CN105172790A - Vehicle yaw stability control method based on three-step method - Google Patents

Abstract

The invention discloses a vehicle yaw stability control method based on a three-step method. A hierarchical control strategy is adopted, based on the three-step method, the front wheel turn angle and additional yaw moment are obtained, and based on a quadratic programming optimization method, the additional yaw moment is distributed into braking force on four wheels to act on a vehicle. The method includes the steps of firstly, establishing a simplified vehicle dynamics model, wherein the two-degree-of-freedom model is used for representing the relation between the steering stability of the vehicle and the lateral movement and yaw movement of the vehicle; secondly, designing a three-step method controller, wherein expected yaw velocity information is input into the three-step method controller, and the additional yaw moment and the front wheel turn angle are determined in a three-step method algorithm flow according to the value of expected yaw velocity and the lateral acceleration, actual yaw velocity, actual sideslip angle and longitudinal speed, fed back in real time, of the vehicle; thirdly, performing vehicle yaw stability control based on the three-step method controller designed in the second step.

Description

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

Technical field

The present invention relates to a kind of vehicle active safety control method, more concrete, relate to a kind of vehicle yaw stability control method based on three-step approach.

Background technology

Vehicle stabilization control is that it grows up on anti-blocking brake system and Anti-slip regulation systematic research basis from the external auto electronic control technology risen.Originating from of stability control concept utilizes above-mentioned two kinds of systems to solve the thinking of stability problem, but energy is placed on algorithm and improves by the personnel that begin one's study, so can only the subproblem of Treatment Stability.At this moment system did not both carry out deep theoretical analysis, did not also have supporting hardware device, so can not be referred to as stabilitrak truly.At the beginning of nineteen nineties, researchist has breakthrough in theoretical investigation, propose the new idea directly controlling to adjust (DYC:DirectYawControl) for weaving, it specifies the research direction in this field theoretically.This thinking is introduced and is turned to intention to driver, more directly controls to adjust for weaving, ensures that running car is in stabilized zone.This new idea represents the concept formation truly that stability controls.

Three-step approach is a kind of algorithm flow based on model, is mainly used in the tracking control problem of system.Its mentality of designing comes from the control structure of " feedforward+PID feedback " often adopted in engineering.The basic structure of three-step approach is " stable state control-feed forward control-Error Feedback controls ", each walks to have and controls object accordingly, and various piece all comprises systematic status information, or the information of operating mode, the renewal result of each information, makes the gain of controller realize self-regulating effect, in addition, the clear in structure of control algorithm, succinctly, design goal is clear, understands.Be correlated with between three steps, and the order of three steps can not be put upside down, so be referred to as " three-step approach " step by step.

Summary of the invention

The invention provides a kind of vehicle yaw stability control method based on three-step approach, adopt the strategy of hierarchical control, application three-step approach obtains front wheel angle and additional yaw moment, and select the optimization method of quadratic programming to distribute additional yaw moment, additional yaw moment is assigned as Braking on four wheels in vehicle.

The present invention is achieved by the following technical solutions:

The vehicle dynamic model that step one, foundation simplify: characterize the road-holding property of vehicle and the relation between the sideway movement of vehicle and weaving by two-freedom model;

Step 2, three-step approach Controller gain variations: the simplification vehicle dynamic model set up based on step one, design three-step approach controller, expectation yaw velocity information is input to three-step approach controller, according to value and the vehicle lateral acceleration of Real-time Feedback, actual yaw velocity, actual side slip angle and the longitudinal speed of a motor vehicle of expecting yaw velocity, use three-step approach algorithm flow (stable state control-feed forward control-Error Feedback controls), decision-making goes out additional yaw moment and front wheel angle;

Step 3, carry out vehicle yaw stability control based on the three-step approach controller of step 2 design: by front wheel angle information and the additional yaw moment distribution module of additional yaw moment information input, additional yaw moment assignment problem is converted into the constrained quadratic programming optimization problem of band by this module, additional yaw moment is assigned as the braking force on four wheels and exports brake system to, and export gained front wheel angle in step 2 to steering swivel system, the two combined action, in Vehicular system, makes vehicle keep yaw stabilized conditions.

