CN113086000B - A fault-tolerant estimation method for rack force of steer-by-wire system - Google Patents

Abstract

A fault-tolerant estimation method for rack force of a steer-by-wire system belongs to the technical field of automobile steer-by-wire. Building a dynamic modeling of a steering executing mechanism, and determining a state space of the steer-by-wire system; designing an extended disturbance observer, and estimating a generalized rack force; designing feedback gain of the extended disturbance observer based on a stability theory; a rack force fault-tolerant estimation method of a steer-by-wire system is provided. The method is more accurate, and provides a design basis for the fault-tolerant mechanism of the observer. High precision and small influence of motor torque fluctuation. The reliability of rack force estimation is improved, and a fault tolerance strategy of the observer is provided. The method can be used for designing a feedforward controller to improve the accuracy of the steering angle tracking in the steering follow-up control and can also be used for designing a feedback road feel in the road feel simulation. The observation of the rotation angle and the rotation speed of the steering execution motor and the displacement and the speed of the rack can be realized.

Description

A fault-tolerant estimation method for rack force of steer-by-wire system

technical field

The invention relates to a rack force error-tolerant estimation method of a wire-controlled steering system, and belongs to the technical field of automobile wire-controlled steering.

Background technique

Steering-by-wire technology, as the hardware basis of steering automation, cancels the mechanical connection between the steering mechanism and the steering wheel, and uses electrical signals to transmit information in both directions: the steering wheel angle command input by the driver is transmitted to the electronic control unit through the in-vehicle network. , the electronic control unit receives the control command and then controls the steering actuator to complete the driver's steering intention; at the same time, the sensor transmits the relevant information of the road feedback to the electronic control unit, and the electronic control unit calculates the road sense feedback torque and controls the road sense feedback motor output corresponding to The size of the torque, complete the road sense feedback.

The construction of the steer-by-wire system includes two key technologies: one is the steering follow-up control, that is, the wheel angle tracking control. The difficulty lies in the fact that the realigning moment generated by the road surface acting on the tire is an interference that is not easy to measure, which will affect the accuracy of the tracking control. ; The other is the planning and simulation of road feel. In the traditional mechanical steering system, road feel can be understood as the resistance torque transmitted by the wheel's return torque to the driver through the mechanical transmission device, which includes the movement of the whole vehicle and the force on the tires. Status information, which is transmitted to the driver through a mechanical connection to help the driver judge the running state of the car and the road environment, while the mechanical connection of the steering system is canceled in the steer-by-wire system, and the road sense needs to integrate various sensors in the electronic control unit The signal calculation shows that the difficulty lies in how to simulate the road feeling close to the traditional mechanical steering system.

The rack force is the force acting on the rack through the steering rod as the tire aligning torque, which is not only the interference that affects the accuracy of the corner tracking control, but also an important part of the road feeling information used to generate the road feeling feedback torque, so it has been widely studied. Some methods of measuring and estimating rack force are as follows:

The publication date is March 24, 2020, the publication number is CN110901761A, and the Korean invention patent titled "Steer-by-wire system and method for estimating the rack force of the steer-by-wire system" discloses a steering-actuated motor rotation angle sensor Calculate the force of the reducer by using the rack position difference between the front end and the rear end of the reducer measured by the rack displacement sensor, and then calculate the rack force through the dynamic model. The disadvantage of this method is that it requires high accuracy of the sensor, the estimation effect is sensitive to the change of the stiffness parameter of the transmission mechanism, the stiffness of the transmission mechanism cannot be accurately measured, and is affected by various factors such as the use time of the material, and the change of the stiffness parameter will lead to the calculation of the rack force. distortion.

The publication date is January 21, 2020, the publication number is CN110712676A, and the US invention patent titled "Rack Force Estimation of Steering System" discloses that by modeling tires, estimating lateral velocity, calculating slip angle and then calculating tires The lateral force is applied to obtain the rack force. The disadvantage of this method is that it has a strong dependence on the model, and the tire trail cannot be accurately measured, resulting in a low accuracy of rack force estimation.

