Motor-driven tractor-semitrailer driving stability control method

Abstract

The invention discloses a motor-driven tractor-semitrailer driving stability control method which comprises the following steps: firstly, establishing a tractor-semitrailer three-degree-of-freedom dynamic model, and solving yaw velocity expected values and side slip angle expected values of a tractor and a semitrailer according to driver input and actual vehicle states; secondly, according to the deviation between the expected value and the actual value of the vehicle state quantity, an upper-layer controller outputs the expected additional yaw moment, and the adaptive capacity to the parameter change of the semitrailer is achieved; the lower layer controller then outputs a torque on each wheel according to the desired additional yaw moment and the vehicle state, including a driving torque on the driving wheel and a braking torque on all wheels. By the adoption of the method for controlling the running stability of the motor-driven tractor-semitrailer, unstable working conditions such as rollover and folding of the tractor-semitrailer in the running process can be avoided, the running stability is improved, and meanwhile the method has the self-adaptive capacity for load changes of the semitrailer.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle control, and in particular to a method for controlling the driving stability of a motor-driven tractor-semitrailer. Background Art

[0002] In the field of modern logistics transportation, motor-driven tractor-semitrailers have become key equipment for long-distance cargo transportation due to their high transportation efficiency. However, such vehicles face many stability problems during driving, seriously affecting transportation safety and efficiency.

[0003] Due to the large load capacity and high center of mass of the semitrailer, it is extremely prone to unstable conditions such as rollover and folding during high-speed driving, steering, and poor road conditions. Traditional tractor-semitrailer dynamic models are often relatively complex and difficult to accurately reflect the vehicle's state during actual operation, posing challenges to stability control. At the same time, under different working conditions of the semitrailer, the differences in load changes, center of mass position changes, and road adhesion conditions make the vehicle parameters show great uncertainty, which further increases the difficulty of effectively controlling its driving stability.

[0004] In the early stage, fixed-parameter controllers were mostly used for vehicle stability control, such as traditional PID controllers. Although such controllers have a simple structure and are easy to implement, they cannot adaptively adjust according to the real-time changing parameters of the semitrailer. When the vehicle driving conditions change, especially when parameters such as the load of the semitrailer change significantly, the control effect of the fixed-parameter controller will deteriorate significantly, making it difficult to ensure the stable driving of the vehicle, resulting in high safety risks during vehicle driving. For example, when driving on a curve, it may roll over due to the inability to adjust the yaw moment in time; when braking on a low-adhesion road surface, it is easy to fold due to the inability to reasonably distribute the wheel torque.

[0005] With the development of automotive technology, model reference adaptive control (MRAC) has been introduced into the field of vehicle stability control, providing a new idea for solving this problem. However, to effectively apply it to a tractor-semitrailer, a suitable simplified model needs to be established to facilitate the analysis of system control characteristics and as a reference model for the controller. At the same time, an adaptive rate that can adapt to the parameter uncertainty of the semitrailer needs to be designed to improve the driving stability of the vehicle under various working conditions. Therefore, it is urgent to study a method for controlling the driving stability of a motor-driven tractor-semitrailer, aiming to improve the vehicle driving stability through innovative control strategies, reduce potential safety hazards during transportation, and promote the safe and efficient development of the logistics transportation industry. Summary of the Invention

[0006] The object of the present invention is to provide a driving stability control method for a motor-driven tractor-semitrailer. By applying the principle of model reference adaptive control, it can cope with situations such as changes in the load of the semitrailer, changes in the position of the center of mass, and changes in the road surface adhesion conditions. Its comprehensive performance is superior to that of traditional fixed-parameter controllers.

[0007] To achieve the above object, the present invention provides a driving stability control method for a motor-driven tractor-semitrailer, including the following steps:

[0008] S1. Establish a three-degree-of-freedom dynamic model of the tractor-semitrailer;

[0009] S2. Adopt a vehicle electronic stability controller with a hierarchical structure, including an upper-layer controller and a lower-layer controller. Among them, the upper-layer controller is designed by using the indirect model reference adaptive control (MRAC) method;

[0010] S3. Design the lower-layer controller based on the torque distribution algorithm of optimal control, and obtain the optimal solution of the original quadratic programming problem based on the optimal control distribution algorithm of quadratic programming;

[0011] S4. Conduct simulation and analysis of the vehicle electronic stability controller.

[0012] Preferably, in S1, when establishing the three-degree-of-freedom dynamic model of the tractor-semitrailer, it is assumed that only the longitudinal, lateral, and yaw motions of the tractor and the semitrailer on the horizontal plane are considered, and their vertical, pitch, and roll motions are not considered. At the same time, the following assumptions are added:

[0013] The road surface is a horizontal plane;

[0014] The change in the vertical load of the tire does not affect the cornering stiffness of the tire;

[0015] The longitudinal speed of the vehicle remains unchanged;

[0016] The articulation angle between the tractor and the semitrailer is within the range of -20° to 20°;

[0017] The tire stiffness is linearly related to the tire cornering angle.

