CN113479189A - Electric automobile yaw stability control method based on self-adaptive reverse pushing controller - Google Patents

Abstract

The invention discloses an electric vehicle yaw stability control method based on an adaptive thrust reverser controller, comprising the following steps: constructing a lateral dynamics model of an electric vehicle; developing an adaptive thrust reverser controller based on a barrier Lyapunov function, It can be used as an upper-level controller to generate the desired additional yaw moment; an optimal torque distribution algorithm based on the minimum objective function is developed as a lower-level controller to distribute the additional yaw moment; the method of the present invention can finally realize an adaptive thrust reverser controller The design and torque distribution algorithm are of great significance to the yaw stability control of electric vehicles. It solves the problems of tire sideslip that may occur in electric vehicles under dangerous conditions, and effectively improves the maneuverability and driving safety of electric vehicles. .

Description

Yaw stability control method of electric vehicle based on adaptive thrust reverser controller

technical field

The invention belongs to the technical field of yaw stability control of electric vehicles, and particularly relates to a yaw stability control method of electric vehicles based on an adaptive thrust reverser controller.

Background technique

As a clean energy vehicle, electric vehicles have been booming in recent years, and their safety is a major concern, because when electric vehicles drive at high speeds on roads with low adhesion coefficients, traffic such as tire side slip will be more likely to occur. question.

In order to avoid such traffic accidents, more and more scholars have proposed a variety of control methods, such as anti-lock braking system and active front wheel steering system, in order to improve the handling stability and driving quality of electric vehicles. It should be noted that direct yaw moment control is one of the most effective ways to improve the stability of electric vehicles, and has a better ability to stabilize vehicle motion than control methods such as anti-lock braking systems and active front-wheel steering systems. A major problem with direct yaw moment control is how to calculate the ideal control moment.

Another problem with direct yaw moment control is how to generate torque for driving. The traditional centralized drive electric vehicle is similar to the drive structure of the internal combustion engine vehicle. The internal combustion engine is replaced by an electric motor and related components, and the torque output by the electric motor is transmitted to the wheels through a mechanical transmission device. Therefore, the traditional centralized drive electric vehicle has the disadvantages of large volume, heavy weight and low efficiency. The motor and reducer of the in-wheel motor distributed drive electric vehicle are installed in the wheel, the additional yaw moment we need is calculated by the control algorithm, and then directly distributed to the four in-wheel motors by the distribution algorithm, so it can be omitted. The drive system is simplified and the efficiency is improved. In addition, the in-wheel motor-driven electric vehicle also has the advantages of quick response, small volume and weight, flexible distribution and low cost. Therefore, more and more scholars have conducted research on in-wheel motor-driven electric vehicles.

It is worth noting that the vehicle's body mass and driving inertial moment may vary due to the number of passengers and payload, which are often determined as uncertain inertial parameters, which may degrade vehicle stability performance and affect vehicle stability. The design of the controller poses certain difficulties. In order to meet these challenges, in the past few decades, many scholars have chosen adaptive backlash control because of its advantages of anti-input saturation, higher tracking accuracy and better robustness to external disturbances. in the design of controllers for strictly output feedback systems with parameter uncertainties.

One of the difficulties in electric vehicle control is that when alleviating the lateral stability problem caused by vehicle steering, there are constraints that are difficult to satisfy, and it is required that the performance index should be limited to a certain range.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a yaw stability control method of an electric vehicle based on an adaptive thrust reverser controller, which can effectively improve the steering stability of the vehicle.

The technical scheme adopted by the present invention is that the yaw stability control method of electric vehicle based on the adaptive thrust reverser controller comprises the following steps:

Step 1. Build the lateral dynamics model of the electric vehicle;

Step 2, designing an adaptive thrust reverser controller based on the barrier Lyapunov function, and using the adaptive thrust reverser controller as an upper controller to generate the desired additional yaw moment;

Step 3: Design the optimal torque distribution algorithm based on the minimum objective function as the lower controller to distribute the desired additional yaw moment.