The publication date is October 8, 2019, the publication number is CN110304135A, and the Chinese invention patent titled "Rack Force Estimation of Steering System" discloses that the rack force is used as the interference of the steering actuator to model, and the nonlinearity is introduced. The gain function of , completes the design of the observer. The observer has fast convergence speed and good real-time performance, and can meet the requirements of rack force estimation under complex working conditions. The disadvantage of this method is that its model has only one degree of freedom, and the dynamic description of the actual physical system is not accurate enough. The observation effect of the observer is limited by a single rotation angle sensor. If the rotation angle sensor fails, it will seriously affect the estimation of the rack force. Effect.

SUMMARY OF THE INVENTION

In order to solve the problems existing in the background art, the present invention provides a method for estimating fault tolerance of the rack force of a steering-by-wire system.

To achieve the above object, the present invention adopts the following technical scheme: a method for estimating fault tolerance of rack force of a steering-by-wire system, the estimation method comprises the following steps:

S1: Construct the dynamic modeling of the steering actuator and determine the state space of the steer-by-wire system;

S2: Design an expanded disturbance observer to estimate the generalized rack force;

S3: Design the feedback gain of the extended disturbance observer based on stability theory;

S4: A fault-tolerant estimation method for the rack force of the steer-by-wire system is given.

Compared with the prior art, the beneficial effects of the present invention are:

1. The present invention sets two degrees of freedom in the modeling of the steering actuator, which is more accurate than the single-degree-of-freedom model in the prior art, and at the same time, the two degrees of freedom also provide a design basis for the fault-tolerant mechanism of the observer.

2. In the present invention, the method of observing the rack force by using the motor rotation angle, the rack displacement and the motor output torque at the same time combines the observation of the rack force only by the motor rotation angle, the motor output torque and the measurement of the rack force only by the rack displacement and the motor output torque. The advantages of the two methods of output torque observation of rack force: high precision and little influence by the motor torque fluctuation.

3. The invention improves the reliability of rack force estimation, and provides a fault-tolerant strategy for the observer: when the motor rotation angle sensor fails, the rack force using only the rack displacement and the motor output torque as input is given. Observer; when the rack displacement sensor fails, a rack force observer using only the motor rotation angle and the output torque of the motor is given.

4. Both steering follow-up control and road feel simulation have high requirements on the real-time performance of the system. The observer designed in the present invention has fast convergence speed and good real-time performance for estimating the generalized rack force. Therefore, the generalized rack force can not only It is used to design a feedforward controller in steering follow-up control to improve the accuracy of corner tracking, and can also be used to design feedback road feel in road feel simulation.

5. The observer designed in the present invention can also realize the observation of the rotation angle and rotational speed of the steering execution motor, as well as the displacement and speed of the rack.

Description of drawings

1 is a schematic structural diagram of a steering-by-wire system of the present invention;

Fig. 2 is the principle diagram of the expansion disturbance observer;

Figure 3 is a flow chart of the operation of the observer fault tolerance mechanism;

Figure 4 is a schematic diagram of three observers in the observer fault tolerance mechanism;

Fig. 5 is the observation effect curve of three kinds of observers for a given generalized rack force under the step input of rotation angle;

Figure 6 is the observation effect curve of three kinds of observers for a given generalized rack force under the double-shift linear route input.

Detailed ways

The technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments, based on the present invention The embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work, fall within the protection scope of the present invention.

A method for estimating rack force fault tolerance of a steering-by-wire system, the steering-by-wire system includes a steering actuator, a road-sensing feedback mechanism, and a controller 12 that performs coordinated control of the steering actuator and the road-sensing feedback mechanism; the steering actuator The mechanism includes steering execution motor 5, steering execution motor reducer 6, torque angle sensor 1 7, displacement sensor 8, pinion 9, rack 10 and wheels 11; the road sense feedback mechanism includes steering wheel 1, torque angle Sensor 2 2, road sense feedback motor reducer 3 and road sense feedback motor 4;

The output shaft of the steering execution motor 5 is connected with the pinion 9 through the steering execution motor reducer 6, and is provided with a torque angle sensor 7, the pinion 9 is meshed with the rack 10, and the rack 10 is connected to the pinion 9. Displacement sensor 8 is provided and connected with wheel 11;

The output shaft of the road sense feedback motor 4 is connected with the steering wheel 1 through the road sense feedback motor reducer 3, and is provided with a torque and angle sensor 2 2;

It is characterized in that: the estimation method comprises the following steps:

S1: Construct the dynamic modeling of the steering actuator and determine the state space of the steer-by-wire system;

Model the steering actuator and describe it as a second-order system with two degrees of freedom, in which the rack structure and the steering actuator motor shaft are regarded as rigid bodies, ignoring the friction loss on the motor shaft, the differential equation of the dynamics is :

in,

J _m is the moment of inertia equivalent to the motor shaft of the rotor and the reducer of the steering execution motor 5;

是转向执行电机5转子的角加速度；

is the angular acceleration of the steering actuator motor 5 rotor;

B _m is the viscous damping coefficient of the steering actuator motor 5 and the steering actuator motor reducer 6;

是转向执行电机5转子的旋转角速度；

is the rotational angular velocity of the rotor of the steering execution motor 5;

K _m is the torsional stiffness of the steering actuator motor 5;

θ _m is the angular speed of the rotor of the steering executive motor 5;

G _m is the reduction ratio of the steering execution motor reducer 6;

X _r is the lateral displacement of the rack 10;

r _p is the indexing circle radius of the pinion 9;

T _m is the output torque of the steering execution motor 5;

m _r is the mass of the rack 10;

是齿条10的加速度；

is the acceleration of the rack 10;

B _r is the damping of the rack 10;

是齿条10的速度；

is the speed of the rack 10;

F _f,r is the friction force received by the rack 10 when it moves;

_Fr is the force of the steering rod received when the rack 10 moves.

The determination of the state space of the steer-by-wire system includes the following steps:

S101: Ignore the friction torque T _f,m during the operation of the motor, and at the same time take the sum of the friction force F _f,r and the steering rod force F _r received during the movement of the rack as the generalized rack force F _e , that is, in the system The part that needs to be estimated, assuming its first derivative is bounded:

F _e =F _r +F _f,r ;

x₃＝X_r、

输出y₁＝θ_m、y₃＝X_r，则线控转向系统状态空间为：S102: Define the state variable x ₁ =θ _m ,

x ₃ =X _r ,

Output y ₁ =θ _m , y ₃ =X _r , the state space of the steer-by-wire system is:

The state space of the extended disturbance observer of the steer-by-wire system based on expression (2) is described as follows:

In the formula,

Z ₁ , Z ₂ , Z ₃ , Z ₄ , Z ₅ and Z ₆ are the observer feedback gains:

in,

α ₁ , α ₂ , α ₃ , β ₁ , β ₂ , β ₃ and ε are variable (to be designed) parameters;

和

分别表示状态x₁、x₂、x₃、x₄和x₅的估计值。

and

represent the estimated values of states x ₁ , x ₂ , x ₃ , x ₄ and x ₅ , respectively.

S2: Design an expanded disturbance observer to estimate the generalized rack force;

The estimating generalized rack force includes the following steps:

S201: Take the generalized rack force Fe described in _S101 of the original system as the system disturbance d, and define it as the expansion state x ₅ of the observer system, assuming that its first-order differential is bounded, it satisfies

in

是系统干扰的一阶微分，

is the first derivative of the system disturbance,

ξ is a positive number.

和

作用生成误差项，并乘以不同的观测器反馈增益之后作用于观测器的不同状态变量上。S202: Introduce the outputs y ₁ and y ₃ of the original system into the observer system, which is consistent with the state of the observer system

and

The action generates an error term, which is multiplied by different observer feedback gains and acts on different state variables of the observer.

S3: Design the feedback gain of the extended disturbance observer based on the stability theory; the feedback gain of the extended disturbance observer includes the following steps:

S301: The estimated error equation of the extended disturbance observer is given as follows: the error vector of the extended disturbance observer is defined as

in:

其中：

S302: Observation error state equation:

in:

是误差向量对时间的一阶导数。

is the first derivative of the error vector with respect to time.

的特征方程写为：matrix

The characteristic equation of is written as:

Among them, λ is the eigenvalue to be solved, and I is the fifth-order unit matrix;

The conditions under which the observer error equation is stable are obtained using the Rouse criterion:

in:

When the parameters α ₁ , α ₂ , α ₃ , β ₁ , β ₂ , β ₃ and ε satisfy the inequality (4), the observer error equation is stable;

If the observation error equation is stable, for any given positive definite matrix Q, a symmetric positive definite matrix P can always be found to satisfy the following Lyapunov equation:

为状态矩阵

的转置；in,

is the state matrix

transpose of ;

The Lyapunov function of the observer can be defined as:

V=εη ^T Pη

where η ^T is the transpose of the error vector η.

