CN102529976A - Vehicle running state nonlinear robust estimation method based on sliding mode observer - Google Patents

Abstract

The invention provides a vehicle running state nonlinear robust estimation method based on a sliding mode observer. The method comprises the following steps of: determining an automotive nonlinear kinetic model closer to the actual situation aiming at high mobility running conditions and complex variable road environments, designing the corresponding sliding mode observer, establishing external input quantity and measurement information of the sliding mode observer system by using low-cost vehicle-mounted wheel speed and steering wheel turning angle sensors, and thus implementing estimation of multiple running states of an automobile by a sliding mode observer estimation recursion algorithm. The method has the characteristics of strong anti-interference capacity, high precision, low cost and the like, and is easy to implement.

Description

A kind of travel condition of vehicle non linear robust method of estimation based on sliding mode observer

Technical field

The present invention relates to a kind of travel condition of vehicle non linear robust method of estimation based on sliding mode observer; The sliding mode observer that its purpose is to pass through to be set up is realized the non-linear On-line Estimation to car running process; Obtain automobile accurate, failure-free running state under motor-driven operating condition of height and road environment complicated and changeable; These states can be used for the relevant control of automobile active safety; The inventive method has that antijamming capability is strong, precision is high, real-time is good and distinguishing feature such as cost is low, belongs to automobile active safety and measures and the control field.

Background technology

For preventing the generation of road traffic accident, the automobile active safety technology has obtained swift and violent development in recent years.The automobile active safety technology can prevent trouble before it happens, and initiatively avoids the generation of accident, has become one of topmost developing direction of modern automobile.Common active safety technology mainly comprises anti-skid brake system (ABS), vehicle electric stability program (ESP), anti-slip regulation (TCS), automatically controlled driving skid control system (ASR), four-wheel steering stabilizing control system (4WS) etc. at present.These systems are usually directed to the measurement or the estimation of running statees such as vertical speed of advance, side velocity, yaw velocity and side slip angle of speed, the automobile of motor tire; Measurement to these running statees can be used for follow-up automobile active safety control; Therefore the driving safety of its precision direct relation automobile and stability, promptly above-mentioned active safety control system can effectively be operated in depend on travel condition of vehicle to a great extent can be by in real time, measure accurately or estimate.

In the automobile active safety field, state of motion of vehicle is mainly measured through three kinds of methods or is estimated.The one, utilize onboard sensor (like inertial sensor and wheel speed sensors etc.) cheaply; The signal of its measurement is carried out simple mathematical to be calculated and obtains relevant travel condition of vehicle; This method cost is low; But relatively poor and calculate to handle and too simply to have bigger measured error, thereby influenced the control effect owing to low-cost sensor accuracy.The 2nd, utilize high-precision sensor that relevant travel condition of vehicle is directly measured (as utilizing photoelectricity fifth wheel gauge or high-precision global navigation satellite system GNSS; Especially high precision global position system GPS etc.); This method precision is high but cost an arm and a leg, and can't apply on a large scale.The third method is a modelling tool; Promptly carry out kinematics or Dynamic Modeling through operational process to automobile; Simultaneously with relevant onboard sensor cheaply (like wheel speed sensors, gyroscope, accelerometer and GPS etc.) information as observation information, and then utilize suitable Filtering Estimation algorithm to realize estimation to motoring condition.The third method (being modelling tool) can realize that the dimension that expanded is estimated also can improve the relevant straight precision of measuring to being difficult to straight estimation of measuring, and cost is lower simultaneously.But the modelling tool that has proposed at present mainly is based on the kinematics model of automobile or car load or tire has been done the kinetic model than the polytenization supposition; And often consider not enough to the variation of outside road environment; Can obtain estimation effect and precision preferably at vehicle than smooth running and external environment condition interference more after a little while; But under motor-driven operation conditions of height and road environment complicated and changeable, cause estimated accuracy lower even disperse, and obstacle overcome ability have much room for improvement owing to be difficult to reflect real kinetic behavior and the situation of vehicle.

Summary of the invention

For under motor-driven operating mode of height and environment complicated and changeable, realizing accurate, failure-free vehicle state estimation the present invention proposes a kind of travel condition of vehicle non linear robust method of estimation based on sliding mode observer.The method that the present invention proposes is established more near actual automobile non-linear dynamic model to high motor-driven operation conditions of automobile and road environment complicated and changeable; And design corresponding sliding mode observer; Utilize vehicle-mounted cheaply outside input and the metrical information that speed and steering wheel angle sensor are set up the sliding mode observer system of taking turns in addition; And then estimate that through the sliding mode observer that proposes recursive algorithm realizes the estimation to running statees such as automobile longitudinal speed of advance, yaw velocity, side velocity and side slip angles, have that antijamming capability is strong, precision is high, be prone to realize and characteristics such as cost is low.

A kind of travel condition of vehicle non linear robust method of estimation based on sliding mode observer; The present invention is directed to the more front-wheel steering four-wheel automobile of present application; For adapt to the control of automobile active safety under high motor-driven operating condition and the road conditions complicated and changeable to the measurement of travel condition of vehicle with estimate needs; Utilize vehicle-mounted cheaply take turns speed and steering wheel angle sensor confirm to set up outside input and metrical information; Designed sliding mode observer based on non-linear automobile dynamic quality model; Estimation recursion through sliding mode observer realizes accurate, Robust Estimation to information such as automobile longitudinal speed of advance, yaw velocity, side velocity and side slip angles, and concrete steps comprise:

1) set up the sliding mode observer of travel condition of vehicle:

Adopt the automobile non-linear dynamic model of three degree of freedom, the state space equation form of this model is following:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=f_1(x_1,x_2,x_3,{\mathrm{\δ}}_f)+g_1({\mathrm{\δ}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})\\ {\stackrel{\·}{x}}_2=f_2(x_1,x_2,x_3,{\mathrm{\δ}}_f)+g_2({\mathrm{\δ}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})\\ {\stackrel{\·}{x}}_3=f_3(x_1,x_2,x_3,{\mathrm{\δ}}_f)+g_3({\mathrm{\δ}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})\end{array}\right.---\left(1\right)$

In the formula (1), x ₁, x ₂And x ₃Be three states of sliding mode observer, and x ₁=v _x, x ₂=ω _z, x ₃=v _y, v _x, v _yAnd ω _zBe respectively vertical speed of advance, side velocity and the yaw velocity of automobile;

δ _f, F _TfAnd F _TrBe three outer input variables, wherein δ _fBe front wheel steering angle, F _TfBe the longitudinal force that acts on the single front-wheel, F _TrIt is the longitudinal force that acts on the single trailing wheel;

Each function f in the formula (1) _j(j=1,2,3) and g _jThe value of (j=1,2,3) is following

$f_1(x_1,x_2,x_3,{\mathrm{\δ}}_f)=\frac{1}{m}[{\mathrm{mv}}_y{\mathrm{\ω}}_z+2\frac{v_y+{\mathrm{a\ω}}_z}{v_x}{C}_{\mathrm{\αf}}{\mathrm{\δ}}_f-\frac{1}{2}{C}_d{A}_f{\mathrm{\ρ}}_a{v}_x^2]$

$f_2(x_1,x_2,x_3,{\mathrm{\δ}}_f)=\frac{1}{I_z}[2a({\mathrm{\δ}}_f-\frac{(v_y+{\mathrm{a\ω}}_z)}{v_x})C_{\mathrm{\αf}}-2b{C}_{\mathrm{\αr}}\frac{({\mathrm{b\ω}}_z-v_y)}{v_x}]$

$f_3(x_1,x_2,x_3,{\mathrm{\δ}}_f)=\frac{1}{m}[-{\mathrm{mv}}_x{\mathrm{\ω}}_z+2({\mathrm{\δ}}_f-\frac{(v_y+a{\mathrm{\ω}}_z)}{v_x})C_{\mathrm{\αf}}+2C_{\mathrm{\αr}}\frac{{\mathrm{b\ω}}_z-v_y}{v_x}]$

$g_1({\mathrm{\δ}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})=\frac{2}{m}(F_{\mathrm{tf}}+F_{\mathrm{tr}})$

$g_2({\mathrm{\δ}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})=\frac{2a}{I_z}{F}_{\mathrm{tf}}{\mathrm{\δ}}_f$

$g_3({\mathrm{\δ}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})=\frac{2}{m}{F}_{\mathrm{tf}}{\mathrm{\δ}}_f$

At said f _j(j=1,2,3) and g _jIn (j=1,2,3), m and I _zBe respectively the quality and the rotor inertia of walking around the vertical axle of barycenter of vehicle, a is the distance of vehicle front wheel shaft center to barycenter, and b is the distance of automobile back wheel wheel shaft center to barycenter, C _{α f}, C _{α r}The cornering stiffness of representing forward and backward tire respectively, C _dThe expression aerodynamic drag factor, A _fExpression vehicle forward direction area, ρ _aRepresent density of air;

For state x ₁And x ₂, the corresponding v of difference _xAnd ω _z, the wheel speed of two non-steered wheels has following relation on they and the hind axle:

v _x＝(V _RL+V _RR)/2

ω _z＝(V _RL-V _RR)/T _W (2)

In the formula (2), T _WBe the wheelspan between two trailing wheels on the hind axle, V _RLAnd V _RRRepresent the linear velocity of left rear wheel and off hind wheel respectively, i.e. the wheel linear velocity of two non-wheel flutters;

State x ₁And x ₂Be the amount that can directly record, and state x ₃For the amount that can't directly record needs to estimate through sliding mode observer;

For the auto model shown in the formula (1), propose and set up following sliding mode observer model:

$\left\{\begin{array}{c}{\stackrel{\stackrel{\&CenterDot;}{^}}{x}}_1=f_1({\hat{x}}_1,{\hat{x}}_2,{\hat{x}}_3,{\mathrm{\&delta;}}_f)+g_1({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})+l_1{s}_1+k_1\mathrm{sgn}\left(s_1\right)\\ {\stackrel{\stackrel{\&CenterDot;}{^}}{x}}_2=f_2({\hat{x}}_1,{\hat{x}}_2,{\hat{x}}_3,{\mathrm{\&delta;}}_f)+g_2({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})+l_2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\mathrm{sgn}\left(s_2\right)\\ {\stackrel{\stackrel{\&CenterDot;}{^}}{x}}_3=f_3({\hat{x}}_1,{\hat{x}}_2,{\hat{x}}_3,{\mathrm{\&delta;}}_f)+g_3({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})+{\mathrm{\&tau;}}_1\mathrm{sgn}\left(s_1\right)+{\mathrm{\&tau;}}_2\mathrm{sgn}\left(s_2\right)\end{array}\right.---\left(3\right)$

In the formula (3),

With

Represent x respectively ₁, x ₂And x ₃The calculating estimated valve, l _j(j=1,2) are the error convergence gains outside the sliding-mode surface, and k _j(j=1,2) and τ _jThe error convergence gain on the sliding-mode surface has then been represented in (j=1,2), and sgn (.) is sign function, i.e. symbolic function; s ₁And s ₂What be defined as sliding mode observer can directly survey state x ₁, x ₂With estimated valve separately