The electric vehicle lateral dynamics model includes the electric vehicle lateral dynamics equation, the rotational dynamics equation of the wheel, the lateral acceleration and the lateral acceleration.

The feature of the present invention also lies in:

The specific process of step 1 is:

According to Newton's second law, the lateral dynamics equation of an electric vehicle is:

In formula (1), m is the mass of the car body, I _z is the moment of inertia of the car body; F _yf is the lateral force of the front wheel, F _yr is the lateral force of the rear wheel; β and r are the center of mass slip angle and yaw, respectively. rate; l _f and l _r are the distances from the front and rear axles to the center of mass, respectively; M _z is the additional yaw moment; v is the vehicle speed;

Among them, F _yf and F _yr expressions are:

In formula (2), C _f is the cornering stiffness of the front wheel, C _r is the cornering stiffness of the rear wheel; α _f is the side slip angle of the front wheel, α _r is the side slip angle of the rear wheel; α _f and α _r are expressed as :

Substituting formulas (2) and (3) into (1), we get:

a₂＝2l_rC_r-2l_fC_f，

c₂＝2C_fl_f；in,

a ₂ =2l _r C _r -2l _f C _f ,

c ₂ =2C _f l _f ;

The rotational dynamics equation of the wheel is expressed as:

where R is the wheel rolling radius, w _ij is the wheel angular velocity, I _w is the wheel moment of inertia, and T _ij is the wheel torque;

The lateral acceleration a _x and the lateral acceleration a _y are respectively:

The specific process of step 2 is:

Choose ψ as the desired virtual control variable, and r as the actual control variable, if r=ψ is satisfied, the error e ₁ =β-β _d between the actual centroid slip angle and the preset centroid slip angle converges to 0 Or the limit value, where β _d is the reference trajectory of the center of mass slip angle; define e2 as the error between the actual control variable and the virtual control variable, that is, e ₂ =r-ψ;

Taking the derivation _of the error e1 gives:

The expected dummy control variables are:

In the formula, k ₁ , γ ₁ are the adjustment coefficients in the controller design, which are positive numbers;

A positive semi-definite Lyapunov function is defined as:

Taking the derivation of (9), we get:

Taking the first derivative with respect to e2, we get:

where θ=1/I _z , θ _min =1/I _zmax , θ _max =1/I _{zmin ,} I _zmin , I _zmax are the lower and upper bounds of the moment of inertia, respectively,

The design additional yaw moment M _z is:

是θ的估计值，

In the formula, k ₂ is a constant number,

is an estimate of θ,

The adaptive control rate is:

成立。The adaptive control rate (13) can guarantee that the estimated parameters are always within known bounds, ie θ _min ≤ θ ≤ θ _max , for all τ, the inequality

established.

An adaptive thrust reverser that satisfies the above adaptive control rate is used as an upper-level controller to generate the desired additional yaw moment.

Step 3 The specific process of designing the optimal torque distribution algorithm based on the minimum objective function is as follows:

The relationship between the total longitudinal force F _x of the tire and the longitudinal force F _xij of each tire is:

F _x =F _xfl +F _xfr +F _xrl +F _xrr (21)

F _xfl represents the longitudinal force of the front left wheel, F _xfr represents the longitudinal force of the front right wheel, F _xrl represents the longitudinal force of the rear left wheel, and F _xrr represents the longitudinal force of the rear right wheel;

The maximum driving force that the in-wheel motor can provide is:

F _xijmax = μF _zij (22)

where μ is the friction coefficient of the road surface;

The four-wheel torque distribution is transformed into a quadratic programming standard form as the objective function of optimal torque distribution, and the minimum objective function is used as the optimal torque distribution calculation function, then the minimum objective function is expressed as:

lb＝[-μF_zfl -μF_zrl -μF_zrl -μF_rrl]^T，A₁＝0，b＝0，f^T＝0，beq＝M_z，ub＝[μF_zfl μF_zrl μF_zrl μF_rrl]^T。In the formula, p=[F _xfl F _xfr F _xrl F _xrr ] ^T ,

lb=[-μF _zfl - μF _zrl - μF _zrl - μF _rrl ] ^T , A ₁ =0, b=0, f ^T =0, beq=M _z , ub=[μF _zfl μF _zrl μF _zrl μF _rrl ] ^T .

