CN103303367B - Vehicle body stability control method for four-wheel drive electric vehicle - Google Patents

Abstract

The invention provides a vehicle body stability control method for a four-wheel drive electric vehicle. The method comprises the steps of establishing a reference model, obtaining expected yaw velocity rm, subtracting the practical yaw velocity rp of the four-wheel drive electric vehicle from the expected yaw velocity rm to obtain an error e1, finally calculating and controlling controlling quantity u(t) according to the error e1 and a front wheel steering angle delta, inputting the controlling quantity u(t) to a practical four-wheel drive electric vehicle control system, continuously adjusting torques of inside wheels and outside wheels to generate a torque difference, namely an additional yaw moment, correcting understeering and oversteering of the vehicle, and allowing the vehicle to run according to an expected track. The vehicle body stability is improved effectively.

Description

A kind of Vehicle body stability control method for four-wheel drive electric vehicle

Technical field

The invention belongs to control technology for electric motor car field, more specifically say, relate to a kind of four-wheel driving electric vehicle vehicle body stable control method, namely when four-wheeled electric vehicle runs, the problem how yaw velocity controlled.

Background technology

Vehicle body stability control technology is the technology of road-holding property for vehicle, active safety aspect.If run into emergency case in high vehicle speeds process, such as need suddenly to beat direction, emergency braking, acceleration situation or the attachment condition between tire and road surface to undergo mutation, keep the stability of vehicle movement and the good handling life security being sometimes related to chaufeur and occupant.For the vehicle not being equipped with the chassis control technology such as vehicle body stability, driver just needs complete self-dependent experience to process emergency case with reaction, and this proposes very high requirement to the adaptability to changes of driver.Therefore in order to improve vehicle active safety, need a kind of vehicle body stability control techniques to improve the handling and stability of vehicle under limiting condition.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, a kind of four-wheel driving electric vehicle vehicle body stable control method is provided, for the full-vehicle control of four-wheeled electric vehicle, ensure that vehicle body is stablized.

For realizing above object, four-wheel driving electric vehicle vehicle body stable control method of the present invention, is characterized in that, comprise the following steps:

(1), reference model is set up

Laplace transform is done to the two degrees of freedom differential equation, obtains four-wheel driving electric vehicle front wheel steering angle δ to expectation yaw velocity r _mtransfer function be reference model:

$W_m\left(s\right)=\frac{r_m\left(s\right)}{\mathrm{\δ}\left(s\right)}=\frac{l_f\mathrm{mV}{k}_{1}s+(l_f+l_r)k_1{k}_2}{\mathrm{mV}{I}_z{s}^2+\left[m\right(l_f^2{k}_1+l_r^2{k}_2)+I_z(k_1+k_2)]s+\frac{{(l_f+l_r)}^2}{V}{k}_1{k}_2-\mathrm{mV}(l_f{k}_1-l_r{k}_2)}$

Wherein: δ (s) is the Laplace transform of front wheel steering angle δ, r _ms (), for expecting the Laplace transform of yaw velocity, s is variable, and m is the quality of car load, V is that vehicle travels absolute velocitye, I _zfor automobile is around the rotor inertia of z-axis, Δ M is the additional yaw moment be applied on automobile, k ₁, k ₂be respectively and do not consider front wheel side drift angle a _ffront-wheel cornering stiffness and do not consider rear wheel-side drift angle a _rtrailing wheel cornering stiffness, l _f, l _rbe respectively the wheelbase of front and back wheel;

(2), by front wheel steering angle δ be input to reference model, obtain expecting yaw velocity r _m, then will expect yaw velocity r _mdeduct the actual yaw velocity r of four-wheel driving electric vehicle _p, obtain error e ₁;

(3), according to error e ₁and front wheel steering angle δ calculates control controlling quantity u (t):

u(t)=k ₀(t)δ(t)+c ₁(t)v ₁(t)+d ₀(t)r _p(t)+d ₁(t)v ₂(t)

Wherein, δ (t) is the time-domain expression of front wheel steering angle δ, r _pt () is actual yaw velocity r _ptime-domain expression, t is the time, v ₁(t)=v ₂(t)=l _fδ (t), and:

$k_0\left(t\right)=-{\∫}_0^t\mathrm{\δ}\left(\mathrm{\τ}\right)e_1\left(\mathrm{\τ}\right)\mathrm{d\τ}+{\stackrel{\‾}{k}}_0$

$c_1\left(t\right)=-{\∫}_0^t{v}_1\left(\mathrm{\τ}\right)e_1\left(\mathrm{\τ}\right)\mathrm{d\τ}+{\stackrel{\‾}{c}}_1$

$d_0\left(t\right)=-{\∫}_0^t{r}_p\left(\mathrm{\τ}\right)e_1\left(\mathrm{\τ}\right)\mathrm{d\τ}+{\stackrel{\‾}{d}}_0$