[0018] Preferably, in S1, based on the assumption that the change in the vertical load of the tire does not affect the cornering stiffness of the tire, the two tires on both sides of the same axle of the vehicle are simplified into one, and the vehicle is simplified into a single-track vehicle model. Then, for the tractor, there is:

[0019]

[0020] Among them, m is the mass of the tractor, u is the longitudinal speed of the tractor, is the change rate of the sideslip angle of the tractor's center of mass, r is the yaw angular velocity of the tractor, f 1 ,f2 ,f 3 is the lateral force of the tractor tire, f h is the lateral force of the saddle on the tractor, I z is the moment of inertia of the tractor in the yaw direction, a, b, c are the longitudinal distances from each axle of the tractor to its center of mass, d h is the longitudinal distance from the saddle of the tractor to its center of mass, ΔM is the control input, and is the additional yaw moment acting on the tractor;

[0021] For semi-trailers, there are:

[0022]

[0023] Among them, m t is the mass of the semitrailer, u t is the longitudinal speed of the semitrailer, is the rate of change of the semitrailer's center of mass sideslip angle, r t is the yaw angular velocity of the semitrailer, f 4 ,f 5 ,f 6 is the lateral force of the semitrailer tire, Γ is the articulation angle between the tractor and the semitrailer, I zt is the moment of inertia of the semitrailer in the yaw direction, a t ,b t ,c t are the longitudinal distances from each axle of the semitrailer to its center of mass, d ht is the longitudinal distance from the semitrailer saddle to its center of mass, ΔM t is the control variable input, which is the additional yaw moment acting on the semi-trailer;

[0024] There are the following kinematic constraints between the tractor and the semi-trailer:

[0025]

[0026] Based on the assumption that tire stiffness is linearly related to tire slip angle, the tire force on each axle is calculated as follows:

[0027]

[0028] Among them, k i is the linear cornering stiffness of each tire, δ is the tractor front wheel steering angle input;

[0029] Combining equations (1)-(6), we can eliminate the force f acting on the saddle: h , and let cosΓ=1, we get the linear simplified tractor-trailer dynamic model:

[0030]

[0031] Among them, \(x\) is the state variable, \(M\) is the generalized mass matrix, and \(u\) is the control input, which has the following form:

[0032]

[0033] \(k\) 11 \(=(d\) h \(-a)k\) 1 \(+(d\) h \(+b)k\) 2 \(+(d\) h \(+c)k\) 3 (11);

[0034]

[0035] \(k\) 33 \(=(d\) ht \(+a\) t )k\) 4 \(+(d\) ht \(+b\) t )k\) 5 \(+(d\) ht \(+c\) t )k\) 6 (13);

[0036]

[0037] Multiply both sides of equation (7) on the left by \(M\) -1 , to obtain the model of the state-space expression, that is:

[0038]

[0039] Among them, \(A = M\) -1 \(K\), \(B = M\) -1 \(L\).

[0040] Preferably, in S2, the indirect MRAC method adjusts the estimated system parameters by applying the adaptive law by estimating the output error between the system and the reference model, and then adjusts the gains of the feedforward control and the feedback control according to the parameters of the estimated system and the reference model;

[0041] For the following controlled system:

[0042]

[0043] Among them, \(x\in R\) n is the state variable of the system, \(u\in R\) m is the input of the system, \(A\) and \(\Lambda\) are the parameter matrices of the system and are unknown or slowly varying, \(B\) is known, assuming that the state variable of the system and its derivative are bounded, and the control objective of the system is to control the state variable \(x\) to track the reference signal \(x\) m ;

[0044] Assume the reference model is as follows:

[0045]

[0046] where x m ∈R n is the system reference state, r ∈ R m is the reference system control input, A m and B m are the reference system parameters;

[0047] At this time, the control law is:

[0048]

[0049] where

[0050]

[0051] Take the parameter adaptation law:

[0052]

[0053] where Γ A and Γ Λ are the adaptation coefficients used to adjust the effect of the adaptation rate, P is the solution of the equation A m T P + PA m + Q = 0, and Q is a positive definite matrix.

[0054] Preferably, in S2, before designing the upper controller, it is also necessary to determine the vehicle state safety region and the reference state. Among them, the vehicle state safety region is described by the vehicle speed and the curvature during steady-state turning, and the boundary of the vehicle state safety region is determined by the steering wheel angle constraint, the road adhesion constraint, and the vehicle rollover constraint;

[0055] The reference state includes the reference yaw rate and the reference sideslip angle of the center of mass. By comprehensively considering the road adhesion constraint and the rollover constraint to be satisfied in the vehicle state safety region, the reference yaw rate is obtained; at the same time, by comprehensively considering the vehicle path tracking performance, the adhesion condition, and the phase lag of the sideslip angle of the center of mass at high speeds, the reference sideslip angle of the center of mass is set to be constantly 0.