The beneficial effects of the present invention are:

Aiming at the uncertainty in the electric vehicle model, the present invention designs a corresponding adaptive control law according to the adaptive inversion method, and can estimate the uncertain parameters in the model online in real time, so as to adjust the influence of the uncertain parameters on the vehicle, and at the same time The output response of the vehicle's center of mass slip angle and yaw rate is significantly reduced, effectively improving the handling stability.

Compared with the general direct distribution algorithm, the optimal torque distribution algorithm proposed in the present invention has better control effect and can ensure that the output torque is less than the maximum driving force that the in-wheel motor can provide.

The method of the invention is simple and easy to implement, the system does not need redundant hardware, and the cost is low.

Description of drawings

Fig. 1 is the working flow chart of the yaw stability control method of electric vehicle based on adaptive thrust reverser controller of the present invention;

Fig. 2 is the lateral dynamics model of the electric vehicle of the present invention;

Fig. 3 is the principle block diagram of the self-adaptive pushback control system of the present invention;

Fig. 4 is the front wheel steering angle input curve diagram of the present invention;

Fig. 5 is the response curve diagram of the center of mass sideslip angle of the present invention;

6 is a yaw rate response curve diagram of the present invention;

Fig. 7 is the left front wheel torque response curve diagram of the present invention;

FIG. 8 is a right front wheel torque response curve diagram of the present invention;

Fig. 9 is the left rear wheel torque response curve diagram of the present invention;

Fig. 10 is the moment response curve diagram of the right rear wheel of the present invention;

FIG. 11 is a response curve diagram of the vehicle tracking path of the present invention.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

The yaw stability control method of an electric vehicle based on an adaptive thrust reverser controller of the present invention, as shown in FIG. 1 , includes the following steps:

Step 1. Build the lateral dynamics model of the electric vehicle; because it includes the main features of the lateral dynamics of the electric vehicle and has a simple structure, the lateral dynamics model of the electric vehicle has been widely used in the field of yaw stability control of the electric vehicle . The present invention proposes a lateral dynamics model of an electric vehicle, as shown in FIG. 2 . The lateral dynamics model of the electric vehicle includes the lateral dynamics equation of the electric vehicle, the rotational dynamics equation of the wheel, the lateral acceleration and the lateral acceleration; the specific process is:

According to Newton's second law, the lateral dynamics equation of an electric vehicle is:

In formula (1), m is the mass of the car body, I _z is the moment of inertia of the car body; F _yf is the lateral force of the front wheel, F _yr is the lateral force of the rear wheel; β and r are the center of mass slip angle and yaw, respectively. rate; l _f and l _r are the distances from the front and rear axles to the center of mass, respectively; M _z is the additional yaw moment; v is the vehicle speed;

Among them, F _yf and F _yr expressions are:

In formula (2), C _f is the cornering stiffness of the front wheel, C _r is the cornering stiffness of the rear wheel; α _f is the side slip angle of the front wheel, α _r is the side slip angle of the rear wheel; α _f and α _r are expressed as :

Substituting formulas (2) and (3) into (1), we get:

a₂＝2l_rC_r-2l_fC_f，

c₂＝2C_fl_f；in,

a ₂ =2l _r C _r -2l _f C _f ,

c ₂ =2C _f l _f ;

The rotational dynamics equation of the wheel is expressed as:

where R is the wheel rolling radius, w _ij is the wheel angular velocity, I _w is the wheel moment of inertia, and T _ij is the wheel torque;

The lateral acceleration a _x and the lateral acceleration a _y are respectively:

Step 2. Design an adaptive thrust reverser controller based on the barrier Lyapunov function, and use the adaptive thrust reverser controller as an upper-level controller to generate the desired additional yaw moment; the specific process of step 2 is as follows:

Choose ψ as the desired virtual control variable, and r as the actual control variable, if r=ψ is satisfied, the error e ₁ =β-β _d between the actual centroid slip angle and the preset centroid slip angle converges to 0 Or the limit value, where β _d is the reference trajectory of the center of mass slip angle; define e2 as the error between the actual control variable and the virtual control variable, that is, e ₂ =r-ψ;

Taking the derivation _of the error e1 gives:

The expected dummy control variables are:

In the formula, k ₁ , γ ₁ are the adjustment coefficients in the controller design, which are positive numbers;

A positive semi-definite Lyapunov function is defined as:

Taking the derivation of (9), we get:

Taking the first derivative with respect to _e2 , we get:

In the formula, θ=1/I _z , θ _min =1/I _zmax , θ _max =1/I _zmin , I _zmin , I _zmax are the lower and upper bounds of the moment of inertia, respectively,

The design additional yaw moment M _z is:

是θ的估计值，

In the formula, k ₂ is a constant number,

is an estimate of θ,

The adaptive control rate is:

成立。The adaptive control rate (13) can guarantee that the estimated parameters are always within known bounds, ie θ _min ≤ θ ≤ θ _max , for all τ, the inequality

established.

Define another positive semi-definite Lyapunov function as:

Derivating formula (14) we get:

Integrating both sides of equation (15) from 0 to t gives:

The above _formula shows that e1 and _e2 are bounded in the whole time domain, namely:

Further, it can be obtained from formula (17):

That is, the following formula (19) holds:

a ₂ β+b ₂ r+c ₂ δ+M _z ∈L _∞ (19)

进一步可以得出：therefore,

Further it can be concluded that:

也是有界的，所以

是一致连续的，通过Barbalat’s引理可知，随着t→∞，则

进一步可得到e₁→0，e₂→0，所以e₁和e₂是渐进稳定的；Therefore,

is also bounded, so

is consistent and continuous, according to Barbalat's lemma, as t→∞, then

Further e ₁ →0, e ₂ →0 can be obtained, so e ₁ and e ₂ are asymptotically stable;

An adaptive thrust reverser that satisfies the above adaptive control rate is used as an upper-level controller to generate the desired additional yaw moment.

Step 3: Design the optimal torque distribution algorithm based on the minimum objective function as the lower controller to distribute the desired additional yaw moment. The specific process of designing the optimal torque distribution algorithm based on the minimum objective function is as follows:

In order to reasonably distribute the additional yaw moment generated in the upper controller, torque distribution algorithms are widely used. The present invention proposes an optimal torque distribution algorithm. The algorithm is designed to:

F _x =F _xfl +F _xfr +F _xrl +F _xrr (21)

F _xfl represents the longitudinal force of the front left wheel, F _xfr represents the longitudinal force of the front right wheel, F _xrl represents the longitudinal force of the rear left wheel, and F _xrr represents the longitudinal force of the rear right wheel;

The maximum driving force that the in-wheel motor can provide is:

F _xijmax = μF _zij (22)

where μ is the friction coefficient of the road surface;

The four-wheel torque distribution is transformed into a quadratic programming standard form as the objective function of optimal torque distribution, and the minimum objective function is used as the optimal torque distribution calculation function, then the minimum objective function is expressed as:

lb＝[-μF_zfl -μF_zrl -μF_zrl -μF_rrl]^T，A₁＝0，b＝0，f^T＝0，beq＝M_z，ub＝[μF_zfl μF_zrl μF_zrl μF_rrl]^T。In the formula, p=[F _xfl F _xfr F _xrl F _xrr ] ^T ,

lb=[-μF _zfl - μF _zrl - μF _zrl - μF _rrl ] ^T , A ₁ =0, b=0, f ^T =0, beq=M _z , ub=[μF _zfl μF _zrl μF _zrl μF _rrl ] ^T .