$d_1\left(t\right)=-{\∫}_0^t{v}_2\left(\mathrm{\τ}\right)e_1\left(\mathrm{\τ}\right)\mathrm{d\τ}+{\stackrel{\‾}{d}}_1$

E ₁(τ) be error e ₁time-domain expression, and:

${\stackrel{\‾}{k}}_0=\frac{k_1}{k_1\left(a_f\right)}$

${\stackrel{\‾}{c}}_1=\frac{(l_f+l_r)k_2\left(a_r\right)}{l_f\mathrm{mV}}-\frac{(l_f+l_r)k_2}{l_f\mathrm{mV}}$

${\stackrel{\‾}{d}}_0=\frac{\frac{{l_f}^2(k_1-k_1\left(a_f\right))+{l_r}^2(k_2-k_2\left(a_f\right))}{V}+\frac{[(k_1-k_1\left(a_f\right))+(k_2-k_2\left(a_f\right))]I_z}{\mathrm{mV}}}{l_f{k}_1\left(a_f\right)}$

$\begin{array}{c}{\stackrel{\‾}{d}}_1=[\frac{{(l_r+l_f)}^2}{m{V}^2{I}_z}(k_1{k}_2-k_1\left(a_f\right)k_2\left(a_r\right))-\frac{l_f(k_1-k_1\left(a_f\right))-l_r(k_2-k_2\left(a_r\right))}{I_z}\\ -\frac{{l_f}^2(k_1-k_1\left(a_f\right))-{l_r}^2(k_2-k_2\left(a_r\right))}{V}-\frac{(k_1-k_1\left(a_f\right))+(k_2-k_2\left(a_f\right))}{\mathrm{mV}}]\·\frac{I_z}{l_f{k}_1\left(a_f\right)}\end{array}$

K ₁(a _f) represent and consider front wheel side drift angle a _fafter front-wheel cornering stiffness, k ₂(a _r) represent and consider front wheel side drift angle, rear wheel-side drift angle a _rtrailing wheel cornering stiffness;

(4), controlling quantity u (t) is input to actual four-wheel driving electric vehicle control system, by constantly adjusting nearside wheel and off-side wheel torque, produce torque differences i.e. additional yaw moment, correct understeering and the oversteer of automobile, make its desirably track traveling, effectively improve vehicle body stability.

The object of the present invention is achieved like this:

Four-wheel driving electric vehicle vehicle body stable control method of the present invention, by setting up reference model, then obtains expecting yaw velocity r _m, then yaw velocity r will be expected _mdeduct the actual yaw velocity r of four-wheel driving electric vehicle _pobtain error e ₁; Last according to error e ₁and front wheel steering angle δ calculating control controlling quantity u (t) controlling quantity u (t) is input to actual four-wheel driving electric vehicle control system, by constantly adjusting nearside wheel and off-side wheel torque, produce torque differences i.e. additional yaw moment, correct understeering and the oversteer of automobile, make its desirably track traveling, effectively improve vehicle body stability.

Accompanying drawing explanation

Fig. 1 is four-wheel driving electric vehicle vehicle body stable control method schematic diagram of the present invention;

Fig. 2 is that the vehicle body of four-wheel driving electric vehicle shown in Fig. 1 stable control method specifically implements constructional drawing;

Fig. 3 is four-wheel driving electric vehicle driving trace figure;

Fig. 4 is the front wheel steering angle diagram of curves of four-wheel driving electric vehicle;

Fig. 5 is the yaw velocity diagram of curves of four-wheel driving electric vehicle;

Fig. 6 is the side slip angle diagram of curves of four-wheel driving electric vehicle.

Detailed description of the invention

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described, so that those skilled in the art understands the present invention better.Requiring particular attention is that, in the following description, when perhaps the detailed description of known function and design can desalinate main contents of the present invention, these are described in and will be left in the basket here.

In classical automobile operation kinetic theory, linear two-freedom model is used to study vehicle handling stability.Set up automobile linear two-freedom model, make the following assumptions:

1. the impact of steering swivel system is ignored, directly using front wheel angle as input;

2. ignore the effect of suspension, namely automobile is along the displacement of z-axis (vertical direction), and the pitch angle around y-axis (side direction) is zero with the angle of roll around x-axis (longitudinal direction);

3. and suppose that automobile is considered as constant along the speed of advance of x-axis, automobile only has sideway movement and weaving;

4. automobile side angle acceleration/accel is limited to 0.4g(g and represents acceleration due to gravity) below, in model, side force of tire is directly proportional to sideslip angle;

5. have ignored the impact of ground tangential force on tire cornering characteristics;

6. aerodynamic effect is ignored;

7. ignore left and right wheel tyre and cause the change of tire characteristics and the effect of tyre moment due to the change of load.