[0056] Preferably, in S2, the vehicle electronic stability controller calculates the reference state quantity according to the driver's steering wheel angle input and the vehicle state. The linear quadratic tracker LQT calculates the input to the reference system according to the reference state quantity and the actual state quantity. The input to the reference system and the actual vehicle state quantity pass through the model reference adaptive controller to obtain the input to the actual model, and finally, the torque distributed to each axis is obtained through the lower controller.

[0057] Preferably, in S2, a linear quadratic tracker LQT is designed to calculate the input to the reference system based on the reference state quantity and the actual state quantity.

[0058] For the reference model y = Cx + Du, it is required that the system output y follows the desired output y r while ensuring relatively low energy consumption. The performance index function of the control is written as:

[0059]

[0060] where the error e = y r - y, and the matrices Q and R are weight coefficients;

[0061] The corresponding optimal control input is:

[0062] u * (t) = -R -1 B T (Px(t) - g)(24);

[0063] where P is the solution of the Riccati equation A T P + PA - PBR -1 B T P + C T QC = 0, and g is approximately obtained by the following formula:

[0064] g ≈ (PBR -1 B T - A T ) -1 C T Qy r (25).

[0065] Preferably, in S3, the torque distribution algorithm based on optimal control is specifically as follows:

[0066] The drive shaft of the tractor is equipped with in-wheel motors. First, calculate the maximum output yaw moment of the drive shaft. Based on the output characteristic curve of the in-wheel motor and the wheel speed, obtain the maximum torque of the motor, and then obtain the maximum output yaw moment of the drive shaft;

[0067] Distribute the torque to each wheel. Considering the tire adhesion limit constraint, the longitudinal force constraint of the non-driving wheels, and the motor output torque constraint conditions, with the goal of minimizing the tire longitudinal force and preventing wheel slip, wear, and improving control reliability, construct an objective function and summarize the torque distribution problem as a quadratic programming optimal control problem.

[0068] Preferably, in S3, the optimal control allocation algorithm based on quadratic programming is specifically as follows:

[0069] The active set algorithm is used to solve the quadratic programming problem with inequality constraints. The inequality constraints are transformed into equality constraints, and through iterative solution, it is judged whether the KKT conditions are satisfied according to the current solution and the working set in each iteration. If not, the corresponding quadratic programming sub-problem is solved, and the working set and the iterative feasible point are updated according to the solution result until the optimal solution of the original quadratic programming is obtained. Finally, the obtained longitudinal force is converted into wheel torque output.

[0070] Therefore, the present invention adopts the above-mentioned method for controlling the driving stability of a motor-driven tractor-semitrailer, and the beneficial effects are as follows:

[0071] (1) In the present invention, in order to cope with the uncertainty of the parameters of the semi-trailer, the upper-layer controller adopts the method of model reference adaptive control, and dynamically adjusts the controller parameters according to the deviation between the output of the reference model and the output of the actual model, so that the performance of the actual model is close to that of the reference model; the lower-layer torque distribution controller adopts the optimal control principle, which can minimize the longitudinal force load rate of the tire, and has good real-time performance while ensuring the control effect.

[0072] (2) In order to give full play to the advantages of the electric braking of the in-wheel motor, the lower-layer torque distribution controller of the tractor-semitrailer based on optimal control will first obtain the maximum yaw moment that can be output when only using the electric braking and electric drive of the drive wheels according to the output torque characteristics of the in-wheel motor; if the desired yaw moment is less than the maximum yaw moment, the mechanical braking is not used, otherwise it is used; finally, the wheel torque is distributed according to the optimal control method, which has high accuracy while taking into account the longitudinal force load rate of the tire.

[0073] The technical solution of the present invention will be further described in detail below with reference to the drawings and embodiments. Description of the Drawings

[0074] Figure 1 is a single-track vehicle model of an embodiment of the method for controlling the driving stability of a motor-driven tractor-semitrailer according to the present invention;

[0075] Figure 2 is an indirect MRAC structure diagram of an embodiment of the method for controlling the driving stability of a motor-driven tractor-semitrailer according to the present invention;

[0076] Figure 3 is a schematic diagram of the vehicle state safety area of an embodiment of the method for controlling the driving stability of a motor-driven tractor-semitrailer according to the present invention, where (a) is the vehicle state safety area on a high-adhesion road surface, and (b) is the vehicle state safety area on a low-adhesion road surface;

[0077] Figure 4It is the relationship between the reference yaw rate and vehicle speed of a vehicle in an embodiment of the driving stability control method for a motor-driven tractor-semitrailer of the present invention under different road surface adhesion coefficients and steering wheel angles, where (a) is a low-adhesion road surface, (b) is a medium-adhesion road surface, and (c) is a high-adhesion road surface;