Between error, promptly

$s_1=x_1-{\hat{x}}_1,$ ${\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2=x_2-{\hat{x}}_2---\left(4\right)$

2) carry out the estimation recursion of discretization:

In the estimation procedure of reality, need to adopt the estimation recursive form of discretization, for this reason, be that formula (3) is carried out the discretization processing with above-mentioned design-calculated sliding mode observer,

${\hat{x}}_1\left(k\right)={\hat{x}}_1(k-1)+T{\hat{x}}_2(k-1){\hat{x}}_3(k-1)+2T{C}_{\mathrm{\&alpha;f}}{\mathrm{\&delta;}}_f(k-1)\frac{{\hat{x}}_3(k-1)+a{\hat{x}}_2(k-1)}{m{\hat{x}}_1(k-1)}-\frac{T}{2m}{C}_d{A}_f{\mathrm{\&rho;}}_a{{\hat{x}}_1}^2(k-1)$

$+\frac{2T}{m}[F_{\mathrm{tf}}(k-1)+F_{\mathrm{tr}}(k-1)]+l_{1}T[v_x^{\&prime;}(k-1)-{\hat{x}}_1(k-1)]+k_{1}T\&CenterDot;\tanh [\mathrm{\&lambda;}{v}_x^{\&prime;}(k-1)-\mathrm{\&lambda;}{\hat{x}}_1(k-1)]$

${\hat{x}}_2\left(k\right)={\hat{x}}_2(k-1)+\frac{2{\mathrm{TaC}}_{\mathrm{\&alpha;f}}}{I_z}[{\mathrm{\&delta;}}_f(k-1)+\frac{-{\hat{x}}_3(k-1)-a{\hat{x}}_2(k-1)}{{\hat{x}}_1(k-1)}]-2{\mathrm{TbC}}_{\mathrm{ar}}\frac{b{\hat{x}}_2(k-1)-{\hat{x}}_3(k-1)}{I_z{\hat{x}}_1(k-1)}$

$+\frac{2\mathrm{Ta}}{I_z}{F}_{\mathrm{tf}}(k-1){\mathrm{\&delta;}}_f(k-1)+l_{2}T[{\mathrm{\&omega;}}_z^{\&prime;}(k-1)-{\hat{x}}_2(k-1)]+k_{2}T\&CenterDot;\tanh [{\mathrm{\&lambda;\&omega;}}_z^{\&prime;}(k-1)-\mathrm{\&lambda;}{\hat{x}}_2(k-1)]---\left(5\right)$

${\hat{x}}_3(k-1)={\hat{x}}_3(k-1)-T{\hat{x}}_1(k-1){\hat{x}}_2(k-1)+\frac{{2\mathrm{TC}}_{\mathrm{\&alpha;f}}}{m}[{\mathrm{\&delta;}}_f(k-1)-\frac{({\hat{x}}_3(k-1)+a{\hat{x}}_2(k-1))}{{\hat{x}}_1(k-1)}]$

$+2{\mathrm{TC}}_{\mathrm{\&alpha;r}}\frac{b{\hat{x}}_2(k-1)-{\hat{x}}_3(k-1)}{m{\hat{x}}_1(k-1)}+\frac{2T}{m}{F}_{\mathrm{tf}}(k-1){\mathrm{\&delta;}}_f(k-1)$

In the formula (5), k representes discretization constantly, and T representes cycle of dispersing, and tanh (.) is a hyperbolic tangent function, and λ is a design parameters that is used for adjusting the hyperbolic tangent function inclined degree, v ' _xAnd ω ' _zExpression is measured longitudinal direction of car speed of advance and the yaw velocity that obtains, i.e. v ' through wheel speed sensors respectively _xAnd ω ' _zRepresent v respectively _xAnd ω _zThe observed reading that contains noise;

In above-mentioned filtering recursion computation process, can confirm that automobile is at each vertical speed of advance v constantly _x(k), yaw velocity ω _z(k) and side velocity v _y(k), and then according to following formula can confirm each side slip angle constantly

β(k)＝arctan[v _y(k)/v _x(k)] (6)。

Vertically speed of advance and yaw velocity are the amounts that can directly record, and promptly measure through wheel speed sensors and obtain longitudinal direction of car speed of advance and yaw velocity, are specially and utilize two left rear wheel angular velocity omegas that wheel speed sensors records on the hind axle _RLWith the off hind wheel angular velocity omega _RRMultiply by tire radius R and obtain V ' _RL=R ω _RLAnd V ' _RR=R ω _RR, V ' _RLAnd V ' _RRRepresent V respectively _RLAnd V _RRContain noise observed reading and

Wherein

With Represent that respectively the additivity of the wheel linear velocity of left rear wheel and off hind wheel measures noise, and then utilize formula (2) to obtain the observed reading v ' that vertical speed of advance and yaw velocity contain noise again _xAnd ω ' _z

For three outer input variables in the formula (3), confirm through following method:

Front wheel steering angle δ _fBut the steering wheel angle δ that direction of passage dish rotary angle transmitter records is divided by the steering gear ratio q from the bearing circle to the front-wheel _tConfirm, i.e. δ _f=δ/q _t

Longitudinal force of tire F _TfAnd F _TrCan confirm according to the non-linear tire model of Dugoff;

For confirming F _TfAnd F _Tr, introduce longitudinal direction of car slip rate i _Sj(j=f, r), i _SjBe divided into front wheel spindle straight skidding rate i again _SfWith hind axle straight skidding rate i _Sr, subscript j gets f or r representes front or rear wheel shaft, i respectively in this method _SjMethod of calculating is:

and j=f; R (7)

In the formula (7), v _TfAnd v _TrThe speed of representing forward and backward wheel shaft upper edge tire direction respectively, v _TfAnd v _TrCan unify to be designated as v _Tj(j=f, r); ω _fThe spin velocity on the front wheel spindle is converted in the spin velocity equivalence of two wheels on the expression front wheel spindle; ω _rThe spin velocity on the hind axle, ω are converted in the equivalence of two wheel revolutions cireular frequencys on the expression hind axle _fAnd ω _rCan unify to be designated as ω _j(j=f, r) and

${\mathrm{\&omega;}}_f=\frac{1}{2}({\mathrm{\&omega;}}_{\mathrm{fR}}+{\mathrm{\&omega;}}_{\mathrm{fL}})$

(8)

${\mathrm{\&omega;}}_r=\frac{1}{2}({\mathrm{\&omega;}}_{\mathrm{rR}}+{\mathrm{\&omega;}}_{\mathrm{rL}})$

In the formula (8), ω _FL, ω _FR, ω _RLAnd ω _RRThe spin velocity of representing the near front wheel, off front wheel, left rear wheel and off hind wheel respectively obtains through utilizing four wheel speed sensors to measure;

v _Tj(j=f, r) can confirm by formula (9):

v _tf＝v _xcosδ _f+(v _y+aω _z)sinδ _f

(9)

v _tr＝v _x

And then, longitudinal force of tire F _TfAnd F _TrBut through type (10) is confirmed

$F_{\mathrm{tj}}=\frac{C_{\mathrm{tj}}{i}_{\mathrm{sj}}}{1-i_{\mathrm{sj}}}{f}_t\left(p_j\right)$ (j＝f，r) (10)

In the formula (10), C _TfAnd C _TrThe longitudinal rigidity of representing single forward and backward tire respectively, the unified C that is designated as _Tj(j=f, r); Variable p _j(j=f, r) and function f _t(p _j) (j=f, r) confirm by following formula:

$p_j=\frac{{\mathrm{\&mu;F}}_{\mathrm{zj}}(1-{\mathrm{\&epsiv;}}_r{v}_{\mathrm{<figure-callout\; id="2"\; label="x\; i\; sj"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">x</figure-callout>}}\sqrt{{i_{\mathrm{sj}}}^{}}\sqrt{{{}_{}}^2+{\tan }^2{\mathrm{\&alpha;}}_j})(1-i_{\mathrm{sj}})}{2\sqrt{{C_{\mathrm{tj}}}^2{i_{\mathrm{<figure-callout\; id="2"\; label="sj"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">sj</figure-callout>}}}^2+{C_{\mathrm{\&alpha;<figure-callout\; id="2"\; label="j"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">j</figure-callout>}}}^2{\mathrm{<figure-callout\; id="2"\; label="tan"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">tan</figure-callout>}}^2{\mathrm{\&alpha;}}_j}}$ (j＝f，r) (11)

$f_t\left(p_j\right)=\left\{\begin{array}{cc}{p}_j(2-p_j)& p_j<1\\ 1& p_j\&GreaterEqual;1\end{array}\right.$ (j＝f，r) (12)

In formula (11) and (12), μ representes the vertical friction coefficient between tire and ground; ε _rThe expression road adheres to decay factor; α _f, α _rThe sideslip angle of representing forward and backward tire respectively, the unified α that is designated as _j(j=f r), can be calculated as follows

${\mathrm{\&alpha;}}_f={\mathrm{\&delta;}}_f-\frac{v_y+{\mathrm{a\&omega;}}_z}{v_x},$ ${\mathrm{\&alpha;}}_r=\frac{{\mathrm{b\&omega;}}_z-v_y}{v_x}---\left(13\right)$

And F _Zj(j=f, r) expression is assigned to the vertical load on the front or rear wheel shaft and can be calculated as follows

$F_{\mathrm{zf}}=\frac{\mathrm{mgb}}{2(a+b)},$ $F_{\mathrm{zr}}=\frac{\mathrm{mga}}{2(a+b)}---\left(14\right)$

In the formula (14), g representes acceleration due to gravity;

For each gain of sliding mode observer in the formula (3), design definitely according to the convergence stability principle of observer, particularly can confirm gain l according to following formula ₁, k ₁, l ₂, k ₂, τ ₁And τ ₂,

$l_1>\frac{{\&PartialD;f}_1}{\&PartialD;x_1},$ $k_1>\left|\frac{{\&PartialD;f}_1}{{\&PartialD;x}_2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2\right|+\left|\frac{{\&PartialD;f}_1}{{\&PartialD;x}_3}{\tilde{x}}_3\right|+{\mathrm{\&eta;}}_1---\left(15\right)$

${\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">l</figure-callout>}}_2>\frac{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_2},$ ${\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_2>\left|\frac{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{{\&PartialD;x}_1}{s}_1\right|+\left|\frac{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{{\&PartialD;x}_3}{\tilde{x}}_3\right|+{\mathrm{\&eta;}}_2---\left(16\right)$

τ ₁＝τ ₂＝0 (17)

In formula (15) and the formula (16),

(j=1,2,3) representative function f ₁For x _jThe partial derivative of (j=1,2,3),

(j=1,2,3) representative function f ₂For x _jThe partial derivative of (j=1,2,3), η _j(j=1,2) are given positive number, ${\tilde{x}}_3=x_3-{\hat{\mathrm{<figure-callout\; id="3"\; label="x\; ^"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">x</figure-callout>}}}_3;$

In the actual recursion, sgn (.) function that occurs in the formula (3) is with following sgn _Eq(.) function replaces:

sgn _eq(s _j)＝tanh(λ _sj)(j＝1，2) (18)。

The representative value of discrete cycle T is taken as 10 milliseconds, 20 milliseconds or 50 milliseconds.