By Newton's second law and four-wheel driven electric vehicle structure, setting up the binary differential equation is:

$-(k_1+k_2)\mathrm{\β}-\frac{1}{V}(l_f{k}_1-l_r{k}_2)r+k_1\mathrm{\δ}=\mathrm{mV}(\stackrel{\·}{\mathrm{\β}}+r)---\left(1\right)$

$-(l_f{k}_1-l_r{k}_2)\mathrm{\β}-\frac{1}{V}(l_f^2{k}_1+l_r^2{k}_2)r+l_f{k}_1\mathrm{\δ}+\mathrm{\ΔM}=I_z\stackrel{\·}{r}---\left(2\right)$

Wherein, m is the quality of car load, and V is that vehicle travels absolute velocitye, and β is vehicle centroid sideslip angle, for vehicle centroid yaw angle speed, δ is front wheel angle, and r is Vehicular yaw cireular frequency, for Vehicular yaw angular acceleration, I _zfor automobile is around the rotor inertia of z-axis, Δ M is the additional yaw moment be applied on automobile, k ₁, k ₂be respectively and do not consider front wheel side drift angle a _ffront-wheel cornering stiffness and do not consider rear wheel-side drift angle a _rtrailing wheel cornering stiffness, l _f, l _rbe respectively the wheelbase of front and back wheel.

The concrete steps of four-wheel driving electric vehicle vehicle body stable control method of the present invention are:

The first step, set up reference model

Do Laplace transform to equation (1) and (2), simultaneous is obtained the transfer function of front wheel of electric motorcar deflection angle to yaw velocity and is reference model, as follows:

$W_m\left(s\right)=\frac{r_m\left(s\right)}{\mathrm{\δ}\left(s\right)}=\frac{l_f\mathrm{mV}{k}_{1}s+(l_f+l_r)k_1{k}_2}{\mathrm{mV}{I}_Z{s}^2+\left[m\right(l_f^2{k}_1+l_r^2{k}_2)+I_Z(k_1+k_2)]s+\frac{{(l_f+l_r)}^2}{V}{k}_1{k}_2-\mathrm{mV}(l_f{k}_1-l_r{k}_2)}---\left(3\right)$

Wherein: δ (s) is the Laplace transform of front wheel steering angle δ, r _ms (), for expecting the Laplace transform of yaw velocity, s is variable.

Second step, front wheel steering angle δ is input to reference model, obtains expecting yaw velocity r _m, then will expect yaw velocity r _mdeduct the actual yaw velocity r of four-wheel driving electric vehicle _p, obtain error e ₁;

3rd step, design adaptive control laws are namely according to error e ₁and front wheel steering angle δ calculates control controlling quantity u (t).

Because automobile is in actual travel, due to the change of surface friction coefficient, automotive pitch motion and lateral deviation etc. all can cause the change of vehicle condition parameter, consider sideway movement and the weaving of automobile, therefore the cornering stiffness of tire is no longer a constant value in the model, but slowly change along with the change of the sideslip angle of wheel, the differential equation of the side direction and cross motion that so obtain this model is:

$-(k_1\left(a_f\right)+k_2\left(a_r\right)){\mathrm{\β}}_p-\frac{1}{V}(l_f{k}_1\left(a_f\right)-l_r{k}_2\left(a_r\right))r_p+k_1\left(a_f\right)u=\mathrm{mV}({\stackrel{\·}{\mathrm{\β}}}_p+r_p)---\left(4\right)$

$-(l_f{k}_1\left(a_f\right)-l_r{k}_2\left(a_r\right)){\mathrm{\β}}_p-\frac{1}{V}{l_f}^2{k}_1\left(a_f\right)-{l_r}^2{k}_2\left(a_r\right)r_p+l_f{k}_1\left(a_f\right)u=I_z{\stackrel{\·}{r}}_p---\left(5\right)$

In formula, k ₁(a _f) represent that front-wheel cornering stiffness is the function of front wheel side drift angle, represent that trailing wheel cornering stiffness is the function of rear wheel-side drift angle, β _pfor actual vehicle side slip angle, r _pfor actual yaw velocity, in formula, symbol is added some points and represent the differential of this amount.

Carry out Laplace transform to formula (4) and (5), simultaneous obtains actual four-wheel driving electric vehicle front wheel steering angle and to the transfer function of yaw velocity is:

$W_p\left(s\right)=\frac{r_p\left(s\right)}{\mathrm{\δ}\left(s\right)}=\frac{l_f\mathrm{mV}{k}_1\left(a_f\right)s+(l_f+l_r)k_1\left(a_f\right)k_2\left(a_r\right)}{(\mathrm{mV}{I}_Z{s}^2+(m(l_f^2{k}_1\left(a_f\right)+l_r^2{k}_2\left(a_r\right))+I_Z(k_1\left(a_f\right)+k_2\left(a_r\right)))s}---\left(6\right)$

Wherein r _ps () represents the Laplace transform of actual yaw velocity.