[0078] Figure 5 It is the electronic stability controller architecture in an embodiment of the driving stability control method for a motor-driven tractor-semitrailer of the present invention;

[0079] Figure 6 It is the flowchart of the lower-layer torque distribution algorithm in an embodiment of the driving stability control method for a motor-driven tractor-semitrailer of the present invention;

[0080] Figure 7 It is the motor output characteristic curve in an embodiment of the driving stability control method for a motor-driven tractor-semitrailer of the present invention;

[0081] Figure 8 It is the flowchart of the active set algorithm in an embodiment of the driving stability control method for a motor-driven tractor-semitrailer of the present invention;

[0082] Figure 9 It is the relationship between the steering wheel angle and time in an embodiment of the driving stability control method for a motor-driven tractor-semitrailer of the present invention;

[0083] Figure 10 It is the schematic diagram of the anti-rollover condition simulation results in an embodiment of the driving stability control method for a motor-driven tractor-semitrailer of the present invention, where (a) is the roll angle of the semitrailer body, (b) is the yaw rate without control, (c) is the PID yaw rate, (d) is the MRAC yaw rate; (e) is the sideslip angle of the tractor centroid, (f) is the sideslip angle of the semitrailer centroid, (g) is the PID output tractor torque, (h) is the MRAC output tractor torque, (i) is the PID output semitrailer torque, and (j) is the MRAC output semitrailer torque;

[0084] Figure 11 It is the target path in the trajectory tracking condition simulation in an embodiment of the driving stability control method for a motor-driven tractor-semitrailer of the present invention;

[0085] Figure 12It is a schematic diagram of the simulation results of the trajectory tracking condition of a motor-driven tractor-semitrailer running stability control method according to an embodiment of the present invention under the condition of a fully-loaded semitrailer. Among them, (a) is the steering wheel input, (b) is the position of the center of mass of the vehicle without control, (c) is the position of the center of mass of the vehicle with PID control, (d) is the position of the center of mass of the vehicle with MRAC control; (e) is the yaw rate without control, (f) is the yaw rate with PID control, (g) is the yaw rate with MRAC control, (h) is the sideslip angle of the center of mass of the tractor; (i) is the sideslip angle of the center of mass of the semitrailer, (j) is the torque output of the tractor by PID control, (k) is the torque output of the tractor by MRAC control, (l) is the torque output of the semitrailer by PID control, (m) is the simulation result of the J-turn of the semitrailer under full load;

[0086] Figure 13 It is a schematic diagram of the simulation results of the trajectory tracking condition of a motor-driven tractor-semitrailer running stability control method according to an embodiment of the present invention under the condition of an empty semitrailer. Among them, (a) is the steering wheel input, (b) is the position of the center of mass of the vehicle with MRAC control, (c) is the position of the center of mass of the vehicle with PID control, (d) is the yaw rate with MRAC control, (e) is the yaw rate with PID control, (f) is the sideslip angle of the center of mass of the tractor, (g) is the sideslip angle of the center of mass of the semitrailer, (h) is the torque output of the tractor by MRAC control, (i) is the torque output of the tractor by PID control, (j) is the torque output of the semitrailer by MRAC control, (k) is the torque output of the semitrailer by PID control;

[0087] Figure 14 It is a schematic diagram of the simulation results of the anti-folding condition of a motor-driven tractor-semitrailer running stability control method according to an embodiment of the present invention. Among them, (a) is the yaw rate of the vehicle, (b) is the sideslip angle of the center of mass of the vehicle body, (c) is the articulation angle of the vehicle. Detailed implementation manners

[0088] The technical solutions of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0089] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those of ordinary skill in the field to which the present invention belongs.

[0090] The present invention designs an electronic stability controller for a tractor-semitrailer based on the principle of direct yaw moment control. First, a linear simplified model of the tractor-semitrailer is established. In the simplified model, the tractor-semitrailer system is simplified to a single-track vehicle system, and it is assumed that the longitudinal speed of the tractor remains unchanged. The tractor has two degrees of freedom in the yaw and lateral directions, plus one yaw degree of freedom of the semitrailer, and the entire linear simplified model has three degrees of freedom. The controller adopts a hierarchical structure, divided into upper and lower layers: the upper-layer controller determines the reference vehicle state according to the driver input, and outputs the desired additional yaw moment acting on the vehicle through the deviation between the actual vehicle state and the reference vehicle state; the lower-layer controller calculates the torque acting on each wheel according to the desired additional yaw moment output by the upper-layer controller.