Beneficial effect

1. the present invention proposes a kind of travel condition of vehicle non linear robust method of estimation, can be used for the robust measure and estimation needs of relevant automobile active safety control travel condition of vehicle based on sliding mode observer.

2. the inventive method proposes to high motor-driven operation conditions of automobile and road environment complicated and changeable, can under motor-driven operating mode of height and road environment complicated and changeable, realize the accurate, reliable of travel condition of vehicle estimated.

3. the travel condition of vehicle non linear robust method of estimation based on the synovial membrane observer of the present invention's proposition not only can significantly improve the straight precision of measuring such as automobile longitudinal speed of advance and yaw velocity, and can realize that side slip angle, side velocity etc. is difficult to the straight robust of measuring accurately to be estimated.

4. the method that proposes of the present invention has that antijamming capability is strong, precision is high, cost is low and characteristics such as real-time is good.

Description of drawings

Fig. 1. vehicle dynamic model

Fig. 2. (meter per second-m/s) and steering wheel angle (degree) be variation diagram in time for vertical speed of advance of setting

Fig. 3. (radian-rad) is curve and partial enlarged drawing (vertical coefficientoffriction=1 between tire and ground o'clock) over time for the side slip angle of the inventive method and Carsim output

Fig. 4. the side slip angle that the inventive method obtains is with respect to the curve of error of the side slip angle reference value of Carsim output (vertical coefficientoffriction=1 between tire and ground o'clock)

Fig. 5. (radian-rad) is curve and partial enlarged drawing (vertical coefficientoffriction=0.8 between tire and ground o'clock) over time for the side slip angle of the inventive method and Carsim output

Fig. 6. the side slip angle that the inventive method obtains is with respect to the curve of error of the side slip angle reference value of Carsim output (vertical coefficientoffriction=0.8 between tire and ground o'clock)

Fig. 7. (radian-rad) is curve and partial enlarged drawing (vertical coefficientoffriction=0.6 between tire and ground o'clock) over time for the side slip angle of the inventive method and Carsim output

Fig. 8. the side slip angle that the inventive method obtains is with respect to the curve of error of the side slip angle reference value of Carsim output (vertical coefficientoffriction=0.6 between tire and ground o'clock)

The specific embodiment

Embodiment 1

Current, topic becomes increasingly conspicuous between traffic safety, has become a global difficult problem.For preventing the generation of road traffic accident, the automobile active safety technology has obtained swift and violent development in recent years.The automobile active safety technology can prevent trouble before it happens, and initiatively avoids the generation of accident, has become one of topmost developing direction of modern automobile.Common active safety technology mainly comprises anti-skid brake system (ABS), vehicle electric stability program (ESP), anti-slip regulation (TCS), automatically controlled driving skid control system (ASR), four-wheel steering stabilizing control system (4WS) etc. at present.These systems are usually directed to the measurement or the estimation of running statees such as vertical speed of advance, side velocity, yaw velocity and side slip angle of speed, the automobile of motor tire; The measurement of these running statees can be used for follow-up automobile active safety control; Therefore the driving safety of its precision direct relation automobile and stability, promptly above-mentioned active safety control system can effectively be operated in depend on travel condition of vehicle to a great extent can be by in real time, measure accurately or estimate.

In the automobile active safety field, state of motion of vehicle is mainly measured through three kinds of following methods at present or is estimated:

The one, utilize onboard sensor (like inertial sensor and wheel speed sensors etc.) cheaply, the signal of its measurement is carried out simple mathematical calculate and obtain relevant travel condition of vehicle.For example, for the automobile side slip angle, vertical and horizontal accelerometer capable of using records the acceleration/accel along both direction earlier, and integral operation obtains vertical speed of advance and side velocity respectively then, and then can try to achieve side slip angle.Although this method cost is low, relatively poor and calculate to handle and too simply to have bigger measured error owing to low-cost sensor accuracy, thereby influenced the control effect.

The 2nd, utilize high-precision sensor that relevant travel condition of vehicle is directly measured (as utilizing photoelectricity fifth wheel gauge or high-precision global navigation satellite system GNSS; Especially high precision global position system GPS etc.); This method precision is high but cost an arm and a leg, and can't apply on a large scale.

The third method is a modelling tool; Promptly carry out kinematics or Dynamic Modeling through operational process to automobile; Simultaneously with relevant onboard sensor cheaply (like wheel speed sensors, gyroscope, accelerometer and GPS etc.) information as observation information, and then utilize suitable Filtering Estimation algorithm (like Long Beige observer, nonlinear observer, Kalman filtering or neural network etc.) to realize estimation to motoring condition.The third method (being modelling tool) can realize being difficult to straight estimation of measuring to relevant, and the dimension that expanded is estimated also can improve the relevant straight precision of measuring, and cost is lower simultaneously.But the modelling tool that has proposed at present mainly is based on the kinematics model of automobile or car load or tire has been done the kinetic model than the polytenization supposition; And often consider not enough to the variation of outside road environment; Can obtain estimation effect and precision preferably at vehicle smooth running and external environment condition interference more after a little while; But under motor-driven operation conditions of height and road environment complicated and changeable, cause estimated accuracy lower even disperse, and obstacle overcome ability have much room for improvement owing to be difficult to reflect real kinetic behavior and the situation of vehicle.

For under motor-driven operating mode of height and environment complicated and changeable, realizing accurate, failure-free vehicle state estimation the present invention proposes a kind of travel condition of vehicle non linear robust method of estimation based on sliding mode observer.The inventive method is accurate to the travel condition of vehicle under high motor-driven operation conditions of automobile and the road environment complicated and changeable, Robust Estimation proposes; Characteristics such as have that antijamming capability is strong, precision is high, real-time is good and cost is low can be used for automobile active safety control field.In the present invention, high motor-driven operation is meant when automotive operation during at common road traffic environment, needs frequent turning to and the operation scene (within the lateral acceleration 0.7g, g representes acceleration due to gravity) of acceleration and deceleration; Antijamming capability is meant that (variation of adhering to environmental factors such as condition like road) observer still can be realized estimation accurate to travel condition of vehicle, robust under traffic environment complicated and changeable.Concrete thinking of the present invention is following:

For adapt to the control of automobile active safety under the high motor-driven environment to the measurement of travel condition of vehicle signal with estimate requirement, at first automobile is carried out suitable Dynamic Modeling.To application of the present invention, the present invention can do following reasonable assumption for the front-wheel steering four wheeler (at present the widest situation should be arranged, the car of exemplary such as front-wheel steering) that goes under common road traffic environment:

1) ignores the pitching, inclination of automobile and bounce motion up and down.

2) ignore automotive suspension to the influence on the tire axle.

3) ignore the inclination campaign, can think on the automobile front axle about deflection angle, sideslip angle, longitudinal force and the side force of two tires identical; Similarly, but about on the assumed vehicle rear axle sideslip angle of two tires, longitudinal force and side force identical.

According to above-mentioned application requirements and supposition; The present invention is directed to the more front-wheel steering four-wheel automobile of present application; Adopt the vehicle dynamic model shown in the accompanying drawing 1 (behind equivalent-simplification, being equivalent to forward and backward wheel) by an imaginary Bicycle model that concentrates on automobile forward and backward axle mid point respectively and constitute, shown in Fig. 1 right side.This model has 3 degree of freedom, is respectively that longitudinal movement, sideway movement and yaw rotate.Defined the vehicle carrier coordinate system among Fig. 1, its initial point o is positioned at the barycenter place, and the ox axle is along the longitudinal axis of vehicle and consistent with vehicle forward direction, the oz axle perpendicular to vehicle operating plane and directed towards ground (promptly downward, around the yaw velocity ω of oz axle _zPositive dirction definition as diagram), and the oy axle can be confirmed by the right-handed helix rule.Vertical speed of advance v _x, side velocity v _yWith yaw velocity ω _zAll be meant the vehicle barycenter.According to Newtonian mechanics, the kinetic model of vehicle can be described as

$m{\stackrel{\&CenterDot;}{v}}_x={\mathrm{mv}}_y{\mathrm{\&omega;}}_z+2F_{\mathrm{tf}}\cos {\mathrm{\&delta;}}_f-2F_{\mathrm{sf}}\sin {\mathrm{\&delta;}}_f+{2F}_{\mathrm{tr}}-\frac{1}{2}{C}_d{A}_f{\mathrm{\&rho;}}_a{\mathrm{<figure-callout\; id="2"\; label="v\; x"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">v</figure-callout>}}_x^{}$

$I_z{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_z=2{\mathrm{aF}}_{\mathrm{tf}}{\mathrm{\&delta;}}_f+2{\mathrm{aF}}_{\mathrm{sf}}\cos {\mathrm{\&delta;}}_f-{2\mathrm{bF}}_{\mathrm{sr}}---\left(1\right)$

$m{\stackrel{\&CenterDot;}{v}}_y=-{\mathrm{mv}}_x{\mathrm{\&omega;}}_z+2F_{\mathrm{tf}}\sin {\mathrm{\&delta;}}_f+{2F}_{\mathrm{sf}}\cos {\mathrm{\&delta;}}_f+{2F}_{\mathrm{sr}}$

In the formula, v _x, v _yAnd ω _zBe respectively vertical speed of advance, side velocity and the yaw velocity of automobile, m and I _zBe respectively the quality of vehicle and around the rotor inertia of oz axle, a is the distance of vehicle front wheel shaft center to barycenter, and b is the distance of automobile back wheel wheel shaft center to barycenter, δ _fBe front wheel steering angle, C _dThe expression aerodynamic drag factor, A _fExpression vehicle forward direction area, ρ _aRepresent density of air, F _TfBe the longitudinal force that acts on the single front-wheel, F _TrBe the longitudinal force that acts on the single trailing wheel, F _SfBe the side force that acts on the single front-wheel, F _SrIt is the side force that acts on the single trailing wheel.