The model reference self-adapting control chosen based on Narendra scheme is theoretical, and design yaw velocity controller, selects auxiliary signal generator F ₁and F ₂it is all the stable dynamic system of single order.By the differential equation of controlled vehicle, obtaining its state-space expression is:

$\begin{array}{c}{\stackrel{\·}{x}}_p=A_p{x}_p+b_{p}u\\ y_p=h^T{x}_p\end{array}---\left(7\right)$

Obtain x _p=[β _pr _p] ^t, h ^t=[0 1] ^t.

$A_p\left(\begin{array}{cc}-\frac{k_1\left(a_f\right)+k_2\left(a_r\right)}{\mathrm{mV}}& -1-\frac{k_1\left(a_f\right)l_f-k_2\left(a_r\right)l_r}{m{V}^2}\\ -\frac{k_1\left(a_f\right)l_f-k_2\left(a_r\right)l_r}{I_z}& -\frac{k_1\left(a_f\right){l_f}^2-k_2\left(a_r\right){l_r}^2}{I_{z}V}\end{array}\right)=\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right);$

$b_p=\left[\begin{array}{c}\frac{k_1\left(a_f\right)}{\mathrm{mV}}\\ \frac{k_1\left(a_f\right)l_f}{I_z}\end{array}\right]=\left[\begin{array}{c}{b}_{11}\\ b_{21}\end{array}\right]---\left(8\right)$

Order:

ω ^T=[δ v ₁y _pv ₂] （9）

In formula, ω is 4 dimensional vectors.If θ ^trepresent adjustable parametric vector, that is:

θ ^T=[k ₀c ₁d ₀d ₁] （10）

Wherein, θ ^tbe 4 dimensional vectors, so being comprehensively input as of controlled vehicle:

u=θ ^Tω （11）

Whole adjustable system can be expressed as follows with equation of state below:

$\left[\begin{array}{c}{\stackrel{\·}{\mathrm{\β}}}_p\\ {\stackrel{\·}{r}}_p\\ {\stackrel{\·}{v}}_1\\ {\stackrel{\·}{v}}_2\end{array}\right]=\left[\begin{array}{cccc}{a}_{11}& a_{12}& 0& 0\\ a_{21}& a_{22}& 0& 0\\ 0& 0& l& 0\\ 0& 1& 0& l\end{array}\right]\left[\begin{array}{c}{\mathrm{\β}}_p\\ r_p\\ v_1\\ v_2\end{array}\right]+\left[\begin{array}{c}{b}_{11}\\ b_{21}\\ 1\\ 0\end{array}\right]u---\left(12\right)$

y _p=r _p（13）

If:

$\mathrm{\θ}=\stackrel{\‾}{\mathrm{\θ}}+\mathrm{\ψ}---\left(14\right)$

In formula, represent parameter when mating completely, ψ represents parameter during mismatch.If adjustable system and reference model completely the same, then ψ=0, $k_0={\stackrel{\‾}{k}}_0,c_1={\stackrel{\‾}{c}}_1,d_0={\stackrel{\‾}{d}}_0,d_1={\stackrel{\‾}{d}}_1.$ U can be write as:

$u={\mathrm{\θ}}^T\mathrm{\ω}={[\stackrel{\‾}{\mathrm{\θ}}+\mathrm{\ψ}]}^T\mathrm{\ω}={\stackrel{\‾}{k}}_0\mathrm{\δ}+{\stackrel{\‾}{c}}_1^T{v}_1+{\stackrel{\‾}{d}}_0^T{r}_p+{\stackrel{\‾}{d}}_1^T{v}_2+{\mathrm{\ψ}}^T\mathrm{\ω}---\left(15\right)$

(12) being brought into (9) will as input, obtaining augmented state equation after arrangement is:

$\left[\begin{array}{c}{\stackrel{\·}{\mathrm{\β}}}_p\\ {\stackrel{\·}{r}}_p\\ {\stackrel{\·}{v}}_1\\ {\stackrel{\·}{v}}_2\end{array}\right]=\left[\begin{array}{cccc}{a}_{11}& a_{12}+{\stackrel{\‾}{d}}_0{b}_{11}& b_{11}{\stackrel{\‾}{c}}_1& b_{11}{\stackrel{\‾}{d}}_1\\ a_{21}& a_{22}+{\stackrel{\‾}{d}}_0{b}_{21}& b_{21}{\stackrel{\‾}{c}}_1& b_{21}{\stackrel{\‾}{d}}_1\\ 0& {\stackrel{\‾}{d}}_0& {\stackrel{\‾}{c}}_1+l& {\stackrel{\‾}{d}}_1\\ 0& 1& 0& l\end{array}\right]\left[\begin{array}{c}{\mathrm{\β}}_p\\ r_p\\ v_1\\ v_2\end{array}\right]+\left[\begin{array}{c}{b}_{11}\\ b_{21}\\ 1\\ 0\end{array}\right]({\stackrel{\‾}{k}}_0\mathrm{\δ}+{\mathrm{\ψ}}^T\mathrm{\ω})---\left(16\right)$