[0091] To cope with the uncertainty of the semitrailer parameters, the upper-layer controller adopts the method of model reference adaptive control, and dynamically adjusts the controller parameters according to the deviation between the output of the reference model and the output of the actual model, so that the actual model performance is close to the reference model. The lower-layer torque distribution controller adopts the principle of optimal control, which can minimize the longitudinal force load rate of the tire, and has good real-time performance while ensuring the control effect. The present invention first determines the vehicle allowable safety state region and the reference state quantity, and designs the upper-layer model reference adaptive controller based on the principles of model reference adaptive control and direct yaw moment control. The lower-layer torque distribution controller of the tractor-semitrailer based on optimal control will first obtain the maximum yaw moment that can be output when only using the electric braking and electric drive of the drive wheels according to the output torque characteristics of the hub motor. If the desired yaw moment is less than the maximum yaw moment, the mechanical braking is not used, otherwise it is used. Finally, the wheel torque is distributed according to the optimal control method, which has high accuracy while taking into account the longitudinal force load rate of the tire.

[0092] As a comparison, in the present invention, an electronic stability controller is also designed with a traditional PID controller in the upper layer and a lower-layer controller based on the vertical load distribution rule in the lower layer. Finally, simulations are carried out for some typical working conditions to compare the control effects of the controller of the present invention and the traditional PID controller.

[0093] As shown in the figure, a method for controlling the driving stability of a motor-driven tractor-semitrailer includes the following steps:

[0094] When establishing the three - degree - of - freedom dynamic model of the tractor - semi - trailer, it is assumed that only the motion of the tractor - semi - trailer on the horizontal plane is considered, that is, only the longitudinal, lateral, and yaw motions of the tractor and semi - trailer on the horizontal plane are considered, and the vertical, pitch, and roll motions are not considered. At the same time, the following assumptions are added: the road surface is a horizontal plane; the change in the vertical load of the tire does not affect the cornering stiffness of the tire; the longitudinal speed of the vehicle remains constant; the articulation angle between the tractor and the semi - trailer is in the range of - 20° to 20°; the tire stiffness is linearly related to the tire side - slip angle.

[0095] Based on the assumption that the change in the vertical load of the tire does not affect the cornering stiffness of the tire, the two tires on both sides of the same axle of the vehicle can be simplified into one, and the vehicle is simplified into a single - track vehicle model. The schematic diagram of the single - track vehicle model of the tractor - semi - trailer is as Figure 1 shown. Then, for the tractor, there is:

[0096]

[0097] where m is the mass of the tractor, u is the longitudinal speed of the tractor, is the change rate of the sideslip angle of the tractor's center of mass, r is the yaw angular velocity of the tractor, f 1 , f 2 , f 3 is the lateral force of the tractor tire, f h is the lateral force acting on the tractor by the saddle, I z is the moment of inertia of the tractor in the yaw direction, a, b, c are the longitudinal distances from each axle of the tractor to its center of mass respectively, d h is the longitudinal distance from the saddle of the tractor to its center of mass, ΔM is the control input, which is the additional yaw moment acting on the tractor. For the semi - trailer, there is:

[0098]

[0099] where m t is the mass of the semi - trailer, u t is the longitudinal speed of the semi - trailer, is the change rate of the sideslip angle of the semi - trailer's center of mass, r t is the yaw angular velocity of the semi - trailer, f 4 , f 5 , f 6 is the lateral force of the semi - trailer tire, Γ is the articulation angle between the tractor and the semi - trailer, I zt is the moment of inertia of the semi - trailer in the yaw direction, a t , b t , c t are the longitudinal distances from each axle of the semi - trailer to its center of mass respectively, d ht is the longitudinal distance from the saddle of the semi - trailer to its center of mass, ΔMt The input of the control quantity is the yaw moment acting on the semi-trailer. There is the following kinematic constraint relationship between the tractor and the semi-trailer:

[0100]

[0101] Based on the assumption that tire stiffness is linearly related to tire slip angle, the tire force on each axle can be calculated as follows:

[0102]

[0103] Among them, k i is the linear cornering stiffness of each tire, and δ is the front wheel steering angle input of the tractor.

[0104] Combining equations (1)-(6), we can eliminate the force f acting on the saddle: h , and let cosΓ=1, we get the linear simplified tractor-trailer dynamic model:

[0105]

[0106] Among them, x is the state variable, M is the generalized mass matrix, and u is the control input, which has the following form:

[0107] k 11 =(d h -a)k 1 +(d h +b)k 2 +(d h +c)k 3 (11);

[0108]

[0109] k 33 =(d ht +a t ) 4 +(d ht +b t ) 5 +(d ht +c t ) 6 (13);

[0110]

[0111] Multiply both sides of equation (7) by M -1 , we get the model of the state space expression, namely:

[0112]

[0113] where A = M -1 K, B = M -1 L.

[0114] S2. The control inputs of the vehicle electronic stability controller designed by the present invention are the steering wheel angle, the accelerator pedal, and the motion state of the vehicle, and the outputs are the torques of the in-wheel motors on each drive axle and the braking torques on each wheel. Since the vehicle system is a highly nonlinear system, it is very difficult to directly design the controller. Therefore, the present invention adopts a hierarchical structure controller to decompose the control tasks, which is convenient for controller design.

