the front wheel steering angle information and the differential braking information can coordinate the stability control, and the conflict between a steering mechanism and a braking mechanism is avoided.

Drawings

FIG. 1 is a block diagram of a vehicle stability control system;

FIG. 2 is a schematic diagram of a two degree-of-freedom model of a vehicle;

FIG. 3 is a graph of yaw rate results for a sinusoidal delay condition;

FIG. 4 is a graph of centroid slip angle results under sinusoidal delay conditions;

FIG. 5 is a graph of the results of the additional yaw moment under a sinusoidal delay condition;

FIG. 6 is a graph of front wheel steering results under a sinusoidal delay condition;

FIG. 7 is a graph of the front left tire braking force results under a sinusoidal delay condition;

FIG. 8 is a graph of the braking force results for the front right tire under a sinusoidal delay condition;

FIG. 9 is a graph of left rear tire braking force results under a sinusoidal delay condition;

FIG. 10 is a graph of left rear tire braking force results for a sinusoidal delay condition.

Detailed Description

The invention provides a vehicle yaw stability control method based on a three-step method, which comprises the following steps: step one, establishing a simplified vehicle dynamic model, such as a graph shown in FIG. 2, for representing the relationship between the steering stability of the vehicle and the lateral motion and yaw motion of the vehicle. Considering the yaw motion and the lateral motion of the vehicle, the kinetic equation is:

wherein, F_y1、F_y2Is the cornering power of the front and rear tires in units of N; m_zFor additional yaw moment, in Nm; l is_f、L_rRespectively the distance from the center of mass of the automobile to the front and rear axes, and the unit is m; i is_zIs the moment of inertia of the automobile around the z-axis and has the unit kg.m²(ii) a r is yaw angular velocity, unit rad/s; m is the mass of the automobile in kg; v. of_xIn m/s for the longitudinal speed of the vehicle, and β for the side slip angle of the center of mass in rad.

The system equation (2) of the vehicle obtained by the formula (1) is as follows

F in equation of state (2) of the vehicle System_yf，F_yrThe invention takes the nonlinear instability factor of the tire into consideration in the design of a control system because the nonlinear characteristic of the tire must be considered when the lateral stability of a vehicle is researched by respectively representing the front and rear lateral deviation forces of the tire.From the description of the split tire model, it can be seen that the tire cornering power can be expressed as:

wherein, F_zIs the vertical longitudinal load of the tire, F_z0Is the nominal tire load, mu is the road adhesion coefficient, mu₀Is the nominal road adhesion coefficient, λ is the longitudinal slip ratio, C_αIs the tire cornering stiffness, α is the tire cornering angle, and γ is_z、γ_λAnd gamma_αAre the model parameters. Since only the lateral motion and the yaw motion of the vehicle are considered in the process of establishing the simplified dynamic model of the vehicle, the influence of the longitudinal slip ratio lambda on the lateral tire force is ignored, so that lambda is 0, and the formula (3) can be simplified as follows:

according to the geometric relationship in fig. 2, there is a relationship as in equation (5) between the front and rear tire slip angles, the vehicle front wheel steering angle, and the longitudinal vehicle speed.

Wherein, α_f，α_rIs the side slip angle of the front and rear tires, unit rad; is the front wheel turning angle, unit rad;

substituting the formulas (4) and (5) into the formula (2) to obtain the system state equation (6)

Step two, three-step method controller design: designing a three-step controller based on the simplified vehicle dynamics model established in the first step, inputting expected yaw velocity information into the three-step controller, and deciding an additional yaw moment and a front wheel corner by using a three-step algorithm flow according to the value of the expected yaw velocity and the vehicle lateral acceleration, the actual yaw velocity, the actual mass center lateral deviation angle and the longitudinal acceleration fed back in real time;

first, the expressions given for the desired centroid yaw angle and yaw rate are as follows,

the design of the three-step controller in the second step comprises the following steps:

(1) steady state control

Based on the simplified vehicle dynamics equation (6) established in step one, letAndthe system satisfies the following equation,