Order:

x ^T＝[β _pr _pv ₁v]

$A_c=\left[\begin{array}{cccc}{a}_{11}& a_{12}+{\stackrel{\‾}{d}}_0{b}_{11}& b_{11}{\stackrel{\‾}{c}}_1& b_{11}{\stackrel{\‾}{d}}_1\\ a_{21}& a_{22}+{\stackrel{\‾}{d}}_0{b}_{21}& b_{21}{\stackrel{\‾}{c}}_1& b_{21}{\stackrel{\‾}{d}}_1\\ 0& {\stackrel{\‾}{d}}_0& {\stackrel{\‾}{c}}_1+l& {\stackrel{\‾}{d}}_1\\ 0& 1& 0& l\end{array}\right]$

${b_c}^T={\left[\begin{array}{c}{b}_{11}\\ b_{21}\\ 1\\ 0\end{array}\right]}^T$

That is:

$\stackrel{\·}{x}=A_{c}x+b_c[{\stackrel{\‾}{k}}_{0}r+{\mathrm{\ψ}}^T\mathrm{\ω}]---\left(17\right)$

Because adjustable system during ψ=0 and reference model match, so make ψ=0 in (16), the augmented state equation of reference model can be obtained.If x _mcrepresent augmented state vector, that is:

x _mc ^T=[β _mr _mv _m1v _m2] （18）

Because x is 4 dimensional vectors, so x _mcalso be 4 dimensional vectors.The augmented state equation of reference model can be write as:

${\stackrel{\·}{x}}_{\mathrm{mc}}=A_c{x}_{\mathrm{mc}}+b_c{\stackrel{\‾}{k}}_0\mathrm{\δ}---\left(19\right)$

y _m=r _m（20）

The transfer function of reference model is:

W _m(s)=h _c ^T(sI _z-A _c) ^-1b _ck ₀（21）

Parameter due to controlled automobile is unavailable, (17) and (19) can be utilized to shift augmented state error equation onto, that is:

$\stackrel{\·}{e}=A_{c}e+b_c{\mathrm{\ψ}}^T\mathrm{\ω}---\left(22\right)$

In formula:

$e=x-x_{\mathrm{mc}}=\left[\begin{array}{c}{\mathrm{\β}}_p-{\mathrm{\β}}_m\\ r_p-r_m\\ v_1-v_{m1}\\ v_2-v_{m2}\end{array}\right]---\left(23\right)$

If controlled object and reference model output error are e ₁, then have:

$e_1=y_p-y_m=r_p-r_m={h_c}^{T}e---\left(24\right)$

So h _c ^t[0 10 0].

The input and output that can obtain error model are thus respectively ψ ^tω, e ₁, then the transfer function of error model is:

$W_e\left(s\right)={h_c}^T{(s{l}_z-A_c)}^{-1}{b}_c---\left(25\right)$

Simultaneous (21) and (25) can obtain:

$W_m\left(s\right)=W_e\left(s\right){\stackrel{\‾}{k}}_0=W_e\left(s\right)\frac{k_m}{k_p}---\left(26\right)$ $W_e\left(s\right)=\frac{k_p}{k_m}{W}_m\left(s\right)---\left(27\right)$

Therefore have:

$e_1=\frac{k_p}{k_m}{W}_m\left(s\right){\mathrm{\ψ}}^T\mathrm{\ω}---\left(28\right)$

In state matrix due to error model e, containing unknown number, therefore adaptive law can not be formed with e, but ω and e in error model ₁directly can obtain, can be used for forming adaptive law.