有：Then for the first derivative of V with respect to time

Have:

为负定，故有不等式：From the Lyapunov stability criterion, we know that

is negative definite, so there is an inequality:

Among them, λ _min (Q) is the minimum eigenvalue of Q, from which the inequality of the first-order differential of the generalized rack moment can be obtained:

From the expression (5), the upper bound of the first-order differential of the generalized rack moment can be obtained. In order to ensure the asymptotic stability of the system, ε should be taken as small as possible. At the same time, in order to ensure the convergence speed of the observer system, a high-gain observer is constructed, so that the dynamic characteristics of the observer system are much higher than the actual physical system, and the value of ε is also required to be as small as possible.

S4: A fault-tolerant estimation method for the rack force of the steer-by-wire system is given.

The fault-tolerant estimation method for the rack force of the steer-by-wire system is given as follows:

When the rotation angle sensor of the steering actuator 5 and the displacement sensor 8 of the rack 10 work normally, an observer with the difference in the rotation angle of the motor and the displacement difference of the rack as feedback signals is given, as shown in Fig. 4(a) , called the motor angle-rack displacement observer;

When the rotation angle sensor fails, the rotation angle difference signal is shielded on the basis of the normal system observer, and only the rack displacement difference is used to construct a feedback loop to form a new observer, as shown in (b) in Figure 4, which is called rack displacement observer;

When the displacement sensor fails, the displacement difference signal is shielded on the basis of the normal system observer, and only the motor angle difference is used to build a feedback loop to form a new observer, as shown in (c) in Figure 4, which is called the motor angle observer ;

When both the motor angle sensor and the rack displacement sensor fail, the system reports an error, and the observer cannot estimate the rack force;

的微分，由此可知T_m对于系统两自由度中的电机转角影响较大，为了减弱其对观测器系统观测效果的影响，将α₃设为零，即取消扩张状态x₅中对应电机转角的部分，只设计α₁、α₂、β₁、β₂、β₃和ε的参数。The output torque T _m of the motor as the input signal of the observer will introduce a lot of clutter, which has a certain influence on the observation effect of the observer. From the expression (3), it can be known that the motor output torque T _m directly acts on the motor angular velocity

It can be seen that T _m has a great influence on the motor rotation angle in the two degrees of freedom of the system. In order to weaken its influence on the observation effect of the observer system, α ₃ is set to zero, that is, the corresponding motor rotation angle in the expansion state x ₅ is cancelled. , only the parameters of α ₁ , α ₂ , β ₁ , β ₂ , β ₃ and ε are designed.

When the motor rotation angle sensor in the system fails and has no signal feedback, and the observer input becomes the rack displacement X _r and the motor output torque T _m , set α ₁ , α ₂ and α ₃ to zero, the feedback in the observer The item is only the difference between the measured value and the estimated value of the rack displacement, and the parameters to be designed are β ₁ , β ₂ , β ₃ and ε;

When the rack displacement sensor in the system fails and has no signal feedback, and the observer input becomes the motor rotation angle θ _m and the motor output torque T _m , set β ₁ , β ₂ and β ₃ to zero, the feedback in the observer The term is only the difference between the measured value and the estimated value of the motor rotation angle, and the parameters that need to be designed in the observer are α ₁ , α ₂ , α ₃ and ε.

The above observers designed to deal with the two sensor faults are only designed to ensure that the estimated value of the generalized rack force can be stably output when the corresponding fault occurs, and the estimation accuracy is inferior to that of the complete observer using the rack displacement difference and the motor angle difference as feedback. .

The invention utilizes the measurement information of multi-sensors, that is, the rotation angle of the steering execution motor, the displacement of the rack and the output torque of the motor, and combines the expression (3) to realize the estimation of the generalized rack force, and provides a fault tolerance method, which improves the The accuracy of rack force estimation, and can estimate the motor rotation angle, rotational speed and rack displacement and speed signals.