Beneficial effect of the present invention is:

1. three-step approach controller of the present invention has the structure of standard-definition, and each step has actual design goal, is convenient to the practical application in engineering.

2. additional yaw moment distribution module is converted into QUADRATIC PROGRAMMING METHOD FOR by the present invention, and considers the strategy that braking force wheel distributes and to constraints such as the amplitude limits of braking force, thus obtains optimal solution.

3. front wheel angle information and difference braking information are all taken into account by the present invention in stability control analysis, and energy stable coordination control both making, avoids steering hardware and stop mechanism clashes.

Accompanying drawing explanation

Fig. 1 is vehicle stability controlled system block diagram;

Fig. 2 is vehicle two-freedom model schematic diagram;

Fig. 3 is yaw angle rate results figure under sinusoidal delay operating mode;

Fig. 4 is side slip angle result figure under sinusoidal delay operating mode;

Fig. 5 is additional yaw moment result figure under sinusoidal delay operating mode;

Fig. 6 is front wheel angle result figure under sinusoidal delay operating mode;

Fig. 7 is left front tire braking force result figure under sinusoidal delay operating mode;

Fig. 8 is right front fire braking force result figure under sinusoidal delay operating mode;

Fig. 9 is left rear tire braking force result figure under sinusoidal delay operating mode;

Figure 10 is left rear tire braking force result figure under sinusoidal delay operating mode.

Detailed description of the invention

The invention provides a kind of vehicle yaw stability control method based on three-step approach, the method comprises following step: step one, foundation simplify vehicle dynamic model, as Fig. 2, for the relation between the sideway movement of the road-holding property and vehicle that characterize vehicle and weaving.Consider weaving and the sideway movement of vehicle, its kinetics equation is:

$\left\{\begin{array}{c}{\mathrm{mv}}_x(\stackrel{\·}{\mathrm{\β}}+r)=(F_{yf}+F_{yr}),\\ I_z\stackrel{\·}{r}=L_f{F}_{y2}-L_r{F}_{y1}+M_z.\end{array}\right.---\left(1\right)$

Wherein, F _y1, F _y2for the lateral deviation power of front and back tire, unit N; M _zfor additional yaw moment, unit Nm; L _f, L _rbe respectively the distance of automobile barycenter to antero posterior axis, unit is m; I _zfor automobile is around the rotor inertia of z-axis, units/kg m ²; R is yaw velocity, unit rad/s; M is car mass, units/kg; v _xfor vehicular longitudinal velocity, unit m/s; β is side slip angle, unit rad.

The system equation (2) obtaining vehicle is arranged as follows by formula (1)

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\β}}=\frac{F_{yf}+F_{yr}}{{\mathrm{mv}}_x}-r,\\ \stackrel{\·}{r}=\frac{L_f{F}_{yf}-L_r{F}_{yr}+M_z}{I_z}.\end{array}\right.---\left(2\right)$

F in Vehicular system equation of state (2) _yf, F _yrrepresent the front and back lateral deviation power of tire respectively, the lateral stability of research vehicle must consider the nonlinear characteristic of tire, and therefore the nonlinear instability factor of tire is considered in the design of control system by the present invention.According to the description of fraction tire model, known tire cornering power can be expressed as:

$F_y=-\frac{{\mathrm{\μF}}_z}{{\mathrm{\μ}}_0{F}_{z0}}\frac{{\mathrm{\γ}}_z}{{\mathrm{\γ}}_z{\mathrm{\λ}}^2+1}\frac{C_{\mathrm{\α}}}{{\mathrm{\γ}}_{\mathrm{\α}}{\mathrm{\α}}^2+1}\mathrm{\α}---\left(3\right)$

Wherein, F _zthe longitudinal vertical load of tire, F _z0be nominal tire load, μ is coefficient of road adhesion, μ ₀be nominal coefficient of road adhesion, λ is straight skidding rate, C _αbe tire cornering stiffness, α is tyre slip angle, meanwhile, and γ _z, γ _λand γ _αit is model parameter.Owing to setting up the sideway movement and the weaving that only considered vehicle in vehicle reduced mechanism process, therefore, ignore the impact of straight skidding rate λ on side direction tire force, make λ=0, formula (3) can be reduced to:

$F_{yi}\left({\mathrm{\α}}_i\right)=-\frac{{\mathrm{\μF}}_{zi}{\mathrm{\γ}}_{zi}{C}_i}{{\mathrm{\μ}}_0{F}_{zi0}}\frac{{\mathrm{\α}}_i}{{\mathrm{\γ}}_{\mathrm{\α}i}{{\mathrm{\α}}^2}_i+1},i=f,r---\left(4\right)$

According to the geometric relationship in Fig. 2, between front and back tyre slip angle, vehicle front wheel angle and longitudinal speed of a motor vehicle, there is the relation such as formula (5).

$\left\{\begin{array}{c}{\mathrm{\α}}_f=\frac{v_y+ar}{v_x}-\mathrm{\δ}\\ {\mathrm{\α}}_r=\frac{v_y-br}{v_x}\end{array}\right.---\left(5\right)$

Wherein, α _f, α _rfor front and back tyre slip angle, unit rad; δ is front wheel angle, unit rad;

Formula (4), (5) are substituted into formula (2) and can obtain system state equation formula (6)

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\β}}=\frac{F_{yf}(\mathrm{\β},r,{\mathrm{\δ}}_f)+F_{yr}(\mathrm{\β},r)}{{\mathrm{mv}}_x}-r,\\ \stackrel{\·}{r}=\frac{L_f{F}_{yf}(\mathrm{\β},r,{\mathrm{\δ}}_f)-L_r{F}_{yr}(\mathrm{\β},r)+M_z}{I_z}.\end{array}\right.---\left(6\right)$

Step 2, three-step approach Controller gain variations: the simplification vehicle dynamic model set up based on step one, design three-step approach controller, expectation yaw velocity information is input to three-step approach controller, according to value and the vehicle lateral acceleration of Real-time Feedback, actual yaw velocity, actual side slip angle and the longitudinal acceleration of expecting yaw velocity, use three-step approach algorithm flow, decision-making goes out additional yaw moment and front wheel angle;

First, the expression formula providing the side slip angle of expectation and yaw velocity is as follows,

$\left\{\begin{array}{c}{\mathrm{\β}}_d=0\\ r_d=\frac{v_x/L}{1+0.0024{v_x}^2}\mathrm{\δ}\end{array}\right.---\left(7\right)$

In above-mentioned steps two, the design of three-step approach controller comprises the following steps:

(1) stable state controls

Based on the simplification vehicle dynamics equation (6) that step one is set up, order with system meets following equation,

$\left\{\begin{array}{c}\frac{F_{yf}(\mathrm{\β},r,{\mathrm{\δ}}_{fs})+F_{yr}(\mathrm{\β},r)}{{\mathrm{mv}}_x}-r=0,\\ \frac{L_f{F}_{yf}(\mathrm{\β},r,{\mathrm{\δ}}_{fs})-L_r{F}_{yr}(\mathrm{\β},r)+M_{zs}}{I_z}=0\end{array}\right.---\left(8\right)$

δ _fsand M _zscan be tried to achieve by formula (8), owing to there is the non-linear of complexity in this system, under the inspiration of the widely used control policy based on tabling look-up of modern automation field, this is also in Vehicle Engineering, the map table measured during stable state that utilizes of frequent use realizes the Dynamic controlling of system, and essence is that stable state controls.Can be as follows in the hope of the stable state control part of controller,

$\left\{\begin{array}{c}{u}_{1s}={\mathrm{\δ}}_{fs}=F_{yf,map}^{-1}({\mathrm{mrv}}_x-F_{yr}(\mathrm{\β},r\left)\right),\\ u_{2s}=M_{zs}=L_r{F}_{yr}(\mathrm{\β},r)-L_f{F}_{yf}(\mathrm{\β},r,{\mathrm{\δ}}_{fs}).\end{array}\right.---\left(9\right)$

(2) control with reference to dynamic Feedforward

Will expect satisfied performance for a complicated nonlinear system, it is far from being enough for only using a stable state to control.Other information also needs to consider, therefore, on the basis of stable state, adds feed forward control, uses