For the vehicle that goes at the Ordinary road traffic environment, can the side force that act on each wheel be expressed as usually

F _sf＝C _αfα _f，F _sr＝C _αrα _r (2)

In the formula (2), C _{α f}, C _{α r}The cornering stiffness of representing forward and backward tire respectively, α _f, α _rRepresent the sideslip angle of forward and backward tire respectively and can be expressed as

${\mathrm{\&alpha;}}_f={\mathrm{\&delta;}}_f-\frac{v_y+{\mathrm{a\&omega;}}_z}{v_x},$ ${\mathrm{\&alpha;}}_r=\frac{b{\mathrm{\&omega;}}_z-v_y}{v_x}---\left(3\right)$

With formula (2), (3) substitution formula (1), and consider δ _fNormally low-angle, i.e. sin δ _f≈ δ _f, cos δ _f≈ 1 and ignore second order and above high-order trace can get after putting in order

${\stackrel{\&CenterDot;}{v}}_x=\frac{1}{m}[{\mathrm{mv}}_y{\mathrm{\&omega;}}_z+2\frac{v_y+a{\mathrm{\&omega;}}_z}{v_x}{C}_{\mathrm{\&alpha;f}}{\mathrm{\&delta;}}_f-\frac{1}{2}{C}_d{A}_f{\mathrm{\&rho;}}_a{v}_x^2]+\frac{2}{m}(F_{\mathrm{tf}}+F_{\mathrm{tr}})$

${\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_z=\frac{1}{I_z}[2a({\mathrm{\&delta;}}_f-\frac{(v_y+{\mathrm{a\&omega;}}_z)}{v_x})C_{\mathrm{\&alpha;f}}-2{\mathrm{bC}}_{\mathrm{\&alpha;r}}-\frac{({\mathrm{b\&omega;}}_z-v_y)}{v_x}]+\frac{2a}{I_z}{F}_{\mathrm{tf}}{\mathrm{\&delta;}}_f---\left(4\right)$

${\stackrel{\&CenterDot;}{v}}_y=\frac{1}{m}[{\mathrm{mv}}_x{\mathrm{\&omega;}}_z+2({\mathrm{\&delta;}}_f-\frac{(v_y+{\mathrm{a\&omega;}}_z)}{v_x})C_{\mathrm{\&alpha;f}}+{2C}_{\mathrm{\&alpha;r}}\frac{{\mathrm{b\&omega;}}_z-v_y}{v_x}]+\frac{2}{m}{F}_{\mathrm{tf}}{\mathrm{\&delta;}}_f$

For the front wheel steering angle δ in the formula (4) _fBut the steering wheel angle δ that direction of passage dish rotary angle transmitter records is divided by the steering gear ratio q from the bearing circle to the front-wheel _tConfirm (to be δ _f=δ/q _t).And for the longitudinal force of tire F in the formula (4) _TfAnd F _TrThe present invention adopts the non-linear tire model of Dugoff to estimate to confirm [but list of references: Dugoff H.; Fancher P.S.; Segel L..An Analysis of Tire Traction Properties and TheirInfluence on Vehicle Dynamic Performance.SAE Transactions, 79:341-366,1970.SAE Paper No.700377].For this reason, introduce longitudinal direction of car slip rate i _Sj(j=f r) (promptly can be divided into front wheel spindle straight skidding rate i again _SfWith hind axle straight skidding rate i _Sr, promptly subscript j gets f or r representes front or rear wheel shaft respectively among the present invention), it calculates with the acceleration and deceleration situation of vehicle closely related, is specially

and j=f, r (5)

In the formula (5), R representes wheel tyre radius (generally, can think that the tire radius of four wheels is identical), v _TfAnd v _TrThe speed of representing forward and backward wheel shaft upper edge tire direction respectively (is mark convenience, v _TfAnd v _TrCan unify to be designated as v _Tj(j=f, r)), ω _fThe spin velocity on the front wheel spindle, ω are converted in the spin velocity equivalence of two wheels on the expression front wheel spindle _rSpin velocity (the ω on the hind axle is converted in the equivalence of two wheel revolutions cireular frequencys on the expression hind axle _fAnd ω _rCan unify to be designated as ω _j(j=f, r)), its computing formula is following

${\mathrm{\&omega;}}_f=\frac{1}{2}({\mathrm{\&omega;}}_{\mathrm{fR}}+{\mathrm{\&omega;}}_{\mathrm{fL}})$

(6)

${\mathrm{\&omega;}}_r=\frac{1}{2}({\mathrm{\&omega;}}_{\mathrm{rR}}+{\mathrm{\&omega;}}_{\mathrm{rL}})$

In the formula (6), ω _FL, ω _FR, ω _RLAnd ω _RRThe spin velocity of representing the near front wheel, off front wheel, left rear wheel and off hind wheel respectively obtains through utilizing four wheel speed sensors to measure.

In addition, according to movement relation shown in Figure 1, v _Tj(j=f r) can confirm by following formula

v _tf＝v _xcosδ _f+(v _y+aω _z)sinδ _f

(7)

v _tr＝v _x

According to Dugoff tire model [but list of references: Dugoff H.; Fancher P.S.; Segel L..AnAnalysis of Tire Traction Properties and Their Influence on Vehicle DynamicPerformance.SAE Transactions; 79:341-366,1970.SAE Paper No.700377], longitudinal force of tire F _TfAnd F _TrCan confirm through following formula

$F_{\mathrm{tj}}=\frac{C_{\mathrm{tj}}{i}_{\mathrm{sj}}}{1-i_{\mathrm{sj}}}{f}_t\left(p_j\right)$ (j＝f，r) (8)

In the formula (8), C _TfAnd C _TrRepresent that respectively the longitudinal rigidity of single forward and backward tire (can unite and be designated as C _Tj(j=f, r)), variable p _j(j=f, r) and function f _t(pj) (j=f r) is confirmed or definition by following formula

$p_j=\frac{\mathrm{\&mu;}{F}_{\mathrm{zj}}(1-{\mathrm{\&epsiv;}}_r{v}_x)\sqrt{{i_{\mathrm{<figure-callout\; id="2"\; label="sj"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">sj</figure-callout>}}}^2+{\tan }^2{\mathrm{\&alpha;}}_j}(1-i_{\mathrm{sj}})}{2\sqrt{{C_{\mathrm{tj}}}^2{i_{\mathrm{<figure-callout\; id="2"\; label="sj"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">sj</figure-callout>}}}^2+{C_{\mathrm{\&alpha;<figure-callout\; id="2"\; label="j"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">j</figure-callout>}}}^2{\tan }^2{\mathrm{\&alpha;}}_j}}$ j＝f，r (9)

$f_t\left(p_j\right)=\left\{\begin{array}{cc}{p}_j(2-p_j)& p_j<1\\ 1& p_j\&GreaterEqual;1\end{array}\right.$ j＝f，r (10)

In formula (9) and (10), μ representes the vertical friction coefficient between tire and ground, ε _rThe expression road adheres to decay factor, F _Zj(j=f, r) expression is assigned to the vertical load on the front or rear wheel shaft and can be calculated as follows

$F_{\mathrm{zf}}=\frac{\mathrm{mgb}}{2(a+b)},$ $F_{\mathrm{zr}}=\frac{\mathrm{mga}}{2(a+b)}---\left(11\right)$

In the formula (11), g representes acceleration due to gravity.

For the model that formula (4) is described, it is a non-linear vehicle dynamic model with 3DOF, is different from the linear auto model of the 2DOF that is often adopted.In the linear auto model of the 2DOF that often adopts, vertical speed of advance of vehicle is considered to permanent, and auto model only is the linear differential equation about side velocity and yaw velocity.Therefore, the generally only suitable forward speed of the linear auto model of 2DOF is constant or change running condition (manoevreability is lower) slowly, and for the motor-driven running condition of high the situation of acceleration and deceleration (promptly need frequently turn to and), there is bigger modeling error in this model.And the 3DOF nonlinear model that the present invention adopted does not have permanent qualification to vertical speed of advance of vehicle, therefore can adapt to the accurate estimation that general motor-driven environment also can adapt to travel condition of vehicle under the high motor-driven environment.

From the kinematics angle, vehicle movement shown in Figure 1 is actually a Planar Compound motion (it is compound that longitudinal movement, sideway movement and yaw rotate), so according to the Planar Compound movement relation, can get

$V_{\mathrm{RL}}=v_x+\frac{{\mathrm{<figure-callout\; id="2"\; label="T\; W"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">T</figure-callout>}}_W}{2}{\mathrm{\&omega;}}_z$

(12)

$V_{\mathrm{RR}}=v_x-\frac{{\mathrm{<figure-callout\; id="2"\; label="T\; W"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">T</figure-callout>}}_W}{2}{\mathrm{\&omega;}}_z$

In the formula, V _RLAnd V _RRRepresent the wheel linear velocity of left rear wheel and off hind wheel (i.e. two non-wheel flutters) respectively, T _WIt is the wheelspan between two trailing wheels on the hind axle.

Formula (12) is rearranged, can obtain

v _x＝(V _RL+V _RR)/2

ω _z＝(V _RL-V _RR)/T _W (13)

The wheel linear velocity that it is pointed out that left rear wheel and off hind wheel can obtain through two wheel speed sensors that are installed on the hind axle, and the cireular frequency that promptly utilizes on the hind axle two wheel speed sensors to record multiply by tire radius and obtains.Consider the measurement noise of wheel speed sensors, V ' _RL=R ω _RLAnd V ' _RR=R ω _RR, V ' wherein _RLAnd V ' _RRRepresent V respectively _RLAnd V _RRThe observed reading that contains noise; And then, V ' _RLAnd V ' _RRAlso can be expressed as respectively

Wherein

With

The additivity of representing the wheel linear velocity of left rear wheel and off hind wheel is respectively measured noise (all can be modeled as average be 0 Gaussian white noise).

In addition, along with the development of automotive electronic technology, the fast information of each wheel wheel also can be obtained through the CAN bus network in the automobile interior, extraly on each is taken turns, does not install wheel speed sensors additional with regard to not needing like this, and is more economical.In being discussed below, vertically speed of advance and yaw velocity will be as the amounts that can directly measure.

After setting up the non-linear vehicle dynamic model shown in the formula (4), next discuss how to design sliding formwork robust observer.

Compare with traditional observer, sliding mode observer has been proved to be the very effective method of estimation that a kind of processing has interference and model uncertainty NLS.Because the property complicated and changeable of road traffic environment; The manoevreability situation of vehicle self tends to take place frequent variation (as needing frequent acceleration or deceleration and turn to etc.); Can receive the influence of various uncertain external disturbance in addition, disturb etc. like the variation and the wind of road-adhesion coefficient.For realize under the high road traffic environment motor-driven, complicated and changeable to travel condition of vehicle accurately, reliably estimate that the present invention will be to the non-linear vehicle dynamic model of formula (4), the sliding mode observer suitable according to the sliding formwork Design Theory, detailed process is following:

(4) are turned to the form of describing with state space equation, promptly

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=f_1(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)+g_1({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})\\ {\stackrel{\&CenterDot;}{x}}_2=f_2(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)+g_2({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})\\ {\stackrel{\&CenterDot;}{x}}_3=f_3(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)+g_3({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})\end{array}\right.---\left(14\right)$

In the formula (14), x ₁, x ₂And x ₃Be three states of sliding mode observer, and x ₁=v _x, x ₂=ω _z, x ₃=v _y, δ _Tf, F _TfAnd F _TrBe three outer input variables, and

$f_1(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)=\frac{1}{m}[{\mathrm{mv}}_y{\mathrm{\&omega;}}_z+2\frac{v_y+{\mathrm{a\&omega;}}_z}{v_x}{C}_{\mathrm{\&alpha;f}}{\mathrm{\&delta;}}_f-\frac{1}{2}{C}_d{A}_f{\mathrm{\&rho;}}_a{v}_x^2]$

$f_2(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)=\frac{1}{I_z}[2a({\mathrm{\&delta;}}_f-\frac{(v_y+{\mathrm{a\&omega;}}_z)}{v_x})C_{\mathrm{\&alpha;f}}-2b{C}_{\mathrm{\&alpha;r}}\frac{({\mathrm{b\&omega;}}_z-v_y)}{v_x}]$

$f_3(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)=\frac{1}{m}[-{\mathrm{mv}}_x{\mathrm{\&omega;}}_z+2({\mathrm{\&delta;}}_f-\frac{(v_y+a{\mathrm{\&omega;}}_z)}{v_x})C_{\mathrm{\&alpha;f}}+2C_{\mathrm{\&alpha;r}}\frac{{\mathrm{b\&omega;}}_z-v_y}{v_x}]$

$g_1({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})=\frac{2}{m}(F_{\mathrm{tf}}+F_{\mathrm{tr}})$

$g_2({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})=\frac{2a}{I_z}{F}_{\mathrm{tf}}{\mathrm{\&delta;}}_f$

$g_3({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})=\frac{2}{m}{F}_{\mathrm{tf}}{\mathrm{\&delta;}}_f$

In addition, notice in formula (14) x ₁And x ₂Be the amount that can directly record (cireular frequency that promptly utilizes on the hind axle two wheel speed sensors to record multiply by the wheel linear velocity that tire radius obtains left rear wheel and off hind wheel, and then utilizes formula (13) to obtain), and x ₃Be the amount that can't directly record, need to estimate through sliding mode observer.The sliding mode observer that the present invention discussed can improve the precision of straight survey state on the one hand; The estimation dimension of extendible state on the other hand; Realization is to the Filtering Estimation (being virtual observation) of non-straight measurement; For active safety control provides more abundant and abundant travel condition of vehicle, be convenient to the realization of controlled target.