The observer uses the rack displacement difference and the motor rotation angle difference as feedback signals, however, the motor rotation angle sensor and the rack displacement sensor may fail to affect the observation effect of the observer:

The motor angle sensor generally uses a photoelectric encoder or a resolver: the photoelectric encoder is greatly affected by the environment, due to mechanical vibration, temperature, humidity, and other problems such as false pulses or stop working, the main control unit can judge whether there is a fault through an algorithm; rotation; The faults of the transformer mainly include circuit breakage, abnormal voltage signal, etc. When a fault occurs, the decoding chip will report to the main control unit.

Rack displacement sensors generally use line displacement sensors. The line displacement sensor may have the problem that the output data does not change after the line is pulled out, or the line is disconnected, resulting in no data output. When the vehicle is steering, it detects that the output data is long. If the time does not update, the sensor is faulty.

In order to reduce the influence on the generalized rack force estimation when the motor rotation angle sensor and the rack displacement sensor fail, a fault-tolerant estimation method for the rack force is designed:

When the system is running normally, the input is the motor rotation angle θ _m , the rack displacement X _r and the motor output torque T _m , and the parameters to be designed in the observer are α ₁ , α ₂ , β ₁ , β ₂ , β ₃ and ε, set α ₃ to zero; when the motor rotation angle sensor in the system fails, the observer input becomes the rack displacement X _r and the motor output torque T _m , set α ₁ , α ₂ and α ₃ are set to zero, and the parameters to be designed in the observer are β ₁ , β ₂ , β ₃ and ε; when the rack displacement sensor in the system fails, the observer input becomes the motor rotation angle θ _m and the motor output torque T _m , β ₁ , β ₂ and β ₃ are set to zero, and the parameters to be designed in the observer are α ₁ , α ₂ , α ₃ and ε.

Example 1:

According to the design requirements of the steering actuator and combined with the expected simulation results, the simulation parameters and the feedback gain of the observer are designed.

The designed simulation run related parameters are as follows:

J _m =0.001kg·m ² , B _m =0.008N·m·s/rad, K _m =132N·m/rad

G _m =10, rp =6.11 mm, m _{r =} 4.125 kg, and B _r =4000 N·s/m.

Feedback gain in motor angle-rack displacement observer:

α ₁ =1, α ₂ =10, β ₁ =1, β ₂ =10, β ₃ =5, ε = 0.001.

Feedback gain in rack displacement observer:

β ₁ =1, β ₂ =10, β ₃ =0.5, ε = 0.001.

Feedback gain in the motor angle observer:

α ₁ =1, α ₂ =10, α ₃ =1, ε = 0.001.

In this embodiment, the steering wheel angle step input and the double-shift linear route input are used to verify the estimation effect of the present invention.

Fig. 5 is the estimation effect of the motor angle-rack displacement observer, the motor angle observer, and the rack displacement observer to the given input generalized rack force when the steering wheel input angle step signal mentioned in the embodiment; Fig. 6 Under the input of the double-shift linear route mentioned in the embodiment, the estimated effect of the motor rotation angle-rack displacement observer, the motor rotation angle observer, and the rack displacement observer for a given input generalized rack force.

The root mean square error of the motor angle-rack displacement observer is 15.17 when the input is the angle step signal, and the root mean square error is 38.91 when the input is the double-shift linear route; the motor angle observer when the input is the angle step signal The root mean square error is 15.26, and the root mean square error is 39.42 when the input is a double-shift linear route; the root mean square error of the rack displacement observer is 62.67 when the input is a corner step signal, and when the input is a double-shift linear route The root mean square error is 54.11.

According to the curves of Fig. 4 and Fig. 5 and the results of the root mean square error, it can be seen that the rack force fault-tolerant estimation strategy designed in this embodiment has high estimation accuracy and real-time performance of rack force during normal operation; When a single motor angle signal is used for feedback under fault, the rack force estimation effect is good and the real-time performance is good, but there is a small amplitude oscillation in the dynamic process; when a single rack displacement signal is used for feedback under the fault of the motor angle sensor, the There is a certain delay in the bar force estimation results. In the case of sensor failure, the requirement of fault-tolerant estimation is to maintain the stability of the steering system and ensure the continuous output of the estimated value of the rack force, so the requirements for the accuracy of the rack force estimation are relaxed. In conclusion, the rack force fault-tolerant estimation strategy proposed by the present invention is meaningful.