[0115] The controller is divided into two layers: an upper-layer controller and a lower-layer controller. The input of the upper-layer controller is the steering wheel angle, the accelerator pedal, and the motion state of the vehicle, and the output is the additional yaw moment acting on the tractor and the semi-trailer; the input of the lower-layer controller is the output of the upper-layer controller, and the output is the drive and braking torques acting on each wheel. Through the hierarchical controller, the uncertainties and nonlinear characteristics in the vehicle system can be transferred to the upper-layer controller for solution, and the lower-layer controller does not need to consider the nonlinear factors, thus becoming a linear problem. In this way, the design of the controller is relatively easy. The vehicle electronic stability controller adopting the hierarchical structure includes an upper-layer controller and a lower-layer controller, and the upper-layer controller is designed by using the indirect model reference adaptive control (MRAC) method.

[0116] Model Reference Adaptive Control (MRAC) is often used to solve the control problems where the parameters of the controlled object are uncertain or change during the control process. MRAC enables the output of the controlled object to be as close as possible to the output of the reference model by applying the adaptation law. According to the different adaptation methods, MRAC can be divided into two types: direct MRAC and indirect MRAC. The former calculates the output error between the controlled object and the reference model and applies the corresponding adaptation law to adjust the gains of the feedforward control and the feedback control; the latter adjusts the estimated system parameters according to the output error between the estimated system and the reference model, and then adjusts the gains of the feedforward control and the feedback control according to the parameters of the estimated system and the reference model.

[0117] As Figure 2 shown, the present invention mainly applies the indirect MRAC method to the following controlled system: where x ∈ R n is the state variable of the system, u ∈ R m is the input of the system, A and Λ are the parameter matrices of the system and are unknown or slowly changing, and B is known. It is assumed that the state variable of the system and its derivative are bounded, and the control objective of the system is to control the state variable x to track the reference signal x m .

[0118] Suppose the reference model is as follows:

[0119] where x m ∈R n is the system reference state, r ∈ R m is the reference system control input, A m and B m are the reference system parameters. At this time, the control law is:

[0120] where

[0121] Take the parameter adaptation law:

[0122] where Γ A and Γ Λ are the adaptation coefficients used to adjust the effect of the adaptation rate, P is the solution of the equation A m T P + PA m + Q = 0, and Q is a positive definite matrix.

[0123] At this time, the derivative of the Lyapunov function is:

[0124]

[0125] Because the matrix A m is a Hurwitz matrix and satisfies:

[0126] A m T P + PA m + Q = 0 (24);

[0127] According to the properties of the Hurwitz matrix, Q is a positive definite matrix. To sum up, from V ≥ 0 and According to the Lyapunov stability criterion, the designed control input and adaptation law can keep the deviation between the estimated parameters and the reference system and the actual system state variables bounded within a finite time, and the tracking error approaches zero. Therefore, the stability of the designed model reference adaptive controller meets the requirements.

[0128] Before designing the upper controller, it is also necessary to determine the vehicle state safety region and the reference state. During the vehicle driving process, each state variable should be within a safe range to ensure that the vehicle does not become unstable. For the driver, the feedback received when driving the vehicle mainly includes the vehicle speed and the relative position between the vehicle and the target path. Therefore, the vehicle state safety region can be described by the vehicle speed and the curvature during steady-state turning, and the boundary of the vehicle state safety region is determined by the steering wheel angle constraint, the road adhesion constraint, and the vehicle rollover constraint.

[0129] The calculation formula for the vehicle steering curvature κ is as follows:

[0130]

[0131] The boundary of the vehicle state safety region is mainly determined by the following constraints:

[0132] 1. Steering wheel angle constraint: The steering wheel angle is restricted by the steering mechanism and has a maximum angle. Assuming the maximum steering wheel angle value is δ max , and the transmission ratio from the steering wheel angle to the front wheel angle is i, then the maximum value of the vehicle's steady-state yaw rate is:

[0133]

[0134] Therefore, the vehicle steering curvature constraint is:

[0135]

[0136] where ε 1 is the safety factor. In the present invention, δ max = 900°, i = 25.

[0137] 2. Road surface adhesion constraint: When the vehicle is steering, the lateral force is completely provided by the tires. To prevent the tires from skidding laterally, the inertial force generated by the maximum lateral acceleration of the vehicle should not exceed the maximum lateral force when the tires reach the road surface adhesion limit. At this time:

[0138] m|a y | ≤ mgμ (28);

[0139] where Note that in the steady state, At this time, the vehicle steering curvature constraint is:

[0140]

[0141] where ε 2 is the safety factor.