For the auto model shown in the formula (14), propose and set up following sliding mode observer (Sliding ModeObserver, SMO) model

$\left\{\begin{array}{c}{\stackrel{\stackrel{\&CenterDot;}{^}}{x}}_1=f_1({\hat{x}}_1,{\hat{x}}_2,{\hat{x}}_3,{\mathrm{\&delta;}}_f)+g_1({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})+l_1{s}_1+k_1\mathrm{sgn}\left(s_1\right)\\ {\stackrel{\stackrel{\&CenterDot;}{^}}{x}}_2=f_2({\hat{x}}_1,{\hat{x}}_2,{\hat{x}}_3,{\mathrm{\&delta;}}_f)+g_2({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})+l_2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\mathrm{sgn}\left(s_2\right)\\ {\stackrel{\stackrel{\&CenterDot;}{^}}{x}}_3=f_3({\hat{x}}_1,{\hat{x}}_2,{\hat{x}}_3,{\mathrm{\&delta;}}_f)+g_3({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})+{\mathrm{\&tau;}}_1\mathrm{sgn}\left(s_1\right)+{\mathrm{\&tau;}}_2\mathrm{sgn}\left(s_2\right)\end{array}\right.---\left(15\right)$

In the formula (15),

With Represent x respectively ₁, x ₂And x ₃Estimated valve.For outer input variable δ _fBut the steering wheel angle δ that direction of passage dish rotary angle transmitter records is divided by the steering gear ratio q from the bearing circle to the front-wheel _tObtain (is δ _f=δ/q _t), and for F _TfAnd F _Tr, can estimate to obtain through above-mentioned Dugoff tire model (promptly utilizing formula (5)-(11)).l _j(j=1,2) are the error convergence gains outside the sliding-mode surface, and k _j(j=1,2) and τ _jThe error convergence gain on the sliding-mode surface has then been represented in (j=1,2), and sgn (.) is sign function (being symbolic function).In addition, s ₁And s ₂What be defined as sliding mode observer can directly survey state x ₁, x ₂With estimated valve separately

With

Between error, promptly

$s_1=x_1-{\hat{x}}_1,$ ${\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2=x_2-{\hat{x}}_2---\left(16\right)$

Formula (14) is deducted formula (15), can obtain the error dynamics equation of sliding mode observer state of the system

${\stackrel{\stackrel{\&CenterDot;}{~}}{x}}_1=\mathrm{\&Delta;}{f}_1-l_1{s}_1-k_1\mathrm{sgn}\left(s_1\right)$

${\stackrel{\stackrel{\&CenterDot;}{~}}{x}}_2=\mathrm{\&Delta;}{f}_2-l_2{s}_2-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\mathrm{sgn}\left(s_2\right)---\left(17\right)$

${\stackrel{\stackrel{\&CenterDot;}{~}}{x}}_3={\mathrm{\&Delta;f}}_3-{\mathrm{\&tau;}}_1\mathrm{sgn}\left(s_1\right)-{\mathrm{\&tau;}}_2\mathrm{sgn}\left(s_2\right)$

In the formula, ${\tilde{x}}_1=x_1-{\hat{x}}_1=s_1,$ ${\tilde{x}}_2=x_2-{\hat{\mathrm{<figure-callout\; id="2"\; label="x\; ^"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">x</figure-callout>}}}_2={\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2,$ ${\tilde{x}}_3=x_3-{\hat{\mathrm{<figure-callout\; id="3"\; label="x\; ^"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">x</figure-callout>}}}_3,$ ${\mathrm{\&Delta;\; f}}_1=f_1(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)-f_1({\hat{x}}_1,{\hat{x}}_2,{\hat{x}}_3,{\mathrm{\&delta;}}_f),$

${\mathrm{\&Delta;<figure-callout\; id="2"\; label="f"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_2=f_2(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)-f_2({\hat{x}}_1,{\hat{x}}_2,{\hat{x}}_3,{\mathrm{\&delta;}}_f),$ ${\mathrm{\&Delta;<figure-callout\; id="3"\; label="f"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_3=f_3(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)-f_3({\hat{x}}_1,{\hat{x}}_2,{\hat{x}}_3,{\mathrm{\&delta;}}_f).$

The sliding mode observer key for design is how to confirm each gain of sliding mode observer in the formula (17) according to stability principle.Construct following Liapunov (Lyapunov) function

$V(s_1,s_2)=\frac{1}{2}(s_1^2+{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2^2)---\left(18\right)$

For guaranteeing sliding formwork state, s in the following formula _j(j=1,2) should satisfy (j=1,2), promptly

$s_j{\stackrel{\&CenterDot;}{s}}_j<-{\mathrm{\&eta;}}_j\left|s_j\right|,$ $\&ForAll;{\mathrm{\&eta;}}_j>0(j=\mathrm{1,2})---\left(19\right)$

In the formula (19), η _j(j=1,2) are given positive number (like positive decimal).

Below with state x ₁Be example, discuss and how to confirm the l that gains ₁And k ₁Δ f in first equation of formula (17) ₁Be a continuously differentiable function, so have

${\mathrm{\&Delta;f}}_1=f_1(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)-f_1({\hat{x}}_1,{\hat{x}}_2,{\hat{x}}_3,{\mathrm{\&delta;}}_f)$

$=\frac{{\&PartialD;f}_1}{{\&PartialD;x}_1}{s}_1+\frac{{\&PartialD;f}_1}{{\&PartialD;x}_2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2+\frac{{\&PartialD;f}_1}{{\&PartialD;x}_3}{\tilde{x}}_3+{\&dtri;}_1---\left(20\right)$

$\&ap;\frac{{\&PartialD;f}_1}{{\&PartialD;x}_1}{s}_1+\frac{{\&PartialD;f}_1}{{\&PartialD;x}_2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2+\frac{{\&PartialD;f}_1}{{\&PartialD;x}_3}{\tilde{x}}_3$

In the formula (20),

Be the high-order trace (can ignore) that causes by differential,

(j=1,2,3) representative function f ₁For x _jThe partial derivative of (j=1,2,3) can be tried to achieve through the method for asking local derviation, as

$\frac{{\&PartialD;f}_1}{{\&PartialD;x}_1}=\frac{-2C_{\mathrm{\&alpha;f}}(v_y+{\mathrm{\&alpha;\&omega;}}_z){\mathrm{\&delta;}}_f}{{{\mathrm{mv}}_x}^2}-\frac{C_d{A}_f{\mathrm{\&rho;}}_a{v}_x}{m}$

First equation and formula (20) substitution formula (19) with formula (17) can get

$s_1[\frac{{\&PartialD;f}_1}{{\&PartialD;x}_1}{s}_1+\frac{{\&PartialD;f}_1}{{\&PartialD;x}_2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2+\frac{{\&PartialD;f}_1}{{\&PartialD;x}_3}{\tilde{x}}_3-l_1{s}_1-k_1\mathrm{sgn}\left(s_1\right)]<-{\mathrm{\&eta;}}_1\left|s_1\right|---\left(21\right)$

Putting above-mentioned inequality in order can get

$(\frac{{\&PartialD;f}_1}{{\&PartialD;x}_1}-l_1){s_1}^2+\frac{{\&PartialD;f}_1}{{\&PartialD;x}_2}{s}_1{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2+\frac{{\&PartialD;f}_1}{{\&PartialD;x}_3}{s}_1{\tilde{x}}_3-k_1\left|s_1\right|<-{\mathrm{\&eta;}}_1\left|s_1\right|---\left(22\right)$

Can find out from formula (22), as long as following two are not waited condition to satisfy simultaneously,

$\frac{{\&PartialD;f}_1}{{\&PartialD;x}_1}<l_1,$ $\left|s_1\right|\left(\right|\frac{{\&PartialD;f}_1}{{\&PartialD;x}_2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2|+|\frac{{\&PartialD;f}_1}{{\&PartialD;x}_3}{\tilde{x}}_3|-k_1)<-{\mathrm{\&eta;}}_1\left|s_1\right|---\left(23\right)$

Sliding mode just can be guaranteed, and can confirm gain l according to the following condition that do not wait ₁And k ₁

$l_1>\frac{{\&PartialD;f}_1}{{\&PartialD;x}_1},$ $k_1>\left|\frac{{\&PartialD;f}_1}{{\&PartialD;x}_2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2\right|+\left|\frac{{\&PartialD;f}_1}{\&PartialD;x_3}{\tilde{x}}_3\right|+{\mathrm{\&eta;}}_1---\left(24\right)$

In like manner, utilize second equation and formula (19) in the formula (17), and according to Δ f ₂Continuous differentiability, can confirm and state x ₂Relevant gain l ₂And k ₂, promptly

${\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">l</figure-callout>}}_2>\frac{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{{\&PartialD;x}_2},$ ${\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_2>\left|\frac{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{{\&PartialD;x}_1}{s}_1\right|+\left|\frac{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_3}{\tilde{x}}_3\right|+{\mathrm{\&eta;}}_2---\left(25\right)$

In the formula (25),

(j=1,2,3) representative function f ₂For x _jThe partial derivative of (j=1,2,3) can be tried to achieve through the method for asking local derviation, as

$\frac{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{{\&PartialD;x}_2}=\frac{-2(a^2{C}_{\mathrm{\&alpha;f}}+b^2{C}_{\mathrm{\&alpha;r}})}{I_z{v}_x}.$