_fsand M_zsIt can be obtained from equation (8), because of the complex nonlinearity of the system, it is inspired by the control strategy based on table lookup widely used in modern automatic control field, and this is also in vehicle engineering, and it is the dynamic control of the system that is often used and uses the map table measured in steady state, and it is the steady state control in essence. The steady state control portion of the controller may be sought as follows,

(2) reference dynamic feedforward control

For a complex nonlinear system to achieve satisfactory performance, the steady state control alone is far from sufficient. Other information needs to be considered, therefore, on the basis of steady state, feedforward control is added and used

Wherein u is_1sAnd u_2sGiven in equation (9), u_1fAnd u_2fAnd (5) waiting for solving. By substituting formula (10) for formula (6)

By using in u_1sTaylor expression of points, we can obtain F_yfThe approximate expression of (a) is as follows,

then equation (11) can be rewritten as

By substituting formula (8) into formula (13), can be obtained

Order toAndthen the formula (14) becomes

Thus, the feedforward part can be obtained

(3) Tracking error feedback control

In the previous derivation process, external interference and modeling errors are not considered, in order to obtain better control effect, a small deviation system is controlled, on the basis of steady state control and feedforward control, finally, feedback control for error tracking is added,

by substituting formula (17) for formula (6)

Then, the Taylor expansion is used again to obtain

Then the formula (18) can be rewritten as

By substituting the formulae (8) and (15) into the formula (20), can be obtained

Defining an error as

The formula (21) is rewritten into

It can be obtained from the formula (23),

wherein k is₁Is greater than 0, and take

At the same time can obtain

u_2e＝k₂I_ze_r-k₁L_fmv_xe_β(26)

Wherein k is₂Is greater than 0, and take

(4) Control law and parameter selection principle

The overall control law obtained by combining equations (9), (16), (24) and (26) is as follows

Wherein,

the first step is steady-state control, the second step is reference dynamic feedforward control, and the third step is error feedback control, the three steps have clear design purposes, and the steps are mutually related, and the sequence of the steps cannot be reversed. The outputs of the three steps are added to obtain the control quantity of the three-step method.

k₁And k₂Is a regulating parameter, k, of the control algorithm₁How fast the decay rate, k, of the tracking error determines the centroid slip angle β₂The speed of the attenuation speed of the tracking error of the yaw rate r is determined. Therefore, k should be made to reduce the error as soon as possible₁And k₂Larger values of (b) are better, but larger values may cause high gain of the controller while amplifying noise, which is also undesirable. We need to make a compromise between avoiding the contradiction between high gain of the controller and reducing the tracking error to determine the value of the parameter.

Step three, based on the additional yaw moment and the front wheel turning angle information obtained in the step two, converting the additional yaw moment distribution into a quadratic programming problem to solve, wherein the specific method comprises the following steps:

in the allocation of the additional yaw moment, the allocation objective function is

In the formula,_xand_urespectively, a control magnitude matrix and an incremental weight matrix, and are diagonal matrices. Equation (30) is converted to a standard form of quadratic programming below. Due to the fact that

Δu_Fx＝u_Fx(k)-u_Fx(k-1) (31)

The formula (30) can be rewritten as

Due to u_Fx(k-1) is a value at the last moment, and can be regarded as known, soIs a constant number, which is equal to u_FxIrrelevant, do not influence the optimizing result. A standard form of additional yaw moment distribution can be obtained

Wherein,

Q＝_x+_u(34)

c^T＝-u_Fx(k-1)^T _u(35)

in the optimized allocation, the equation is constrained to

M_z＝Bu_Fx(36)

Wherein,

u_Fx＝[ΔF_xfl,ΔF_xfr,ΔF_xrl,ΔF_xrr](38)

equation (36) is a distribution equation of the braking force of the additional yaw moment distribution in the vehicle dynamics principle. This constraint ensures that the optimization results satisfy the vehicle dynamics principles.