Based on the CarSim model, the adaptive backtracking controller developed in the above step 2 and the optimal torque distribution algorithm developed in 3 are verified:

The description of the uncertainty of the moment of inertia of the lateral dynamic system is: 1250≤I _z ≤1450;

Consider selecting the steering angle of the front wheel as an input;

The CarSim model was imported into Simulink as the controlled object, and the adaptive reverse thrust controller and torque distribution algorithm were built, and then verified with the corresponding parameters, and the following three modes were discussed and analyzed:

1) PS: In the case of no controller;

2) ADA: The lower controller is a direct allocation algorithm;

3) ODA: the lower controller is the optimal torque distribution algorithm;

4) Ref: reference curve;

In order to verify the validity of the constructed controller, the present invention establishes a lateral dynamics model of an electric vehicle in the MATLAB/Simulink environment, and simulates and verifies the accuracy of the controller through the above method. Figure 4 is the input curve of the front wheel steering angle; the response curve of the system performance index in different modes is shown in Figure 5-Figure 11. It can be seen from Fig. 5 and Fig. 6 that the controller proposed by the present invention can significantly reduce the side-slip angle and yaw rate of the center of mass, and the tracking accuracy and performance of the optimal torque distribution algorithm are better than those of the direct distribution algorithm. The yaw stability of the vehicle is improved. It can be seen from Figure 7, Figure 8, Figure 9 and Figure 10 that the torque response of the optimal torque distribution algorithm is smoother than that of the direct distribution algorithm, as shown in the partial enlarged views. On the other hand, although the average distribution algorithm is simpler and easier to implement, the distributed torque may be larger than the limit that may exceed the maximum driving force provided by the motor, and the optimal torque distribution algorithm can avoid this situation, justifying the optimal torque distribution strategy The problem is better than the even distribution algorithm. It can be seen from Fig. 7-11 that the tracking trajectories of the two controllers are much smoother than that of the uncontrolled vehicle, and the optimal torque distribution algorithm is closer to the reference trajectory than the average distribution algorithm, indicating that the proposed optimal torque distribution algorithm can Achieve better steering stability.

Simulation shows that the adaptive thrust reverser controller proposed in the present invention can reduce the lateral dynamic performance index of the electric vehicle, and the optimal distribution algorithm can reasonably distribute the additional yaw moment to the four tires, thus verifying the performance of the present invention. The effectiveness and accuracy of the composite controller improves the yaw stability and safety of the vehicle, which is of great significance for the yaw stability control applied to the lateral dynamics of electric vehicles.

Through the above method, the present invention is based on the yaw stability control method of the electric vehicle based on the adaptive thrust reverser controller, aiming at the uncertainty in the model of the electric vehicle, according to the adaptive thrust reverse method, the corresponding adaptive control law is designed, and the model is adjusted accordingly. The uncertain parameters in can be estimated online in real time to adjust the influence of uncertain parameters on the vehicle, and the output response of the vehicle's center of mass slip angle and yaw rate is significantly reduced, effectively improving the handling stability; the proposed optimal torque distribution Compared with the general direct distribution algorithm, the algorithm has better control effect, and can ensure that the output torque is less than the maximum driving force that the in-wheel motor can provide; the method of the invention is simple and easy to implement, the system does not need redundant hardware, and the cost is low.

Claims (5)

1. The electric vehicle yaw stability control method based on the adaptive reverse-pushing controller is characterized by comprising the following steps of:

step 1, constructing a lateral dynamics model of the electric automobile;

step 2, designing a self-adaptive reverse-pushing controller based on a barrier Lyapunov function, and taking the self-adaptive reverse-pushing controller as an upper-layer controller to generate an expected additional yaw moment;

and 3, designing an optimal torque distribution algorithm based on a minimum objective function as a lower-layer controller to distribute the expected additional yaw moment.

2. The adaptive-reactive-controller-based yaw stability control method for the electric vehicle according to claim 1, wherein the electric vehicle lateral dynamics model comprises electric vehicle lateral dynamics equations, rotational dynamics equations of wheels, lateral acceleration and lateral acceleration.