When sliding mode reaches, there is first equation of

substitution formula (17) to get

${\stackrel{\&CenterDot;}{s}}_1=\frac{{\&PartialD;f}_1}{{\&PartialD;x}_1}{s}_1+\frac{\&PartialD;f_1}{{\&PartialD;x}_2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2+\frac{\&PartialD;f_1}{\&PartialD;x_3}{\tilde{x}}_3-l_1{s}_1-k_1\mathrm{sgn}\left(x_1\right)$

Can obtain through abbreviation

$\mathrm{sgn}\left(s_1\right)=\frac{1}{k_1}\frac{\&PartialD;f_1}{{\&PartialD;x}_3}{\tilde{x}}_3---\left(26\right)$

In like manner, when sliding mode reaches, utilize second equation of formula (17) to obtain

$\mathrm{sgn}\left(s_2\right)=\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{{\&PartialD;x}_3}{\tilde{x}}_3---\left(27\right)$

And then, when sliding mode reaches,, consider simultaneously the 3rd equation of formula (26) and formula (27) substitution formula (17) ${\mathrm{\&Delta;\; <figure-callout\; id="3"\; label="f"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_3\&ap;\frac{{\&PartialD;\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_3}{{\&PartialD;x}_1}{s}_1+\frac{{\&PartialD;\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_3}{{\&PartialD;x}_2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2+\frac{{\&PartialD;\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_3}{{\&PartialD;x}_3}{\tilde{x}}_{3,}$ Can obtain

${\stackrel{\stackrel{\&CenterDot;}{~}}{x}}_3\&ap;\frac{{\&PartialD;\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_3}{{\&PartialD;x}_1}{s}_1+\frac{{\&PartialD;\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_3}{{\&PartialD;x}_2}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2+\frac{{\&PartialD;\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_3}{{\&PartialD;x}_3}{\tilde{x}}_3-{\mathrm{\&tau;}}_1\mathrm{sgn}\left(s_1\right)-{\mathrm{\&tau;}}_2\mathrm{sgn}\left(s_2\right)$

$\frac{{\&PartialD;\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_3}{{\&PartialD;x}_3}{\tilde{x}}_3-{\mathrm{\&tau;}}_1\mathrm{sgn}\left(s_1\right)-{\mathrm{\&tau;}}_2\mathrm{sgn}\left(s_2\right)---\left(28\right)$

$=(\frac{{\&PartialD;\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_3}{{\&PartialD;x}_3}-\frac{{\mathrm{\&tau;}}_1}{k_1}\frac{{\&PartialD;f}_1}{{\&PartialD;x}_3}-\frac{{\mathrm{\&tau;}}_2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}\frac{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{{\&PartialD;x}_3}){\tilde{x}}_3$

In the formula (28),

(j=1,2,3) representative function f _j(j=1,2,3) are for x ₃Partial derivative.According to formula (14), can try to achieve each local derviation item in the formula (28), promptly

$\frac{{\&PartialD;f}_1}{{\&PartialD;x}_3}={\mathrm{\&omega;}}_z+\frac{2C_{\mathrm{\&alpha;f}}{\mathrm{\&delta;}}_f}{{\mathrm{mv}}_x}$

$\frac{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{{\&PartialD;x}_3}=\frac{2({\mathrm{bC}}_{\mathrm{\&alpha;r}}-a{C}_{\mathrm{\&alpha;f}})}{I_z{v}_x}---\left(29\right)$

$\frac{{\&PartialD;\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_3}{{\&PartialD;x}_3}=-\frac{2(C_{\mathrm{\&alpha;f}}+C_{\mathrm{\&alpha;r}})}{{\mathrm{mv}}_x}$

In the product coefficient with (29) substitution formula (28) right side

, can get

$\frac{{\&PartialD;\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_3}{{\&PartialD;x}_3}-\frac{{\mathrm{\&tau;}}_1}{k_1}\frac{\&PartialD;f_1}{\&PartialD;x_3}-\frac{{\mathrm{\&tau;}}_2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}\frac{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{{\&PartialD;x}_3}=\frac{2(C_{\mathrm{\&alpha;f}}+C_{\mathrm{\&alpha;r}})}{{\mathrm{mv}}_x}-\frac{{\mathrm{\&tau;}}_1}{k_1}({\mathrm{\&omega;}}_z+\frac{{2C}_{\mathrm{\&alpha;f}}{\mathrm{\&delta;}}_f}{{\mathrm{mv}}_x})-\frac{{\mathrm{\&tau;}}_2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}\frac{2({\mathrm{bC}}_{\mathrm{\&alpha;r}}-a{C}_{\mathrm{\&alpha;f}})}{I_z{v}_x}---\left(30\right)$

Can find out by formula (30) and formula (28), for guaranteeing about state x ₃The convergence of estimation procedure is stable, and the method for a simple possible is order gain τ ₁=τ ₂=0, because this moment, following formula was set up

$\frac{\&PartialD;{\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="HDA0000120443810000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_3}{\&PartialD;x_3}-\frac{{\mathrm{\&tau;}}_1}{k_1}\frac{\&PartialD;f_1}{\&PartialD;x_3}-\frac{{\mathrm{\&tau;}}_2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}\frac{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000120443810000011.png,HDA0000120443810000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{{\&PartialD;x}_3}=-\frac{2(C_{\mathrm{\&alpha;f}}+C_{\mathrm{\&alpha;r}})}{{\mathrm{mv}}_x}<0---\left(31\right)$

Definite method of all gains in the sliding mode observer formula (15) so far, has been discussed.In addition, be the excessive jitter of avoiding symbolic function to cause, in the estimation procedure of reality, above-mentioned various middle sgn (.) function that occurs replaces with following sgneq (.) function

sgn _eq(s _j)＝tanh(λs _j)(j＝1，2) (32)

In the formula (32), tanh (.) is a hyperbolic tangent function, and λ is a design parameters that is used for adjusting the hyperbolic tangent function inclined degree.

In the estimation procedure of reality, need to adopt the estimation recursive form of discretization.For this reason, with above-mentioned design-calculated sliding mode observer, promptly formula (15) is carried out the discretization processing, promptly

${\hat{x}}_1\left(k\right)={\hat{x}}_1(k-1)+T{\hat{x}}_2(k-1){\hat{x}}_3(k-1)+2T{C}_{\mathrm{\&alpha;f}}{\mathrm{\&delta;}}_f(k-1)\frac{{\hat{x}}_3(k-1)+a{\hat{x}}_2(k-1)}{m{\hat{x}}_1(k-1)}-\frac{T}{2m}{C}_d{A}_f{\mathrm{\&rho;}}_a{{\hat{x}}_1}^2(k-1)$

$+\frac{2T}{m}[F_{\mathrm{tf}}(k-1)+F_{\mathrm{tr}}(k-1)]+l_{1}T[v_x^{\&prime;}(k-1)-{\hat{x}}_1(k-1)]+k_{1}T\&CenterDot;\tanh [\mathrm{\&lambda;}{v}_x^{\&prime;}(k-1)-\mathrm{\&lambda;}{\hat{x}}_1(k-1)]$

${\hat{x}}_2\left(k\right)={\hat{x}}_2(k-1)+\frac{2{\mathrm{TaC}}_{\mathrm{\&alpha;f}}}{I_z}[{\mathrm{\&delta;}}_f(k-1)+\frac{-{\hat{x}}_3(k-1)-a{\hat{x}}_2(k-1)}{{\hat{x}}_1(k-1)}]-2{\mathrm{TbC}}_{\mathrm{\&alpha;r}}\frac{b{\hat{x}}_2(k-1)-{\hat{x}}_3(k-1)}{I_z{\hat{x}}_1(k-1)}$

$+\frac{2\mathrm{Ta}}{I_z}{F}_{\mathrm{tf}}(k-1){\mathrm{\&delta;}}_f(k-1)+l_{2}T[{\mathrm{\&omega;}}_z^{\&prime;}(k-1)-{\hat{x}}_2(k-1)]+k_{2}T\&CenterDot;\tanh [{\mathrm{\&lambda;\&omega;}}_z^{\&prime;}(k-1)-\mathrm{\&lambda;}{\hat{x}}_2(k-1)]$

${\hat{x}}_3(k-1)={\hat{x}}_3(k-1)-T{\hat{x}}_1(k-1){\hat{x}}_2(k-1)+\frac{{2\mathrm{TC}}_{\mathrm{\&alpha;f}}}{m}[{\mathrm{\&delta;}}_f(k-1)-\frac{({\hat{x}}_3(k-1)+a{\hat{x}}_2(k-1))}{{\hat{x}}_1(k-1)}]$

$+2{\mathrm{TC}}_{\mathrm{\&alpha;r}}\frac{b{\hat{x}}_2(k-1)-{\hat{x}}_3(k-1)}{m{\hat{x}}_1(k-1)}+\frac{2T}{m}{F}_{\mathrm{tf}}(k-1){\mathrm{\&delta;}}_f(k-1)$

(33)

In the formula (33), k representes discretization constantly, the cycle that T representes to disperse (in the present invention, according to the survey sensor characteristic, the representative value of T can be taken as 10 milliseconds, 20 milliseconds or 50 milliseconds etc.), v ' _xAnd ω ' _zExpression is measured longitudinal direction of car speed of advance and the yaw velocity of acquisition through wheel speed sensors (cireular frequency that promptly utilizes on the hind axle two wheel speed sensors to record multiply by the wheel linear velocity that tire radius obtains left rear wheel and off hind wheel respectively; And then utilize formula (13) to obtain), i.e. v ' _xAnd ω ' _zRepresent v respectively _xAnd ω _zThe observed reading that contains noise.Consider the measurement noise of wheel speed sensors, v ' _x, ω ' _zCan be expressed as respectively

Wherein Vertical speed of advance observation noise of expression equivalence (can be modeled as average and be 0, variance does

Gaussian white noise),

The yaw velocity observation noise of expression equivalence (can be modeled as average and be 0, variance does

Gaussian white noise).

In above-mentioned estimation recursive process, can confirm that automobile is at each automobile longitudinal speed of advance v constantly _x(k), yaw velocity ω _z(k) and side velocity v _y(k), and then according to following formula can confirm each side slip angle constantly

β(k)＝arctan[v _y(k)/v _x(k)] (34)

Embodiment 2

For the actual effect that check the present invention proposes, utilize the CarSim of automobile dynamic quality simulation software of specialty to carry out the simulating, verifying experiment based on the travel condition of vehicle non linear robust method of estimation of sliding mode observer.

CarSim is the special simulation software to vehicle dynamics by the exploitation of U.S. MSC (Mechanical Simulation Corporation) company; Adopted by numerous in the world automakers, components supplying merchant at present; Be widely used in the business development of modern automobile control system; Become the standard software of auto trade, enjoyed a very good reputation.Vehicle dynamic model in the Carsim be through respectively to car body, the suspension of automobile, turn to, the modeling high true to nature of each subsystem such as braking and each tire realizes; Has very high degree of freedom; Can provide very near the actual information of travel condition of vehicle accurately; Therefore, the travel condition of vehicle information of Carsim output can be used as the reference output of vehicle.