[0142] 3. Vehicle rollover constraint: Considering that the center of mass of a semi-trailer is generally relatively high, on a road surface with good adhesion conditions, rollover may generally occur before tire side slip. Therefore, the vehicle rollover constraint needs to be considered. When rollover occurs, the vertical force of the outer tire is 0, and the resultant force line of the vehicle body gravity and the inertial force of the lateral acceleration passes through the inner tire contact point. That is, a moment balance equation is listed for the inner tire contact point:

[0143]

[0144] where Z is the height from the vehicle body's center of mass to the ground, and B is the vehicle's track width. Assuming they remain unchanged during the roll process, the vehicle steering curvature constraint is obtained as follows:

[0145]

[0146] where ε 3 is the safety factor. In summary, the vehicle state safety region should satisfy the above three constraint conditions simultaneously. Taking the safety factor ε 1 = 0.9, ε 2 = 0.8, ε 3 = 0.8. In the full-load state of the tractor-semitrailer system in this embodiment, when the road surface adhesion coefficient μ = 0.8 and μ = 0.4, the vehicle state safety region is as Figure 3 shown.

[0147] As can be seen from the figure, when the vehicle speed is relatively low, lower than 5 m / s, the vehicle state safety region is only limited by the steering wheel angle, and it can be considered that the vehicle will not become unstable at this time. As the vehicle speed continues to increase, the safety region rapidly shrinks. When the road surface adhesion coefficient is relatively high, the area of the safety region is mainly determined by the rollover constraint; as the road surface adhesion coefficient decreases, the adhesion constraint curve drops below the rollover constraint curve, and the area of the safety region is mainly determined by the adhesion constraint, and the smaller the road surface adhesion coefficient, the smaller the area of the safety region. The vehicle reference state is obtained based on the ideal model and may not necessarily be within the safety region. Therefore, the final result needs to be obtained by comprehensively considering the vehicle state safety region.

[0148] The reference state includes the reference yaw rate and the reference sideslip angle of the center of mass. By comprehensively considering the vehicle state safety region to determine the road surface adhesion constraint and rollover constraint that it needs to satisfy, the reference yaw rate is obtained. The ideal vehicle yaw rate should be the steady-state yaw rate when the tire is in the linear sideslip characteristic, and at this time, the driver feels that the vehicle is easy to control. However, when the road surface adhesion coefficient is relatively low, or the vehicle speed is relatively high, the reference yaw rate calculated by the linear sideslip characteristic tire may not be within the vehicle state safety region. Therefore, the reference yaw rate needs to be obtained by comprehensively considering the vehicle state safety region.

[0149] Reference yaw rate: The steady-state response of the vehicle refers to the output characteristics of each state quantity of the vehicle when the time approaches infinity under the condition of a step input of the steering wheel angle. The steady-state response of the vehicle reflects the degree of reproduction of each state quantity of the vehicle to the steering wheel angle input. The steady-state response of the vehicle is manifested as a constant-speed circular driving, and the steady-state gain, which is the ratio of the steady-state vehicle state quantity to the steering wheel angle, can be used to evaluate the steady-state response of the vehicle.

[0150] When the front wheel angle is δ, the steady-state yaw rate of the linear simplified vehicle model is:

[0151] ω zss = Grss δ (32);

[0152] where G rss is the steady-state gain of the yaw rate r with respect to the front-wheel steering angle; at steady state, the derivatives of all vehicle state variables are 0. Therefore, setting the in Equation (7) to 0 gives:

[0153] Kx = -Lu (33);

[0154] Solving for the steady-state gains of the yaw rates r, r t and sideslip angles β, β t of the tractor and semi-trailer with respect to the front-wheel steering angle:

[0155]

[0156]

[0157] where k ij , l ij refer to the elements in the i-th row and j-th column of the coefficient matrices K and L, respectively. Multiplying the numerator and denominator of the steady-state yaw rate gain G rss by the longitudinal velocity u and then simplifying gives:

[0158]

[0159] where L is the equivalent wheelbase and K is the stability factor, in the following form:

[0160]

[0161] where

[0162] sum 1 = k 1 a - k 2 b - k 3 c (57);

[0163] sum 2 = k 4 a t + k 5 b t + k 6 c t (58);

[0164] sum 3 = (d ht + a t ) k 4 a t + (d ht + b t ) k 5 b t+(d ht +c t )k 6 c t (39);

[0165] sum 4 =(d h -a)k 1 a-(d h +b)k 2 b-(d h +c)k 3 c(40);

[0166] In order to ensure that the reference yaw rate is within the safe vehicle state region, the reference yaw rate also needs to satisfy the road adhesion constraint and the rollover constraint; the angular velocity constraint obtained from the road adhesion constraint is:

[0167]

[0168] The angular velocity constraint obtained from the rollover constraint is:

[0169]

[0170] Therefore, the final reference yaw rate is:

[0171]

[0172] From Figure 4 it can be seen that when the vehicle speed is low, the reference yaw rate is approximately linearly related to the vehicle speed; when the vehicle speed increases to a certain value, the reference yaw rate changes according to the adhesion constraint and the rollover constraint, and the greater the steering wheel angle, the lower the transition speed.