Choosing liapunov function is:

$V=\frac{1}{2}(e^T\mathrm{Pe}+{\mathrm{\ψ}}^T{\mathrm{\Γ}}^{-1}\mathrm{\ψ})---\left(29\right)$

In formula, P and Γ is positive definite symmetric matrices.Ask the derivative of the time of V, and consider ψ ^tω=ω ^tψ, can obtain:

$\begin{array}{c}\stackrel{\·}{V}=\frac{1}{2}{e}^T(P{A}_c+{A_c}^{T}p)e+{\mathrm{\ψ}}^T\mathrm{\ω}{b_c}^T\mathrm{Pe}+{\mathrm{\ψ}}^T{\mathrm{\Γ}}^{-1}\mathrm{\ψ}\\ =\frac{1}{2}{e}^T(P{A}_c+{A_c}^{T}p)e+{\mathrm{\ψ}}^T(\mathrm{\ω}{b_c}^T\mathrm{Pe}+{\mathrm{\Γ}}^{-1}\stackrel{\·}{\mathrm{\ψ}})\end{array}---\left(30\right)$

According to positive real lemma, and by formula (30), system transter molecule exponent number is herein less than denominator by 1, and the molecule of the transfer function of reference model and denominator are all Stable Polynomials, just necessarily there is positive definite symmetric matrices P and Q(positive definite matrix) meet:

$\begin{array}{c}{\mathrm{\ψ}}^T\mathrm{\ω}{b_c}^T\mathrm{Pe}+{\mathrm{\ψ}}^T{\mathrm{\Γ}}^{-1}\stackrel{\·}{\mathrm{\ψ}}=0\\ \stackrel{\·}{V}=\frac{1}{2}{e}^T(P{A}_c+{A_c}^{T}p)e=\frac{1}{2}{e}^T(-Q)e\end{array}---\left(31\right)$

So adaptive law can be write as:

$\stackrel{\·}{\mathrm{\θ}}=\stackrel{\·}{\mathrm{\ψ}}=-\mathrm{\Γ\ω}{e}_1---\left(32\right)$

$\mathrm{\θ}\left(t\right)=-{\∫}_0^t\mathrm{\Γ\ω}\left(\mathrm{\τ}\right)e_1\left(\mathrm{\τ}\right)\mathrm{d\τ}+\mathrm{\θ}\left(0\right)---\left(33\right)$

So in formula (31), make Γ be unit matrix, self adaptation device can be obtained as follows:

u(t)=k ₀(t)δ(t)+c ₁(t)v ₁(t)+d ₀(t)y _p(t)+d ₁(t)v ₂(t)

Due to y _p(t)=r _p(t), so: (34)

u(t)=k ₀(t)δ(t)+c ₁(t)v ₁(t)+d ₀(t)r _p(t)+d ₁(t)v ₂(t)

Wherein, δ (t) is front wheel angle, y _pt () is actual yaw velocity r for namely controlled object exports _p(t).

$\begin{array}{c}{k}_0\left(t\right)=-{\∫}_0^t\mathrm{\δ}\left(\mathrm{\τ}\right)e_1\left(\mathrm{\τ}\right)\mathrm{d\τ}+{\stackrel{\‾}{k}}_0\\ c_1\left(t\right)=-{\∫}_0^t{v}_1\left(\mathrm{\τ}\right)e_1\left(\mathrm{\τ}\right)\mathrm{d\τ}+{\stackrel{\‾}{c}}_1\\ d_0\left(t\right)=-{\∫}_0^t{r}_p\left(\mathrm{\τ}\right)e_1\left(\mathrm{\τ}\right)\mathrm{d\τ}+{\stackrel{\‾}{d}}_0\\ d_1\left(t\right)=-{\∫}_0^t{v}_2\left(\mathrm{\τ}\right)e_1\left(\mathrm{\τ}\right)\mathrm{d\τ}+{\stackrel{\‾}{d}}_1\end{array}---\left(35\right)$

E ₁(τ) be error e ₁time-domain expression, and:

${\stackrel{\‾}{k}}_0=\frac{k_1}{k_1\left(a_f\right)}$

${\stackrel{\‾}{c}}_1=\frac{(l_f+l_r)k_2\left(a_r\right)}{l_f\mathrm{mV}}-\frac{(l_f+l_r)k_2}{l_f\mathrm{mV}}$

${\stackrel{\‾}{d}}_0=\frac{\frac{{l_f}^2(k_1-k_1\left(a_f\right))+{l_r}^2(k_2-k_2\left(a_f\right))}{V}+\frac{[(k_1-k_1\left(a_f\right))+(k_2-k_2\left(a_f\right))]I_z}{\mathrm{mV}}}{l_f{k}_1\left(a_f\right)}$

$\begin{array}{c}{\stackrel{\‾}{d}}_1=[\frac{{(l_r+l_f)}^2}{m{V}^2{I}_z}(k_1{k}_2-k_1\left(a_f\right)k_2\left(a_r\right))-\frac{l_f(k_1-k_1\left(a_f\right))-l_r(k_2-k_2\left(a_r\right))}{I_z}\\ -\frac{{l_f}^2(k_1-k_1\left(a_f\right))-{l_r}^2(k_2-k_2\left(a_r\right))}{V}-\frac{(k_1-k_1\left(a_f\right))+(k_2-k_2\left(a_f\right))}{\mathrm{mV}}]\·\frac{I_z}{l_f{k}_1\left(a_f\right)}\end{array}$

K ₁(a _f) represent and consider front wheel side drift angle a _fafter front-wheel cornering stiffness, k ₂(a _r) represent and consider front wheel side drift angle, rear wheel-side drift angle a _rtrailing wheel cornering stiffness;

Controlling quantity u (t) is input to actual four-wheel driving electric vehicle control system, by constantly adjusting nearside wheel and off-side wheel torque, produce torque differences i.e. additional yaw moment, correct understeering and the oversteer of automobile, make its desirably track traveling, effectively improve vehicle body stability.