The Robust Estimation effect of the algorithm that proposes for check the present invention under the motor-driven operating mode of height and different road circumstance states; Vertical speed of advance that automobile is set in the emulation experiment is constantly being done acceleration, braking deceleration and is at the uniform velocity being waited variation; Automobile steering wheel corner δ changes by the sinusoidal rule of 60 ° of amplitudes simultaneously; Vertically speed of advance and steering wheel angle specifically over time process shown in accompanying drawing 2; (simulated roadway is from being dried to the variation that wet and slippery road adheres to condition and the vertical coefficientoffriction between tire and ground carries out emulation respectively by μ=1, μ=0.8 and μ=0.6 3 kind of situation; Be the variation of road conditions environment), the emulation duration that different roads adhere under the condition all is set to 100 seconds (s).Used vehicle is the four-wheeled of a front-wheel steering, and principal parameter is following: m=960 (kilogram), I _z=1382 (kilogram-meters ²), a=0.948 (rice), b=1.422 (rice), C _{α f}=C _{α r}=25692 (newton/radians), T _w=1.390 (rice).The measurement noise of setting the linear velocity (cireular frequency that records through wheel speed sensors multiply by tire radius and obtains) of four wheels is that average is 0, standard deviation is the Gaussian white noise of 0.05 (meter per second), and the measurement noise of steering wheel angle sensor is that average is 0, standard deviation is the Gaussian white noise of 0.0873 (radian).

Table 1 and Fig. 3～shown in Figure 4 have provided the result of μ=1 o'clock.Table 1 has been listed the statistics contrast of directly surveying method and the inventive method reckoning travel condition of vehicle for whole process utilization, and the error in the table all is (just the representing to utilize the error of vertical speed of advance of straight survey method reckoning with respect to vertical speed of advance reference value of Carsim output like vertical speed of advance error of straight survey method) for the corresponding reference value of Carsim output.Be pointed out that in addition; The concrete implication of straight survey method and the inventive method is following: directly survey method is meant vertical speed of advance and the yaw velocity that converts and obtain through direct measurement; The cireular frequency that promptly utilizes on the hind axle two wheel speed sensors to record multiply by the wheel linear velocity that tire radius obtains left rear wheel and off hind wheel, and then directly calculates vertical speed of advance and the yaw velocity that obtains according to the formula in the embodiment 1 (13); The inventive method be meant utilize that the present invention proposes calculate the method for each running state of vehicle based on the travel condition of vehicle non linear robust method of estimation of sliding mode observer.Fig. 3 has provided the result curve (indicating with SMO dot-dash dotted line among the figure) of the side slip angle β of μ=1 o'clock the inventive method estimation, and the reference output valve of corresponding C arsim (indicating with the real black line of Carsim among the figure).Fig. 4 has then provided the curve of error of the β of μ=1 o'clock the inventive method estimation with respect to the β reference value of Carsim output.

Two kinds of methods of table 1 are calculated the contrast table of effect

The item that the straight survey method of "--" expression can't be calculated in the table

Table 2 and Fig. 5～shown in Figure 8 have provided the relevant result of μ=0.8 and μ=0.6 o'clock.Wherein, table 2 provides the statistics (error in the table all is for the corresponding reference value of Carsim output) that other two kinds of roads adhere to the relevant reckoning result under the condition.Fig. 5 has provided the result curve (indicating with SMO dot-dash dotted line among the figure) of the side slip angle β of μ=0.8 o'clock the inventive method estimation, and the reference output valve of corresponding C arsim (indicating with the real black line of Carsim among the figure); Fig. 6 has then provided the curve of error of the β of μ=0.8 o'clock the inventive method estimation with respect to the β reference value of Carsim output.And Fig. 7 has provided the result curve (indicating with SMO dot-dash dotted line among the figure) of the side slip angle β of μ=0.6 o'clock the inventive method estimation, and the reference output valve of corresponding C arsim (indicating with the real black line of Carsim among the figure); Fig. 8 has then provided the curve of error of the β of μ=0.6 o'clock the inventive method estimation with respect to the β reference value of Carsim output.

Table 2 the inventive method is adhered to the reckoning effect comparison under the condition at different roads

By contrast (especially standard deviation) and Fig. 3～Fig. 4 of table 1, can find out that the inventive method has had significantly raising with respect to straight survey method in precision aspect the reckoning of vertical speed of advance and yaw velocity.In addition, according to table 1 and Fig. 3～Fig. 4, it can also be seen that the inventive method also has very high precision aspect the estimation of side velocity and side slip angle.

In addition; Statistics (especially standard deviation) and Fig. 3～Fig. 8 according to table 1～table 2; Can find out that the inventive method is not almost changing aspect the travel condition of vehicle estimated accuracy when bigger variation takes place the road condition of adhering to; Still kept higher precision, promptly the inventive method has shown good robustness and antijamming capability.

To sum up; Even when motor-driven operating condition of height and road circumstance state generation significant change; The travel condition of vehicle non linear robust method of estimation based on sliding mode observer that the present invention proposes still can estimate information such as longitudinal direction of car speed of advance, side velocity, yaw velocity and side slip angle exactly, and these information can satisfy the needs of relevant automobile active safety control.

Claims (3)

1. travel condition of vehicle non linear robust method of estimation based on sliding mode observer; It is characterized in that: this method is to using more front-wheel steering four-wheel automobile at present; Designed sliding mode observer based on non-linear automobile dynamic quality model; Estimation recursion through sliding mode observer realizes accurate, Robust Estimation to information such as automobile longitudinal speed of advance, yaw velocity, side velocity and side slip angles, and concrete steps comprise:

1) set up the sliding mode observer of travel condition of vehicle:

Adopt the automobile non-linear dynamic model of three degree of freedom, the state space equation form of this model is following:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=f_1(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)+g_1({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})\\ {\stackrel{\&CenterDot;}{x}}_2=f_2(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)+g_2({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})\\ {\stackrel{\&CenterDot;}{x}}_3=f_3(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)+g_3({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})\end{array}\right.---\left(1\right)$

In the formula (1), x ₁, x ₂And x ₃Be three states of sliding mode observer, and x ₁=v _x, x ₂=ω _z, x ₃=v _y, v _x, v _yAnd ω _zBe respectively vertical speed of advance, side velocity and the yaw velocity of automobile;

δ _f, F _TfAnd F _TrBe three outer input variables, wherein δ _fBe front wheel steering angle, F _TfBe the longitudinal force that acts on the single front-wheel, F _TrIt is the longitudinal force that acts on the single trailing wheel;

Each function f in the formula (1) _j(j=1,2,3) and g _jThe value of (j=1,2,3) is following

$f_1(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)=\frac{1}{m}[{\mathrm{mv}}_y{\mathrm{\&omega;}}_z+2\frac{v_y+{\mathrm{a\&omega;}}_z}{v_x}{C}_{\mathrm{\&alpha;f}}{\mathrm{\&delta;}}_f-\frac{1}{2}{C}_d{A}_f{\mathrm{\&rho;}}_a{v}_x^2]$

$f_2(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)=\frac{1}{I_z}[2a({\mathrm{\&delta;}}_f-\frac{(v_y+{\mathrm{a\&omega;}}_z)}{v_x})C_{\mathrm{\&alpha;f}}-2b{C}_{\mathrm{\&alpha;r}}\frac{({\mathrm{b\&omega;}}_z-v_y)}{v_x}]$

$f_3(x_1,x_2,x_3,{\mathrm{\&delta;}}_f)=\frac{1}{m}[-{\mathrm{mv}}_x{\mathrm{\&omega;}}_z+2({\mathrm{\&delta;}}_f-\frac{(v_y+a{\mathrm{\&omega;}}_z)}{v_x})C_{\mathrm{\&alpha;f}}+2C_{\mathrm{\&alpha;r}}\frac{{\mathrm{b\&omega;}}_z-v_y}{v_x}]$

$g_1({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})=\frac{2}{m}(F_{\mathrm{tf}}+F_{\mathrm{tr}})$

$g_2({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})=\frac{2a}{I_z}{F}_{\mathrm{tf}}{\mathrm{\&delta;}}_f$

$g_3({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})=\frac{2}{m}{F}_{\mathrm{tf}}{\mathrm{\&delta;}}_f$

At said f _j(j=1,2,3) and g _jIn (j=1,2,3), m and I _zBe respectively the quality and the rotor inertia of walking around the vertical axle of barycenter of vehicle, a is the distance of vehicle front wheel shaft center to barycenter, and b is the distance of automobile back wheel wheel shaft center to barycenter, C _{α f}, C _{α r}The cornering stiffness of representing forward and backward tire respectively, C _dThe expression aerodynamic drag factor, A _fExpression vehicle forward direction area, ρ _aRepresent density of air;

For state x ₁And x ₂, the corresponding v of difference _xAnd ω _z, the wheel speed of two non-steered wheels has following relation on they and the hind axle:

v _x＝(V _RL+V _RR)/2

ω _z＝(V _RL-V _RR)/T _W (2)

In the formula (2), T _WBe the wheelspan between two trailing wheels on the hind axle, V _RLAnd V _RRRepresent the linear velocity of left rear wheel and off hind wheel respectively, i.e. the wheel linear velocity of two non-wheel flutters;

State x ₁And x ₂Be the amount that can directly record, and state x ₃For the amount that can't directly record needs to estimate through sliding mode observer;

For the auto model shown in the formula (1), propose and set up following sliding mode observer model:

$\left\{\begin{array}{c}{\stackrel{\stackrel{\&CenterDot;}{^}}{x}}_1=f_1({\hat{x}}_1,{\hat{x}}_2,{\hat{x}}_3,{\mathrm{\&delta;}}_f)+g_1({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})+l_1{s}_1+k_1\mathrm{sgn}\left(s_1\right)\\ {\stackrel{\stackrel{\&CenterDot;}{^}}{x}}_2=f_2({\hat{x}}_1,{\hat{x}}_2,{\hat{x}}_3,{\mathrm{\&delta;}}_f)+g_2({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})+l_2{s}_2+k_2\mathrm{sgn}\left(s_2\right)\\ {\stackrel{\stackrel{\&CenterDot;}{^}}{x}}_3=f_3({\hat{x}}_1,{\hat{x}}_2,{\hat{x}}_3,{\mathrm{\&delta;}}_f)+g_3({\mathrm{\&delta;}}_f,F_{\mathrm{tf}},F_{\mathrm{tr}})+{\mathrm{\&tau;}}_1\mathrm{sgn}\left(s_1\right)+{\mathrm{\&tau;}}_2\mathrm{sgn}\left(s_2\right)\end{array}\right.---\left(3\right)$

In the formula (3), With

Represent x respectively ₁, x ₂And x ₃The calculating estimated valve, l _j(j=1,2) are the error convergence gains outside the sliding-mode surface, and k _j(j=1,2) and τ _jThe error convergence gain on the sliding-mode surface has then been represented in (j=1,2), and sgn (.) is sign function, i.e. symbolic function; s ₁And s ₂What be defined as sliding mode observer can directly survey state x ₁, x ₂With estimated valve separately