When the rotation angle sensor of the steering actuator and the displacement sensor of the rack work normally, an observer is given which takes the motor rotation angle difference and the rack displacement difference as feedback signals; when the rotation angle sensor fails, based on the normal system observer Shield the angle difference signal, only use the rack displacement difference to build a feedback loop, and change the feedback gain of the original observer to form a new observer; when the displacement sensor fails, shield the displacement difference signal on the basis of the normal system observer, and only use the motor The angle difference builds a feedback loop and changes the feedback gain of the original observer to form a new observer.

The invention provides a rack force fault-tolerant estimation method with mature theory, high precision and strong reliability, which is mainly used to solve the problems of insufficient precision reading of rack force estimation and poor reliability in engineering implementation.

It will be apparent to those skilled in the art that the present invention is not limited to the details of the above-described exemplary embodiments, but that the present invention may be embodied in other forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments are to be regarded in all respects as illustrative and not restrictive, and the scope of the invention is to be defined by the appended claims rather than the foregoing description, which are therefore intended to fall within the scope of the claims. All changes within the meaning and range of the equivalents of , are embraced within the invention. Any reference signs in the claims shall not be construed as limiting the involved claim.

In addition, it should be understood that although this specification is described in terms of embodiments, not each embodiment only includes an independent technical solution, and this description in the specification is only for the sake of clarity, and those skilled in the art should take the specification as a whole , the technical solutions in each embodiment can also be appropriately combined to form other implementations that can be understood by those skilled in the art.

Claims (3)

1. A fault-tolerant estimation method of rack force of a steer-by-wire system comprises a steering actuating mechanism, a road feel feedback mechanism and a controller (12) for performing coordination control on the steering actuating mechanism and the road feel feedback mechanism; the steering actuating mechanism comprises a steering actuating motor (5), a steering actuating motor reducer (6), a first torque angle sensor (7), a displacement sensor (8), a pinion (9), a rack (10) and wheels (11); the road feel feedback mechanism comprises a steering wheel (1), a torque and angle sensor II (2), a road feel feedback motor reducer (3) and a road feel feedback motor (4);

an output shaft of the steering execution motor (5) is connected with a pinion (9) through a steering execution motor reducer (6) and is provided with a first torque and angle sensor (7), the pinion (9) is meshed with a rack (10), and the rack (10) is provided with a displacement sensor (8) and is connected with wheels (11);

an output shaft of the road feel feedback motor (4) is connected with the steering wheel (1) through a road feel feedback motor reducer (3) and is provided with a second torque and corner sensor (2);

the method is characterized in that: the estimation method comprises the following steps:

s1: building a dynamic modeling of a steering executing mechanism, and determining a state space of the steer-by-wire system;

the differential equation of the dynamics is:

wherein,

J_mthe rotational inertia of a rotor and a reducer of a steering execution motor (5) equivalent to a motor shaft;

is the angular acceleration of the rotor of the steering actuator motor (5);

B_mis the viscous damping coefficient of the steering actuating motor (5) and the steering actuating motor reducer (6);

is the rotational angular velocity of the rotor of the steering actuator motor (5);

K_mis the torsional stiffness of the steering actuator motor (5);

θ_mis the angular velocity of the rotor of the steering actuating motor (5);

G_mthe reduction ratio of a reducer (6) of a steering execution motor;

X_ris the transverse displacement of the rack (10);

r_pis the pitch circle radius of the pinion (9);

T_mis the output torque of the steering actuator motor (5);

m_ris the mass of the rack (10);

is the acceleration of the rack (10);

B_ris the damping of the rack (10);

is the speed of the rack (10);

F_f,ris the friction force received by the rack (10) when moving;

F_ris the force of the steering tie rod received by the rack (10) during its movement

The determination of the steer-by-wire system state space comprises the following steps:

s101: while simultaneously applying the frictional force F to the rack during movement_f,rAnd received steering rod force F_rThe sum is taken as generalized rack force F_eAnd assuming that its first order differential is bounded:

F_e＝F_r+F_f,r；

s102: defining a state variable x₁＝θ_m、

x₃＝X_r、

Output y₁＝θ_m、y₃＝X_rAnd then the state space of the steer-by-wire system is as follows:

the state space of the extended disturbance observer of the steer-by-wire system designed based on expression (2) is described as follows:

in the formula,

Z₁、Z₂、Z₃、Z₄、Z₅and Z₆For observer feedback gain:

wherein,

α₁、α₂、α₃、β₁、β₂、β₃and ε is a variable parameter;

and

respectively represent the state x₁、x₂、x₃、x₄And x₅An estimated value of (d);

s2: designing an extended disturbance observer, and estimating a generalized rack force;

s3: designing feedback gain of the extended disturbance observer based on a stability theory;

the feedback gain of the extended disturbance observer comprises the following steps:

s301: the estimation error equation for the extended disturbance observer is given as follows:

defining an error vector of the extended disturbance observer as

Wherein:

s302: observation error state equation:

wherein:

is the first order of the error vector versus timeA derivative;

matrix array

The characteristic equation of (a) is written as:

wherein, λ is a characteristic value to be solved, and I is a five-order identity matrix;

obtaining the stable condition of the error equation of the observer by utilizing the Laus criterion:

wherein:

when the parameter α is₁、α₂、α₃、β₁、β₂、β₃When the sum epsilon satisfies the inequality (4), the error equation of the observer is stable;

and if the observation error equation is stable, finding a symmetrical positive array P to satisfy the following Lyapunov equation for any given positive array Q:

wherein,

is a state matrix

Transposing;

the Lyapunov function of the observer can be defined as:

V＝εη^TPη

wherein eta^TIs the transpose of the error vector η;

then the first derivative with respect to time of V

Comprises the following steps:

the criterion of Lyapunov stability can be found

Negative, so there is an inequality:

wherein λ is_min(Q) is the minimum eigenvalue of Q, from which the inequality can be derived for the first order differential of the generalized rack moment:

s4: a rack force fault-tolerant estimation method of a steer-by-wire system is provided.

2. The method for fault-tolerant estimation of rack force of the steer-by-wire system according to claim 1, wherein: s2 the estimating the generalized rack force includes the steps of:

s201: the generalized rack force F stated in S101 of the original system_eAs system disturbance d, an extended state x of the observer system is defined₅Assuming that its first order differential is bounded, satisfy

Wherein

Is the first order differential of the system interference,

ξ is a positive number;

s202: output y of the original system₁And y₃Introduction of the observer system, and the state of the observer system

And

the action generates an error term and is multiplied by the observer feedback gain to act on different state variables of the observer.

3. The method for fault-tolerant estimation of the rack force of the steer-by-wire system according to claim 2, wherein: s4, the method for estimating the rack force fault tolerance of the steer-by-wire system is as follows:

when a rotation angle sensor of a steering execution motor (5) and a displacement sensor (8) of a rack (10) work normally, an observer taking a motor rotation angle difference and a rack displacement difference as feedback signals is provided, and the observer is called as a motor rotation angle-rack displacement observer;

when the corner sensor has a fault, shielding a corner difference signal on the basis of a normal system observer, and only using a rack displacement difference to construct a feedback loop to form a new observer called a rack displacement observer;

when the displacement sensor is in fault, a displacement difference signal is shielded on the basis of a normal system observer, and a feedback loop is constructed by using the motor rotation angle difference only to form a new observer which is called a motor rotation angle observer;

when the motor rotation angle sensor and the rack displacement sensor both have faults, the system reports errors, and the observer cannot estimate the rack force;

when a motor rotation angle sensor in the system has a fault and has no signal feedback, the input of the observer is changed into rack displacement X_rAnd motor output torque T_mWhen is, will alpha₁、α₂And alpha₃Setting the feedback term in the observer to be zero, wherein the feedback term only has the difference between the measured value and the estimated value of the rack displacement, and the parameter needing to be designed is beta₁、β₂、β₃And ε;

when the rack displacement sensor in the system has a fault and has no signal feedback, the input of the observer is changed into the rotation angle theta of the motor_mAnd motor output torque T_mWhen is, beta is₁、β₂And beta₃Setting the feedback term in the observer to be zero, wherein the feedback term only has the difference between the measured value and the estimated value of the motor rotation angle, and the parameter needing to be designed in the observer is alpha₁、α₂、α₃And ε.

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