The inequality constraints should also satisfy the strategy of brake wheel distribution and the limitation of the braking force. As a result of the choice of the unilateral wheel braking strategy, the inequality constraints for meeting the braking scheme are as follows,

Au_Fx≤0 (39)

wherein, when M_zWhen the pressure is higher than 0, the pressure is higher,

when M is_zWhen the content is less than or equal to 0,

in addition to meeting the requirements of the braking scheme, the inequality constraints also limit the magnitude of the braking force. The present invention is limited as follows,

-0.5F_z≤u_Fx≤0.5F_z(42)

Claims

1. A vehicle yaw stability control method based on a three-step method is characterized by comprising the following steps:

step two, three-step method controller design: designing a three-step controller based on the simplified vehicle dynamics model established in the first step, inputting expected yaw velocity information into the three-step controller, and deciding an additional yaw moment and a front wheel corner by using a three-step algorithm flow according to the value of the expected yaw velocity and the vehicle lateral acceleration, the actual yaw velocity, the actual mass center lateral deviation angle and the longitudinal vehicle speed which are fed back in real time;

the three-step controller design comprises the following main steps:

1) steady state control;

2) on the basis of steady-state control, reference dynamic feedforward control is added;

3) on the basis of steady-state control and feedforward control, finally, feedback control for error tracking is added;

combining the steps 1) to 3), the overall control law of the three-step controller is as follows:

<mrow> <mi>u</mi> <mo>=</mo> <msub> <mi>f</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>f</mi> <mi>f</mi> </msub> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> <mo>,</mo> <msub> <mover> <mi>r</mi> <mo>&CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>f</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> <mo>,</mo> <mi>e</mi> <mo>)</mo> </mrow> </mrow>

wherein,

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> <mo>,</mo> <mi>m</mi> <mi>a</mi> <mi>p</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <msub> <mi>mrv</mi> <mi>x</mi> </msub> <mo>-</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>r</mi> </mrow> </msub> <mo>(</mo> <mrow> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>L</mi> <mi>r</mi> </msub> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>L</mi> <mi>f</mi> </msub> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> <mo>,</mo> <msub> <mi>&delta;</mi> <mrow> <mi>f</mi> <mi>s</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mi>f</mi> </msub> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> <mo>,</mo> <msub> <mover> <mi>r</mi> <mo>&CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>I</mi> <mi>z</mi> </msub> <msub> <mover> <mi>r</mi> <mo>&CenterDot;</mo> </mover> <mi>d</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> <mo>,</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>mv</mi> <mi>x</mi> </msub> </mrow> <mrow> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> </mrow> </msub> </mrow> <mrow> <mo>&part;</mo> <msub> <mi>u</mi> <mn>1</mn> </msub> </mrow> </mfrac> <msub> <mo>|</mo> <msub> <mi>u</mi> <mrow> <mn>1</mn> <mi>s</mi> </mrow> </msub> </msub> </mrow> </mfrac> <mo>&CenterDot;</mo> <msub> <mi>e</mi> <mi>&beta;</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>k</mi> <mn>2</mn> </msub> <msub> <mi>I</mi> <mi>z</mi> </msub> <msub> <mi>e</mi> <mi>r</mi> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>L</mi> <mi>f</mi> </msub> <msub> <mi>mv</mi> <mi>x</mi> </msub> <msub> <mi>e</mi> <mi>&beta;</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> </mfenced>

in the formula, F_yf、F_yrIs the cornering power of the front and rear tires in units of N; m_zFor additional yaw moment, in Nm; l is_f、L_rRespectively the distance from the center of mass of the automobile to the front and rear axes, and the unit is m; i is_zIs the moment of inertia of the automobile around the z-axis and has the unit kg.m²(ii) a r is yaw angular velocity, unit rad/s; m isMass of car in kg; v. of_xβ is the centroid slip angle, unit rad;_fis the front wheel turning angle, unit rad;in yaw rate derivative, in units of rad/s²；e_βA tracking error representing a centroid slip angle; e.g. of the type_rA tracking error indicating a yaw rate;_fsrepresenting the front wheel corner, unit rad, obtained in step 1) steady state control step of the three-step controller; k is a radical of₁And k₂Is a regulating parameter, k, of the control algorithm₁How fast the decay rate, k, of the tracking error determines the centroid slip angle β₂Determining the speed of the attenuation speed of the tracking error of the yaw rate r;