$\left\{\begin{array}{c}{\mathrm{\δ}}_f=u_{1s}+u_{1f},\\ M_z=u_{2s}+u_{2f}\end{array}\right.---\left(10\right)$

Wherein u _1sand u _2sprovide at formula (9), u _1fand u _2fwait to ask.Formula (10) is substituted into formula (6) can obtain

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\β}}=\frac{F_{yf}(\mathrm{\β},r,u_{1s}+u_{1f})+F_{yr}(\mathrm{\β},r)}{{\mathrm{mv}}_x}-r,\\ \stackrel{\·}{r}=\frac{L_f{F}_{yf}(\mathrm{\β},r,u_{1s}+u_{1f})-L_r{F}_{yr}(\mathrm{\β},r)+u_{2s}+u_{2f}}{I_z}.\end{array}\right.---\left(11\right)$

By being used in u _1sthe Taylor form of point, we can obtain F _yfapproximate expression as follows,

$F_{yf}(\mathrm{\β},r,u_{1s}+u_{1f})=F_{yf}(\mathrm{\β},r,u_{1s})+\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1s}}\·u_{1f}---\left(12\right)$

So formula (11) can be rewritten into

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\β}}=\frac{F_{yf}(\mathrm{\β},r,u_{1s})+F_{yf}(\mathrm{\β},r)}{{\mathrm{mv}}_x}+\frac{1}{{\mathrm{mv}}_x}\frac{\∂F_{yf}}{\∂u_1}\·u_{1f}-r\\ \stackrel{\·}{r}=\frac{L_f{F}_{yf}(\mathrm{\β},r,u_{1s})-L_r{F}_{yf}(\mathrm{\β},r)+u_{1s}}{I_z}\frac{L_f\frac{\∂F_{yf}}{\∂u_1}\·u_{1f}+u_{2f}}{I_z}\end{array}\right.---\left(11\right)$

Formula (8) is substituted in (13), can obtain

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\β}}=\frac{1}{{\mathrm{mv}}_x}\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1s}}\·u_{1f},\\ \stackrel{\·}{r}=\frac{L_f\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1s}}\·u_{1f}+u_{2f}}{I_z}\end{array}\right.---\left(14\right)$

Order with then formula (14) becomes

$\left\{\begin{array}{c}0=\frac{1}{{\mathrm{mv}}_x}\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1s}}\·u_{1f},\\ {\stackrel{\·}{r}}_d=\frac{L_f\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1s}}\·u_{1f}+u_{2f}}{I_z}\end{array}\right.---\left(15\right)$

So just can divide in the hope of feedforward section

$\left\{\begin{array}{c}{u}_{1f}=0,\\ u_{2f}=I_z{\stackrel{\·}{r}}_d.\end{array}\right.---\left(16\right)$

(3) tracking error controlled reset

In derivation above, not considering external disturbance and modeling error, in order to obtain better control effects, little bias system being controlled, stable state control and feed forward control basis on, finally, add to error tracking controlled reset,

$\left\{\begin{array}{c}{\mathrm{\δ}}_f=u_{1s}+u_{1f}+u_{1e},\\ M_z=u_{2s}+u_{2f}+u_{2e}\end{array}\right.---\left(17\right)$

Formula (17) is substituted in formula (6), can obtain

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\β}}=\frac{F_{yf}(\mathrm{\β},r,u_{1s}+u_{1f}+u_{1e})+F_{yr}(\mathrm{\β},r)}{{\mathrm{mv}}_x}-r,\\ \stackrel{\·}{r}=\frac{L_f{F}_{yf}(\mathrm{\β},r,u_{1s}+u_{1f}+u_{1e})-L_r{F}_{yr}(\mathrm{\β},r)+u_{2s}+u_{2f}+u_{2e}}{I_z}\end{array}\right.---\left(18\right)$

Then, use Taylor expansion again, try to achieve

$F_{yf}(\mathrm{\β},r,u_{1s}+u_{1f}+u_{1s})=F_{yf}(\mathrm{\β},r,u_{1s})+\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1s}}\·(u_{1f}+u_{1e})---\left(19\right)$