Example

For total mass 1296kg, around Z axis rotor inertia 1750kgm ², wheelbase 2.57m, barycenter is to the distance 1.25m of front axle, and barycenter is to the distance 1.32m of rear axle, track front 1.405m, track rear 1.399m, and height of center of mass 0.45m, the four-wheel driven electric vehicle of radius of wheel 0.326m is verified.The speed of a motor vehicle is increased to 70km/h by 0km/h, walks around 7 obstacles in 8 ~ 25s simultaneously, and simulation serpentine locomotion operating mode, surface friction coefficient is set to u=0.7, and this surface friction coefficient is the normal friction coefficient of dry asphalt surface.

Shown in Fig. 1, system is made up of chaufeur, reference model, controlled object (four-wheel driving electric vehicle model) and controller.First chaufeur input operation signal, the automobile being calculated chaufeur expectation by vehicle reference model exports yaw velocity, compared with the yaw velocity of the output of actual controlled object.Because the output of controlled vehicle and the output of expectational model exist deviation, by this deviation input adaptive controller, the adaptive control law designed by the present invention, exports the controlling quantity of actual electric vehicle system.Finally controlled volume is added controlled object, the ideal realizing the response output tracking reference model of controlled object exports.

Fig. 2 is the basic controlling block diagram in the model reference self-adapting control theory of Narendra scheme, and system is input as steering wheel angle δ (t), and reference model exports the yaw velocity r for expecting _mt (), controlling quantity is u (t), exports the yaw velocity r into actual electrical motor-car _pt (), has two subcontrol F in controller ₁and F ₂, F ₁be connected on the input end of controlled object, be input as u (t), export as W ₁, have 1 adjustable parameter c ₁.F ₂be connected on the mouth of controlled object, be input as r _pt (), exports as W ₂, have 1 adjustable parameter d ₁.F ₁and F ₂output W ₁and W ₂, add that adjustable gain exports k ₀δ (t), constitutes comprehensive input u (t) of controlled object, controls the output r of controlled object _pt (), makes itself and reference model export r _mt () is identical.

Fig. 3 and Fig. 4 can find out, have the automobile of control to complete around stake, and uncontrolled automobile can not complete around stake, driving trace departs from desired trajectory completely.In uncontrolled situation, the front wheel steering angle of automobile reaches steering lock, illustrates that chaufeur makes automobile return to desired trajectory by hitting bearing circle, but now automobile, beyond the steering range of chaufeur, cannot return to desired trajectory and travel.As can be seen from four wheel driving torque figure, in automobile turning process, by constantly adjusting nearside wheel and off-side wheel torque, producing torque differences, i.e. additional yaw moment, correcting understeering and the oversteer of automobile, make its desirably track traveling.Although there is certain deviation between the actual travel track of automobile and desired trajectory, this control system appoints that so to ensure that automobile has good in stake carrying capacity.

Can be found from Fig. 5 and Fig. 6 by contrast automobile yaw velocity and side slip angle, the vehicle having control has significantly been exceeded without the yaw velocity and side slip angle that control vehicle, this is because Driver Steering Attention amplitude is more caused by fierceness on the one hand, on the other hand, by following the tracks of yaw velocity expectation value and the side slip angle expectation value of the output of desired reference model, have and control the yaw velocity of vehicle and obtain good control, improve automobile hit bearing circle continuously under vehicle body stability.

This shows, under snakelike operating mode, have the automobile of control to cross in the ability of curved and tracking at continuous high speed and be all greatly improved, and ensure that turning ability and the stability of automobile very well

Although be described the illustrative detailed description of the invention of the present invention above; so that those skilled in the art understand the present invention; but should be clear; the invention is not restricted to the scope of detailed description of the invention; to those skilled in the art; as long as various change to limit and in the spirit and scope of the present invention determined, these changes are apparent, and all innovation and creation utilizing the present invention to conceive are all at the row of protection in appended claim.