3. The yaw stability control method of the electric vehicle based on the adaptive back-pushing controller according to claim 2, characterized in that the step 1 is implemented by the following specific processes:

according to Newton's second law, the lateral dynamic equation of the electric vehicle is as follows:

in the formula (1), m is the vehicle body mass, I_zRepresenting the rotational inertia of the vehicle body; f_yfAs lateral force of the front wheel, F_yrIs the lateral force of the rear wheel; beta and r are respectively a centroid slip angle and a yaw rate; l_fAnd l_rThe distances from the front and rear axes to the center of mass respectively; m_zAn additional yaw moment; v is the vehicle speed;

wherein, F_yfAnd F_yrThe expressions are respectively:

in the formula (2), C_fFor front wheel cornering stiffness, C_rIs rear wheel cornering stiffness; alpha is alpha_fIs a front wheel side slip angle, α_rIs a rear wheel side slip angle; alpha is alpha_fAnd alpha_rRespectively expressed as:

substituting equations (2) and (3) into (1) yields:

wherein,

a₂＝2l_rC_r-2l_fC_f，

c₂＝2C_fl_f；

the rotational dynamics equation for a wheel is expressed as:

wherein R is the rolling radius of the wheel, w_ijIs the angular velocity of the wheel, I_wIs the moment of inertia of the wheel, T_ijIs the wheel moment;

lateral acceleration a_xAnd lateral acceleration a_yRespectively as follows:

4. the yaw stability control method of the electric vehicle based on the adaptive reverse-thrust controller according to claim 3, characterized in that the step 2 is implemented by the following specific processes:

selecting psi as the desired virtual control variable and r as the actual control variable, if r is satisfied psi, the error e between the actual centroid slip angle and the preset centroid slip angle₁＝β-β_dConvergence to 0 or a limit value, wherein_dIs the centroid slip angle reference trajectory; definition e₂As error of actual and virtual control variables, i.e. e₂＝r-ψ；

For error e₁The derivation yields:

the desired virtual control variables are designed as:

in the formula, k₁，γ₁The adjustment coefficients in the design of the controller are positive numbers;

defining a semi-positive lyapunov function as:

deriving (9) to obtain:

to e₂The first derivative is calculated to obtain:

wherein θ is 1/I_z，θ_min＝1/I_zmax，θ_max＝1/I_zmin，I_zmin，I_zmaxAre the lower and upper bounds of the moment of inertia respectively,

designing additional yaw moment M_zComprises the following steps:

in the formula, k₂Is a normal number, and is,

is an estimate of the value of theta that,

the self-adaptive control rate is as follows:

an adaptive reactive controller satisfying the adaptive control rate is used as an upper controller to generate a desired additional yaw moment.

5. The yaw stability control method of the electric vehicle based on the adaptive back-pushing controller according to claim 1, characterized in that the step 3 of designing the optimal torque distribution algorithm based on the minimum objective function comprises the following specific processes:

total longitudinal force F of the tire_xAnd respective tire longitudinal forces F_xijThe relationship between them is:

F_x＝F_xfl+F_xfr+F_xrl+F_xrr (21)

F_xflindicating front left wheel longitudinal force, F_xfrRepresenting front right wheel longitudinal force, F_xrlIndicating the rear left wheel longitudinal force, F_xrrRepresenting the rear right wheel longitudinal force;

the maximum driving force that the in-wheel motor can provide does:

F_xijmax＝μF_zij (22)

wherein mu is the friction coefficient of the road surface;

converting the four-wheel torque distribution into a quadratic programming standard form to be used as an objective function of the optimal torque distribution, and using the minimum objective function as an optimal torque distribution calculation function, wherein the minimum objective function is expressed as:

wherein p ═ F_xfl F_xfr F_xrl F_xrr]^T，

lb＝[-μF_zfl -μF_zrl -μF_zrl -μF_rrl]^T，A₁＝0,b＝0，f^T＝0，beq＝M_z，ub＝[μF_zfl μF_zrl μF_zrl μF_rrl]^T。

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