So formula (18) can be rewritten as

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\β}}=\frac{F_{yf}(\mathrm{\β},r,u_{1s})+\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1s}}\·(u_{1f}+u_{1e})+F_{yr}(\mathrm{\β},r)}{{\mathrm{mv}}_x}-r,\\ \stackrel{\·}{r}=\frac{L_f\left(F_{yf}\right(\mathrm{\β},r,u_{1s})+\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1s}}\·(u_{1f}+u_{1e}\left)\right)-L_r{F}_{yr}(\mathrm{\β},r)+u_{2s}+u_{2f}+u_{2e}}{I_z}\end{array}\right.---\left(20\right)$

Formula (8) and (15) are substituted in formula (20), can obtain

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\β}}={\stackrel{\·}{\mathrm{\β}}}_d+\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1e}}+u_{2e}\\ \stackrel{\·}{r}={\stackrel{\·}{r}}_d+\frac{\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1e}}+u_{2e}}{I_z}\end{array}\right.---\left(21\right)$

Definition error is

$\left\{\begin{array}{c}{e}_{\mathrm{\β}}={\mathrm{\β}}_d-\mathrm{\β},\\ e_r=r_d-r\end{array}\right.---\left(22\right)$

Formula (21) is rewritten to be become

$\left\{\begin{array}{c}{\stackrel{\·}{e}}_{\mathrm{\β}}=-\frac{1}{{\mathrm{mv}}_x}\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1s}}\·u_{1e},\\ {\stackrel{\·}{e}}_r=\frac{L_f\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1s}}\·u_{1e}+u_{2e}}{I_z}\end{array}\right.---\left(23\right)$

Can be obtained by formula (23),

$u_{1e}=\frac{k_1{\mathrm{mv}}_x}{\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1s}}}\·e_{\mathrm{\β}}---\left(24\right)$

Wherein k ₁> 0, and get

${\stackrel{\·}{e}}_{\mathrm{\β}}=-k_1{e}_{\mathrm{\β}}---\left(25\right)$

Can obtain simultaneously

u _2e＝k ₂I _ze _r-k ₁L _fmv _xe _β(26)

Wherein k ₂> 0, and get

${\stackrel{\·}{e}}_r=-k_2{e}_r---\left(27\right)$

(4) control law and parameter selection rules

It is as follows that convolution (9), (16), (24) and (26) can obtain overall control law

$u=f_s(\mathrm{\β},r)+f_f(\mathrm{\β},r,{\stackrel{\·}{r}}_d)+f_e(\mathrm{\β},r,e)---\left(28\right)$

Wherein,

$\left\{\begin{array}{c}{f}_s(\mathrm{\β},r)=\left[\begin{array}{c}{F}_{yf,map}^{-1}({\mathrm{mrv}}_x-F_{yr}(\mathrm{\β},r\left)\right)\\ L_r{F}_{yr}(\mathrm{\β},r)-L_f{F}_{yf}(\mathrm{\β},r,{\mathrm{\δ}}_{fs})\end{array}\right]\\ f_f(\mathrm{\β},r,{\stackrel{\·}{r}}_d)=\left[\begin{array}{c}0\\ I_z{\stackrel{\·}{r}}_d\end{array}\right]\\ f_e(e_{\mathrm{\β}},e_r)=\left[\begin{array}{c}\frac{k_1{\mathrm{mv}}_x}{\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1s}}}\·e_{\mathrm{\β}}\\ k_2{I}_z{e}_r-k_1{L}_f{\mathrm{mv}}_x{e}_{\mathrm{\β}}\end{array}\right]\end{array}\right.---\left(29\right)$

The first step, for stable state controls, second step, for controlling with reference to dynamic Feedforward, the 3rd step, for Error Feedback controls, three steps have design goal clearly, and interrelated between step, and the order of each step can not be put upside down.The output of three steps is added the controlling quantity that can obtain three-step approach.

K ₁and k ₂the regulating parameter of control algorithm, k ₁determine the speed of the rate of decay of the tracking error of side slip angle β, k ₂determine the speed of the rate of decay of the tracking error of yaw velocity r.So, reducing the angle of error as early as possible, should k made ₁and k ₂value be the bigger the better, but larger value, can cause the high gain of controller, amplify noise simultaneously, so also not wish to see.So we need to determine the value of parameter avoiding the high gain of controller and the contradiction reduced between tracking error to carry out trading off.