Claims (1)

1. a four-wheel driving electric vehicle vehicle body stable control method, is characterized in that, comprises the following steps:

(1), reference model

Laplace transform is done to the two degrees of freedom differential equation, obtains four-wheel driving electric vehicle front wheel steering angle δ to expectation yaw velocity r _mtransfer function be reference model:

$W_m\left(s\right)=\frac{r_m\left(s\right)}{\mathrm{\δ}\left(s\right)}=\frac{l_f\mathrm{mV}{k}_{1}s+(l_f+l_r)k_1{k}_2}{\mathrm{mV}{I}_Z{s}^2+[m(l_f^2{k}_1+l_r^2{k}_2)+I_Z(k_1+k_2)]s+\frac{{(l_f+l_r)}^2}{V}{k}_1{k}_2-\mathrm{mV}(l_f{k}_1-l_r{k}_2)}$

Wherein: δ (s) is the Laplace transform of front wheel steering angle δ, r _ms (), for expecting the Laplace transform of yaw velocity, s is variable, and m is the quality of car load, V is that vehicle travels absolute velocitye, I _zfor automobile is around the rotor inertia of z-axis, k ₁, k ₂be respectively and do not consider front wheel side drift angle a _ffront-wheel cornering stiffness and do not consider rear wheel-side drift angle a _rtrailing wheel cornering stiffness, l _f, l _rbe respectively the wheelbase of front and back wheel;

(2), by front wheel steering angle δ be input to reference model, obtain expecting yaw velocity r _m, then will expect yaw velocity r _mdeduct the actual yaw velocity r of four-wheel driving electric vehicle _p, obtain error e ₁;

(3), according to error e ₁and front wheel steering angle δ calculates control controlling quantity u (t):

u(t)＝k ₀(t)δ(t)+c ₁(t)v ₁(t)+d ₀(t)r _p(t)+d ₁(t)v ₂(t)

Wherein, δ (t) is the time-domain expression of front wheel steering angle δ, r _pt () is actual yaw velocity r _ptime-domain expression, t is the time, v ₁(t)=v ₂(t)=l _fδ (t), and:

$k_0\left(t\right)=-{\∫}_0^t\mathrm{\δ}\left(\mathrm{\τ}\right)e_1\left(\mathrm{\τ}\right)\mathrm{d\τ}+{\stackrel{\‾}{k}}_0$

$c_1\left(t\right)=-{\∫}_0^t{v}_1\left(\mathrm{\τ}\right)e_1\left(\mathrm{\τ}\right)\mathrm{d\τ}+{\stackrel{\‾}{c}}_1$

$d_0\left(t\right)=-{\∫}_0^t{r}_p\left(\mathrm{\τ}\right)e_1\left(\mathrm{\τ}\right)\mathrm{d\τ}+{\stackrel{\‾}{d}}_0$

$d_1\left(t\right)=-{\∫}_0^t{v}_2\left(\mathrm{\τ}\right)e_1\left(\mathrm{\τ}\right)\mathrm{d\τ}+{\stackrel{\‾}{d}}_1$

E ₁(τ) be error e ₁time-domain expression, and:

${\stackrel{\‾}{k}}_0=\frac{k_1}{k_1\left(a_f\right)}$

${\stackrel{\‾}{c}}_1=\frac{(l_f+l_r)k_2\left(a_r\right)}{l_f\mathrm{mV}}-\frac{(l_f+l_r)k_2}{l_f\mathrm{mV}}$

${\stackrel{\‾}{d}}_0=\frac{\frac{{l_f}^2(k_1-k_1\left(a_f\right))+{l_r}^2(k_2-k_2\left(a_f\right))}{V}+\frac{[(k_1-k_1\left(a_f\right))+(k_2-k_2\left(a_f\right))]I_z}{\mathrm{mV}}}{l_f{k}_1\left(a_f\right)}$

$\begin{array}{c}{\stackrel{\‾}{d}}_1=[\frac{{(l_r+l_f)}^2}{m{V}^2{I}_z}(k_1{k}_2-k_1\left(a_f\right)k_2\left(a_r\right))-\frac{l_f(k_1-k_1\left(a_f\right))-l_r(k_2-k_2\left(a_r\right))}{I_z}\\ -\frac{{l_f}^2(k_1-k_1\left(a_f\right))-{l_r}^2(k_2-k_2\left(a_r\right))}{V}-\frac{(k_1-k_1\left(a_f\right))+(k_2-k_2\left(a_f\right))}{\mathrm{mV}}]\·\frac{I_z}{l_f{k}_1\left(a_f\right)}\end{array}$

K ₁(a _f) represent and consider front wheel side drift angle a _fafter front-wheel cornering stiffness, k ₂(a _r) represent and consider front wheel side drift angle, rear wheel-side drift angle a _rtrailing wheel cornering stiffness;

(4), controlling quantity u (t) is input to actual four-wheel driving electric vehicle control system, by constantly adjusting nearside wheel and off-side wheel torque, produce torque differences i.e. additional yaw moment, correct understeering and the oversteer of automobile, make its desirably track traveling, effectively improve vehicle body stability.