2. A three-step based vehicle yaw stability control method as claimed in claim 1, wherein the simplified vehicle dynamics model created in step one is:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>&beta;</mi> <mo>&CenterDot;</mo> </mover> <mo>=</mo> <mfrac> <mrow> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> <mo>,</mo> <msub> <mi>&delta;</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>mv</mi> <mi>x</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mi>r</mi> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>r</mi> <mo>&CenterDot;</mo> </mover> <mo>=</mo> <mfrac> <mrow> <msub> <mi>L</mi> <mi>f</mi> </msub> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> <mo>,</mo> <msub> <mi>&delta;</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>L</mi> <mi>r</mi> </msub> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>M</mi> <mi>z</mi> </msub> </mrow> <msub> <mi>I</mi> <mi>z</mi> </msub> </mfrac> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>

wherein, F_yf、F_yrIs the cornering power of the front and rear tires in units of N; m_zFor additional yaw moment, in Nm; l is_f、L_rRespectively the distance from the center of mass of the automobile to the front and rear axes, and the unit is m; i is_zIs the moment of inertia of the automobile around the z-axis and has the unit kg.m²(ii) a r is yaw angular velocity, unit rad/s; m is the mass of the automobile in kg; v. of_xβ is the centroid slip angle, unit rad;_fis the front wheel steering angle, in units rad.

3. A three-step based vehicle yaw stability control method as claimed in claim 1, wherein said step two three-step controller design specifically comprises the steps of:

1) a steady-state control section:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mn>1</mn> <mi>s</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>&delta;</mi> <mrow> <mi>f</mi> <mi>s</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> <mo>,</mo> <mi>m</mi> <mi>a</mi> <mi>p</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <msub> <mi>mrv</mi> <mi>x</mi> </msub> <mo>-</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>r</mi> </mrow> </msub> <mo>(</mo> <mrow> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mn>2</mn> <mi>s</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>M</mi> <mrow> <mi>z</mi> <mi>s</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>L</mi> <mi>r</mi> </msub> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>L</mi> <mi>f</mi> </msub> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>,</mo> <mi>r</mi> <mo>,</mo> <msub> <mi>&delta;</mi> <mrow> <mi>f</mi> <mi>s</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>

wherein, F_yf、F_yrIs the cornering power of the front and rear tires in units of N; m_zFor additional yaw moment, in Nm; l is_f、L_rRespectively the distance from the center of mass of the automobile to the front and rear axes, and the unit is m; r is yaw angular velocity, unit rad/s; m is the mass of the automobile in kg; v. of_xβ is the centroid slip angle, unit rad;_fis the front wheel turning angle, unit rad; m_zsRepresenting the additional yaw moment obtained in the step 1) steady state control step of the three-step controller in Nm;_fsrepresenting the front wheel corner, unit rad, obtained in step 1) steady state control step of the three-step controller;

2) adding a reference dynamic feedforward control part on the basis of the step 1), namely:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&delta;</mi> <mi>f</mi> </msub> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mn>1</mn> <mi>s</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>M</mi> <mi>z</mi> </msub> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mn>2</mn> <mi>s</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mn>2</mn> <mi>f</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>

wherein,

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mn>2</mn> <mi>f</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mi>z</mi> </msub> <msub> <mover> <mi>r</mi> <mo>&CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>

3) adding a tracking error feedback control part on the basis of the step 2), namely:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&delta;</mi> <mi>f</mi> </msub> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mn>1</mn> <mi>s</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mn>1</mn> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mn>1</mn> <mi>e</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>M</mi> <mi>z</mi> </msub> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mn>2</mn> <mi>s</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mn>2</mn> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mn>2</mn> <mi>e</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>

wherein,

<mrow> <msub> <mi>u</mi> <mrow> <mn>1</mn> <mi>e</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>mv</mi> <mi>x</mi> </msub> </mrow> <mrow> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> </mrow> </msub> </mrow> <mrow> <mo>&part;</mo> <msub> <mi>u</mi> <mn>1</mn> </msub> </mrow> </mfrac> <msub> <mo>|</mo> <msub> <mi>u</mi> <mrow> <mn>1</mn> <mi>s</mi> </mrow> </msub> </msub> </mrow> </mfrac> <mo>&CenterDot;</mo> <msub> <mi>e</mi> <mi>&beta;</mi> </msub> </mrow>

in the above formula, k₁> 0, and taking:

<mrow> <msub> <mover> <mi>e</mi> <mo>&CenterDot;</mo> </mover> <mi>&beta;</mi> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>e</mi> <mi>&beta;</mi> </msub> </mrow>

at the same time, the following can be obtained:

u_2e＝k₂I_ze_r-k₁L_fmv_xe_β

in the above formula, k₂> 0, and taking:

<mrow> <msub> <mover> <mi>e</mi> <mo>&CenterDot;</mo> </mover> <mi>r</mi> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <msub> <mi>e</mi> <mi>r</mi> </msub> </mrow>2

wherein u is_1fRepresenting step 2) a first quantity of a reference dynamic feedforward control step decision of a three-step controller; u. of_2fRepresenting step 2) of the three-step controller a second quantity that references the dynamic feedforward control step decision; u. of₁A first quantity, u, representing a decision of a three-step controller₁＝u_1s+u_1f+u_1e；u_1eRepresenting the first quantity of step 3) tracking error feedback control step decisions of the three-step controller; u. of_2eA second quantity representing the decision of step 3) tracking error feedback control step of the three-step controller; e.g. of the type_βA tracking error representing a centroid slip angle; e.g. of the type_rA tracking error indicating a yaw rate; k is a radical of₁An adjustment parameter representing a tracking error of the centroid slip angle; k is a radical of₂An adjustment parameter indicating a tracking error of the yaw rate.

4. The yaw stability control method of the vehicle based on the three-step method as claimed in claim 1, wherein the step three is based on the three-step method controller designed in the step two to carry out the yaw stability control of the vehicle, and the method comprises the following specific steps: and converting the additional yaw moment distribution into a quadratic programming problem to solve, wherein the standard form of the additional yaw moment distribution is as follows:

in the optimized allocation, the equality constraint is:

M_z＝Bu_Fx

the inequality constraints for satisfying the braking scheme are as follows,

Au_Fx≤0

wherein, when M_zWhen the pressure is higher than 0, the pressure is higher,

<mrow> <mi>A</mi> <mo>=</mo> <mo>-</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <mfrac> <msub> <mi>d</mi> <mi>f</mi> </msub> <mn>2</mn> </mfrac> <msub> <mi>cos&delta;</mi> <mi>f</mi> </msub> <mo>+</mo> <msub> <mi>L</mi> <mi>f</mi> </msub> <msub> <mi>sin&delta;</mi> <mi>f</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mi>m</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mfrac> <msub> <mi>d</mi> <mi>f</mi> </msub> <mn>2</mn> </mfrac> <msub> <mi>cos&delta;</mi> <mi>f</mi> </msub> <mo>+</mo> <msub> <mi>L</mi> <mi>f</mi> </msub> <msub> <mi>sin&delta;</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <msub> <mi>d</mi> <mi>r</mi> </msub> <mn>2</mn> </mfrac> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mi>m</mi> <mo>&CenterDot;</mo> <mfrac> <msub> <mi>d</mi> <mi>r</mi> </msub> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

when M is_zWhen the content is less than or equal to 0,

<mrow> <mi>A</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>m</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>-</mo> <msub> <mi>d</mi> <mi>f</mi> </msub> </mrow> <mn>2</mn> </mfrac> <msub> <mi>cos&delta;</mi> <mi>f</mi> </msub> <mo>+</mo> <msub> <mi>L</mi> <mi>f</mi> </msub> <msub> <mi>sin&delta;</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mrow> <mo>(</mo> <mfrac> <msub> <mi>d</mi> <mi>f</mi> </msub> <mn>2</mn> </mfrac> <msub> <mi>cos&delta;</mi> <mi>f</mi> </msub> <mo>+</mo> <msub> <mi>L</mi> <mi>f</mi> </msub> <msub> <mi>sin&delta;</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>m</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msub> <mi>d</mi> <mi>r</mi> </msub> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <msub> <mi>d</mi> <mi>r</mi> </msub> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

the magnitude of the braking force is limited to:

-0.5F_z≤u_Fx≤0.5F_z

in the formula: q is a quadratic term coefficient matrix; c. C^TIs a primary coefficient matrix; u. of_FxIs a braking force matrix;b is an additional yaw moment distribution braking force matrix; f_zIs the tire longitudinal vertical load in N.