Step 3, the additional yaw moment obtained based on step 2 and front wheel angle information, distributed by additional yaw moment and be converted into quadratic programming problem and solve, concrete grammar is as follows:

In the distribution of additional yaw moment, its distribution objective function is

$J=\frac{1}{2}{u}_{Fx}^T{\mathrm{\Γ}}_x{u}_{Fx}+\frac{1}{2}{\mathrm{\Δu}}_{Fx}^T{\mathrm{\Γ}}_u{\mathrm{\Δu}}_{Fx}---\left(30\right)$

In formula, Γ _xand Γ _urepresentative controls amplitude matrix and increment weight matrix respectively, and is all diagonal matrix.Formula (30) is changed into the standard form of quadratic programming below.Due to

Δu _Fx＝u _Fx(k)-u _Fx(k-1)(31)

Formula (30) can be rewritten as

$\begin{array}{c}J=\frac{1}{2}{u}_{Fx}{\left(k\right)}^T({\mathrm{\Γ}}_x+{\mathrm{\Γ}}_u)u_{Fx}\left(k\right)-u_{Fx}{(k-1)}^T{\mathrm{\Γ}}_u{u}_{Fx}\left(k\right)\\ +\frac{1}{2}{u}_{Fx}{(k-1)}^T{\mathrm{\Γ}}_u{u}_{Fx}(k-1)\end{array}---\left(32\right)$

Due to u _fx(k-1) be the value at upper a moment, can be considered as known, so be a constant, it and u _fxirrelevant, do not affect optimizing result.So the standard form of additional yaw moment distribution can be obtained

$J=\frac{1}{2}{u}_{Fx}{\left(k\right)}^T{\mathrm{Qu}}_{Fx}\left(k\right)+c^T{u}_{Fx}\left(k\right)---\left(33\right)$

Wherein,

Q＝Γ _x+Γ _u(34)

c ^T＝-u _Fx(k-1) ^TΓ _u(35)

In optimization distributes, equality constraint is

M _z＝Bu _Fx(36)

Wherein,

$B=\[-\frac{d_f}{2}{\mathrm{cos\δ}}_f+L_f{\mathrm{sin\δ}}_f,\frac{d_f}{2}{\mathrm{cos\δ}}_f+L_f{\mathrm{sin\δ}}_f,-\frac{d_r}{2},\frac{d_r}{2}\]---\left(37\right)$

u _Fx＝[ΔF _xfl,ΔF _xfr,ΔF _xrl,ΔF _xrr](38)

Formula (36) is in vehicle dynamics principle, the distribution equations of additional yaw moment assignment system power.This constraint is to ensure that optimum results meets vehicle dynamics principle.

Inequality constrain also should meet the strategy of braking force wheel distribution and the amplitude limit to braking force.Owing to selecting one-sided wheel braking strategy, then the inequality constrain meeting braking scheme is as follows,

Au _Fx≤0(39)

Wherein, M is worked as _zduring > 0,

$A=-\[\begin{array}{cccc}-\frac{d_f}{2}{\mathrm{cos\δ}}_f+L_f{\mathrm{sin\δ}}_f& -m\·(\frac{d_f}{2}{\mathrm{cos\δ}}_f+L_f{\mathrm{sin\δ}}_f)& -\frac{d_r}{2}& -m\·\frac{d_r}{2}\end{array}\]---\left(40\right)$

Work as M _zwhen≤0,

$A=\[\begin{array}{cccc}m\·(\frac{-d_f}{2}{\mathrm{cos\δ}}_f+L_f{\mathrm{sin\δ}}_f)& -(\frac{d_f}{2}{\mathrm{cos\δ}}_f+L_f{\mathrm{sin\δ}}_f)& m\·(-\frac{d_r}{2})& -\frac{d_r}{2}\end{array}\]---\left(41\right)$

Inequality constrain, except meeting the requirement of braking scheme, also will limit the amplitude of braking force.In the present invention, restriction is as follows,

-0.5F _z≤u _Fx≤0.5F _z(42)

Claims (4)