Between error, promptly

$s_1=x_1-{\hat{x}}_1,$ $s_2=x_2-{\hat{x}}_2---\left(4\right)$

2) carry out the estimation recursion of discretization:

In the estimation procedure of reality, need to adopt the estimation recursive form of discretization, for this reason, be that formula (3) is carried out the discretization processing with above-mentioned design-calculated sliding mode observer,

${\hat{x}}_1\left(k\right)={\hat{x}}_1(k-1)+T{\hat{x}}_2(k-1){\hat{x}}_3(k-1)+2T{C}_{\mathrm{\&alpha;f}}{\mathrm{\&delta;}}_f(k-1)\frac{{\hat{x}}_3(k-1)+a{\hat{x}}_2(k-1)}{m{\hat{x}}_1(k-1)}-\frac{T}{2m}{C}_d{A}_f{\mathrm{\&rho;}}_a{{\hat{x}}_1}^2(k-1)$

$+\frac{2T}{m}[F_{\mathrm{tf}}(k-1)+F_{\mathrm{tr}}(k-1)]+l_{1}T[v_x^{\&prime;}(k-1)-{\hat{x}}_1(k-1)]+k_{1}T\&CenterDot;\tanh [\mathrm{\&lambda;}{v}_x^{\&prime;}(k-1)-\mathrm{\&lambda;}{\hat{x}}_1(k-1)]$

${\hat{x}}_2\left(k\right)={\hat{x}}_2(k-1)+\frac{2{\mathrm{TaC}}_{\mathrm{\&alpha;f}}}{I_z}[{\mathrm{\&delta;}}_f(k-1)+\frac{-{\hat{x}}_3(k-1)-a{\hat{x}}_2(k-1)}{{\hat{x}}_1(k-1)}]-2{\mathrm{TbC}}_{\mathrm{ar}}\frac{b{\hat{x}}_2(k-1)-{\hat{x}}_3(k-1)}{I_z{\hat{x}}_1(k-1)}$

$+\frac{2\mathrm{Ta}}{I_z}{F}_{\mathrm{tf}}(k-1){\mathrm{\&delta;}}_f(k-1)+l_{2}T[{\mathrm{\&omega;}}_z^{\&prime;}(k-1)-{\hat{x}}_2(k-1)]+k_{2}T\&CenterDot;\tanh [{\mathrm{\&lambda;\&omega;}}_z^{\&prime;}(k-1)-\mathrm{\&lambda;}{\hat{x}}_2(k-1)]---\left(5\right)$

${\hat{x}}_3(k-1)={\hat{x}}_3(k-1)-T{\hat{x}}_1(k-1){\hat{x}}_2(k-1)+\frac{{2\mathrm{TC}}_{\mathrm{\&alpha;f}}}{m}[{\mathrm{\&delta;}}_f(k-1)-\frac{({\hat{x}}_3(k-1)+a{\hat{x}}_2(k-1))}{{\hat{x}}_1(k-1)}]$

$+2{\mathrm{TC}}_{\mathrm{\&alpha;r}}\frac{b{\hat{x}}_2(k-1)-{\hat{x}}_3(k-1)}{m{\hat{x}}_1(k-1)}+\frac{2T}{m}{F}_{\mathrm{tf}}(k-1){\mathrm{\&delta;}}_f(k-1)$

In the formula (5), k representes discretization constantly, and T representes cycle of dispersing, and tanh (.) is a hyperbolic tangent function, and λ is a design parameters that is used for adjusting the hyperbolic tangent function inclined degree, v ' _xAnd ω ' _zExpression is measured longitudinal direction of car speed of advance and the yaw velocity that obtains, i.e. v ' through wheel speed sensors respectively _xAnd ω ' _zRepresent v respectively _xAnd ω _zThe observed reading that contains noise;

In above-mentioned filtering recursion computation process, can confirm that automobile is at each vertical speed of advance v constantly _x(k), yaw velocity ω _z(k) and side velocity v _y(k), and then according to following formula can confirm each side slip angle constantly

β(k)＝arctan[v _y(k)/v _x(k)] (6)。

2. the travel condition of vehicle non linear robust method of estimation based on sliding mode observer according to claim 1; It is characterized in that vertical speed of advance and yaw velocity are the amounts that can directly record; Promptly measure and obtain longitudinal direction of car speed of advance and yaw velocity, be specially and utilize two left rear wheel angular velocity omegas that wheel speed sensors records on the hind axle through wheel speed sensors _RLWith the off hind wheel angular velocity omega _RRMultiply by tire radius R and obtain V ' _RL=R ω _RLAnd V ' _RR=R ω _RR, V ' _RLAnd V ' _RRRepresent V respectively _RLAnd V _RRContain noise observed reading and

Wherein

With

Represent that respectively the additivity of the wheel linear velocity of left rear wheel and off hind wheel measures noise, and then utilize formula (2) to obtain the observed reading v ' that vertical speed of advance and yaw velocity contain noise again _xAnd ω ' _z

For three outer input variables in the formula (3), confirm through following method:

Front wheel steering angle δ _fBut the steering wheel angle δ that direction of passage dish rotary angle transmitter records is divided by the steering gear ratio q from the bearing circle to the front-wheel _tConfirm, i.e. δ _f=δ/q _t

Longitudinal force of tire F _TfAnd F _TrCan confirm according to the non-linear tire model of Dugoff;

For confirming F _TfAnd F _Tr, introduce longitudinal direction of car slip rate i _Sj(j=f, r), i _SjBe divided into front wheel spindle straight skidding rate i again _SfWith hind axle straight skidding rate i _Sr, subscript j gets f or r representes front or rear wheel shaft, i respectively in this method _SjMethod of calculating is:

and j=f; R (7)

In the formula (7), v _TfAnd v _TrThe speed of representing forward and backward wheel shaft upper edge tire direction respectively, v _TfAnd v _TrCan unify to be designated as v _Tj(j=f, r); ω _fThe spin velocity on the front wheel spindle is converted in the spin velocity equivalence of two wheels on the expression front wheel spindle; ω _rThe spin velocity on the hind axle, ω are converted in the equivalence of two wheel revolutions cireular frequencys on the expression hind axle _fAnd ω _rCan unify to be designated as ω _j(j=f, r) and

${\mathrm{\&omega;}}_f=\frac{1}{2}({\mathrm{\&omega;}}_{\mathrm{fR}}+{\mathrm{\&omega;}}_{\mathrm{fL}})$

(8)

${\mathrm{\&omega;}}_r=\frac{1}{2}({\mathrm{\&omega;}}_{\mathrm{rR}}+{\mathrm{\&omega;}}_{\mathrm{rL}})$

In the formula (8), ω _FL, ω _FR, ω _RLAnd ω _RRThe spin velocity of representing the near front wheel, off front wheel, left rear wheel and off hind wheel respectively obtains through utilizing four wheel speed sensors to measure;

v _Tj(j=f, r) can confirm by formula (9):

v _tf＝v _xcosδ _f+(v _y+aω _z)sinδ _f

(9)

v _tr＝v _x

And then, longitudinal force of tire F _TfAnd F _TrBut through type (10) is confirmed

$F_{\mathrm{tj}}=\frac{C_{\mathrm{tj}}{i}_{\mathrm{sj}}}{1-i_{\mathrm{sj}}}{f}_t\left(p_j\right)$ (j＝f，r) (10)

In the formula (10), C _TfAnd C _TrThe longitudinal rigidity of representing single forward and backward tire respectively, the unified C that is designated as _Tj(j=f, r); Variable p _j(j=f, r) and function f _t(p _j) (j=f, r) confirm by following formula:

$p_j=\frac{{\mathrm{\&mu;F}}_{\mathrm{zj}}(1-{\mathrm{\&epsiv;}}_r{v}_x\sqrt{{i_{\mathrm{sj}}}^2+{\tan }^2{\mathrm{\&alpha;}}_j})(1-i_{\mathrm{sj}})}{2\sqrt{{C_{\mathrm{tj}}}^2{i_{\mathrm{sj}}}^2+{C_{\mathrm{\&alpha;j}}}^2{\tan }^2{\mathrm{\&alpha;}}_j}}$ (j＝f，r) (11)

$f_t\left(p_j\right)=\left\{\begin{array}{cc}{p}_j(2-p_j)& p_j<1\\ 1& p_j\&GreaterEqual;1\end{array}\right.$ (j＝f，r) (12)

In formula (11) and (12), μ representes the vertical friction coefficient between tire and ground; ε _rThe expression road adheres to decay factor; α _f, α _rThe sideslip angle of representing forward and backward tire respectively, the unified α that is designated as _j(j=f r), can be calculated as follows

${\mathrm{\&alpha;}}_f={\mathrm{\&delta;}}_f-\frac{v_y+{\mathrm{a\&omega;}}_z}{v_x},$ ${\mathrm{\&alpha;}}_r=\frac{{\mathrm{b\&omega;}}_z-v_y}{v_x}---\left(13\right)$

And F _Zj(j=f, r) expression is assigned to the vertical load on the front or rear wheel shaft and can be calculated as follows

$F_{\mathrm{zf}}=\frac{\mathrm{mgb}}{2(a+b)},$ $F_{\mathrm{zr}}=\frac{\mathrm{mga}}{2(a+b)}---\left(14\right)$

In the formula (14), g representes acceleration due to gravity;

For each gain of sliding mode observer in the formula (3), design definitely according to the convergence stability principle of observer, particularly can confirm gain l according to following formula ₁, k ₁, l ₂, k ₂, τ ₁And τ ₂,

$l_1>\frac{{\&PartialD;f}_1}{\&PartialD;x_1},$ $k_1>\left|\frac{{\&PartialD;f}_1}{{\&PartialD;x}_2}{s}_2\right|+\left|\frac{{\&PartialD;f}_1}{{\&PartialD;x}_3}{\tilde{x}}_3\right|+{\mathrm{\&eta;}}_1---\left(15\right)$

$l_2>\frac{{\&PartialD;f}_2}{\&PartialD;x_2},$ $k_2>\left|\frac{{\&PartialD;f}_2}{{\&PartialD;x}_1}{s}_1\right|+\left|\frac{{\&PartialD;f}_2}{{\&PartialD;x}_3}{\tilde{x}}_3\right|+{\mathrm{\&eta;}}_2---\left(16\right)$

τ ₁＝τ ₂＝0 (17)

In formula (15) and the formula (16), (j=1,2,3) representative function f ₁For x _jThe partial derivative of (j=1,2,3),

(j=1,2,3) representative function f ₂For x _jThe partial derivative of (j=1,2,3), η _j(j=1,2) are given positive number, ${\tilde{x}}_3=x_3-{\hat{x}}_3;$

In the actual recursion, sgn (.) function that occurs in the formula (3) is with following sgn _Eq(.) function replaces:

sgn _eq(s _j)＝tanh(λs _j)(j＝1，2) (18)。

3. the travel condition of vehicle non linear robust method of estimation based on sliding mode observer according to claim 1, the representative value of the cycle T that it is characterized in that dispersing is taken as 10 milliseconds, 20 milliseconds or 50 milliseconds.

Images