1., based on a vehicle yaw stability control method for three-step approach, it is characterized in that, comprise the following steps:

Step one, foundation simplify vehicle dynamic model: characterize the road-holding property of vehicle and the relation between the sideway movement of vehicle and weaving by two-freedom model;

Step 2, three-step approach Controller gain variations: the simplification vehicle dynamic model set up based on step one, design three-step approach controller, expectation yaw velocity information is input to three-step approach controller, according to value and the vehicle lateral acceleration of Real-time Feedback, actual yaw velocity, actual side slip angle and the longitudinal speed of a motor vehicle of expecting yaw velocity, use three-step approach algorithm flow, decision-making goes out additional yaw moment and front wheel angle;

Step 3, carry out vehicle yaw stability control based on the three-step approach controller of step 2 design: by front wheel angle information and the additional yaw moment distribution module of additional yaw moment information input, additional yaw moment assignment problem is converted into the constrained quadratic programming optimization problem of band by this module, additional yaw moment is assigned as the braking force on four wheels and exports brake system to, and export gained front wheel angle in step 2 to steering swivel system, the two combined action, in Vehicular system, makes vehicle keep yaw stabilized conditions.

2. a kind of vehicle yaw stability control method based on three-step approach as claimed in claim 1, is characterized in that, the simplification vehicle dynamic model that described step one is set up is:

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\β}}=\frac{F_{yf}(\mathrm{\β},r,{\mathrm{\δ}}_f)+F_{yr}(\mathrm{\β},r)}{{\mathrm{mv}}_x}-r,\\ \stackrel{\·}{r}=\frac{L_f{F}_{yf}(\mathrm{\β},r,{\mathrm{\δ}}_f)-L_r{F}_{yr}(\mathrm{\β},r)+M_z}{I_z}\·\end{array}\right.$

Wherein, F _yf, F _yrfor the lateral deviation power of front and back tire, unit N; M _zfor additional yaw moment, unit Nm; L _f, L _rbe respectively the distance of automobile barycenter to antero posterior axis, unit is m; I _zfor automobile is around the rotor inertia of z-axis, units/kg m ²; R is yaw velocity, unit rad/s; M is car mass, units/kg; v _xfor vehicular longitudinal velocity, unit m/s; β is side slip angle, unit rad; δ _ffor front wheel angle, unit rad.

3. a kind of vehicle yaw stability control method based on three-step approach as claimed in claim 1, it is characterized in that, described step 2 three-step approach Controller gain variations specifically comprises the following steps:

1) stable state control part:

$\left\{\begin{array}{c}{u}_{1s}={\mathrm{\δ}}_{fs}=F_{yf,map}^{-1}({\mathrm{mrv}}_x-F_{yr}(\mathrm{\β},r\left)\right),\\ u_{2s}=M_{zs}=L_r{F}_{yr}(\mathrm{\β},r)-L_f{F}_{yf}(\mathrm{\β},r,{\mathrm{\δ}}_{fs})\·\end{array}\right.$

Wherein, F _yf, F _yrfor the lateral deviation power of front and back tire, unit N; M _zfor additional yaw moment, unit Nm; L _f, L _rbe respectively the distance of automobile barycenter to antero posterior axis, unit is m; R is yaw velocity, unit rad/s; M is car mass, units/kg; v _xfor vehicular longitudinal velocity, unit m/s; β is side slip angle, unit rad; δ _ffor front wheel angle, unit rad;

2) in described step 1) basis on increase with reference to dynamic Feedforward control part, that is:

$\left\{\begin{array}{c}{\mathrm{\δ}}_f=u_{1s}+u_{1f},\\ M_z=u_{2s}+u_{2f}\end{array}\right.$

Wherein,

$\left\{\begin{array}{c}{u}_{1f}=0,\\ u_{2f}=I_z{\stackrel{\·}{r}}_d.\end{array}\right.$

3) in described step 2) basis on increase tracking error feedback-system section again, that is:

$\left\{\begin{array}{c}{\mathrm{\δ}}_f=u_{1s}+u_{1f}+u_{1e},\\ M_z=u_{2s}+u_{2f}+u_{2e}\end{array}\right.$

Wherein,

$u_{1e}=\frac{k_1{\mathrm{mv}}_x}{\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1s}}}\·e_{\mathrm{\β}}$

In above formula, k ₁> 0, and get:

${\stackrel{\·}{e}}_{\mathrm{\β}}=-k_1{e}_{\mathrm{\β}}$

Can obtain simultaneously:

u _2e＝k ₂I _ze _r-k ₁L _fmv _xe _β

In above formula, k ₂> 0, and get:

${\stackrel{\·}{e}}_r=-k_2{e}_r$

4) control law and parameter selection rules:

In conjunction with above-mentioned steps 1) to step 3), the control law of three-step approach controller entirety is as follows:

$u=f_s(\mathrm{\β},r)+f_f(\mathrm{\β},r,{\stackrel{\·}{r}}_d)+f_e(\mathrm{\β},r,e)$

Wherein,

$\left\{\begin{array}{c}{f}_s\left(\mathrm{\β},r\right)=\left[\begin{array}{c}{F}_{yf,map}^{-1}\left({\mathrm{mrv}}_x-F_{yr}\left(\mathrm{\β},r\right)\right)\\ L_r{F}_{yr}\left(\mathrm{\β},r\right)-L_f{F}_{yf}\left(\mathrm{\β},r,{\mathrm{\δ}}_{fs}\right)\end{array}\right]\\ f_f\left(\mathrm{\β},r,{\stackrel{\·}{r}}_d\right)=\left[\begin{array}{c}0\\ I_z{\stackrel{\·}{r}}_d\end{array}\right]\\ f_e\left(e_{\mathrm{\β}},e_r\right)=\left[\begin{array}{c}\frac{k_1{\mathrm{mv}}_x}{\frac{\∂F_{yf}}{\∂u_1}{|}_{u_{1s}}}\·e_{\mathrm{\β}}\\ k_2{I}_z{e}_r-k_1{L}_f{\mathrm{mv}}_x{e}_{\mathrm{\β}}\end{array}\right]\end{array}\right.$

In formula, F _yf, F _yrfor the lateral deviation power of front and back tire, unit N; M _zfor additional yaw moment, unit Nm; L _f, L _rbe respectively the distance of automobile barycenter to antero posterior axis, unit is m; I _zfor automobile is around the rotor inertia of z-axis, units/kg m ²; R is yaw velocity, unit rad/s; M is car mass, units/kg; v _xfor vehicular longitudinal velocity, unit m/s; β is side slip angle, unit rad; δ _ffor front wheel angle, unit rad.

4. a kind of vehicle yaw stability control method based on three-step approach as claimed in claim 1, it is characterized in that, described step 3 is carried out vehicle yaw stability based on the three-step approach controller that step 2 designs and is controlled to be specially: additional yaw moment distribution is converted into quadratic programming problem and solves, the standard form that additional yaw moment distributes is:

$J=\frac{1}{2}{u}_{Fx}{\left(k\right)}^T{\mathrm{Qu}}_{Fx}\left(k\right)+c^T{u}_{Fx}\left(k\right)$

In optimization distributes, equality constraint is:

M _z＝Bu _Fx

The inequality constrain meeting braking scheme is as follows,

Au _Fx≤0

Wherein, M is worked as _zduring > 0,

$A=-\left[\begin{array}{cccc}-\frac{d_f}{2}{\mathrm{cos\δ}}_f+L_f{\mathrm{sin\δ}}_f& -m\·(\frac{d_f}{2}{\mathrm{cos\δ}}_f+L_f{\mathrm{sin\δ}}_f)& -\frac{d_r}{2}& -m\·\frac{d_r}{2}\end{array}\right]$

Work as M _zwhen≤0,

$A=\left[\begin{array}{cccc}m\·\left(\frac{-d_f}{2}{\mathrm{cos\δ}}_f+L_f{\mathrm{sin\δ}}_f\right)& -(\frac{d_f}{2}{\mathrm{cos\δ}}_f+L_f{\mathrm{sin\δ}}_f)& m\·\left(-\frac{d_r}{2}\right)& -\frac{d_r}{2}\end{array}\right]$

The amplitude of braking force is restricted to:

-0.5F _z≤u _Fx≤0.5F _z