[0173] Reference sideslip angle of the center of mass: The sideslip angle of the center of mass of the vehicle is highly correlated with the vehicle path tracking performance. Generally speaking, the smaller the sideslip angle of the center of mass, the better the vehicle path tracking performance; on a road surface with good adhesion conditions, the sideslip angle of the center of mass should not be greater than 10°; on a low-adhesion road surface, it should not be greater than 4°; at the same time, at high speeds, there is a large phase lag in the sideslip angle of the center of mass. Considering the above factors, the reference sideslip angle of the center of mass is set to be constantly 0, that is:

[0174] β d =0(44).

[0175] Since the vehicle parameters of the semi-trailer vary greatly with different working states, the upper controller adopts model reference adaptive control to make the control effects of the semi-trailer under different parameters the same as those of a reference model under a certain set of parameters. In order to make the model have better control characteristics, a fully-loaded semi-trailer-tractor with a road adhesion coefficient of 0.8 and a vehicle speed of 40 km / h is selected as the reference model. The structure of the upper controller is asFigure 5 As shown. The vehicle electronic stability controller first calculates the reference state variables according to the driver's steering wheel angle input and the vehicle state. Then, the linear quadratic tracker LQT calculates the input to the reference system based on the reference state variables and the actual state variables. The input to the reference system and the actual vehicle state variables pass through the model reference adaptive controller to obtain the input to the actual model. Finally, the lower-layer controller is used to obtain the torques distributed to each axle.

[0176] Design the linear quadratic tracker LQT to calculate the input to the reference system based on the reference state variables and the actual state variables. For the reference model It is required that the system output y follows the desired output y r , and at the same time ensure that the energy consumption is small. The control performance index function is written as:

[0177]

[0178] where the error e = y r - y, and the matrices Q and R are weight coefficients; the corresponding optimal control input is:

[0179] u * (t) = -R -1 B T (Px(t) - g)(46);

[0180] where P is the solution of the Riccati equation A T P + PA - PBR -1 B T P + C T QC = 0, and g is approximately obtained by the following formula:

[0181] g ≈ (PBR -1 B T - A T ) -1 C T Qy r (47).

[0182] S3. Design the lower-layer controller based on the torque distribution algorithm of optimal control, and obtain the optimal solution of the original quadratic programming problem based on the optimal control distribution algorithm of quadratic programming;

[0183] The torque distribution algorithm based on optimal control is specifically as follows: Since the drive axles of the tractor are equipped with in-wheel motors, the drive axles can use electric braking instead of mechanical braking. In this way, under non-emergency conditions, the electronic stability controller can improve the vehicle handling stability by adjusting the torque acting on the drive axles; in case of emergency, the mechanical brakes participate to provide more yaw torque. In this way, while improving the vehicle handling stability, the wear and heat generation of the brakes can be reduced, thereby extending the brake life. The lower-layer torque distribution algorithm process is as Figure 6 shown.

[0184] First, calculate the maximum yaw torque output of the drive axles. According to the torque output characteristic curve of the in-wheel motors as Figure 7 shown, where the curve part can be approximately fitted with an inverse proportional function. According to the wheel speed ω, the maximum torque T max = ε T f(ω) that the motor can output at this time can be obtained, where ε T is the safety factor; since the moment of inertia of the wheels is small, it can be considered that the wheel rotation is in a balanced state. At this time, for the maximum longitudinal force of the tire, there is:

[0185]

[0186] Furthermore, the maximum yaw torque output of the drive axles can be obtained as:

[0187]

[0188] where B is the vehicle track width. Then, distribute the torque to each wheel. Without loss of generality, taking the tractor with saturated in-wheel motor output as an example, after the in-wheel motor output is saturated, a yaw torque M still needs to be generated by the mechanical brakes. Assume that the longitudinal force generated by the mechanical brakes on each wheel is f xi , i = 1, 2,..., 6. Then, the yaw torque generated by the longitudinal force on the vehicle is:

[0189]

[0190] At the same time, f xi also needs to satisfy the tire adhesion limit constraint:

[0191]

[0192] For the non-drive wheels, the longitudinal force is always non-positive: f xi ≤0 (52);

[0193] For the torque distribution of the in-wheel motors on the drive axles, the motor output torque constraint also needs to be satisfied:

[0194]

[0195] Only from Equation (70) and the above constraints, an infinite number of feasible solutions can be obtained. Therefore, an objective function needs to be given to obtain the optimal solution that minimizes the objective function. Since applying longitudinal force will cause tire wear and consume energy, the longitudinal force of the tire should be as small as possible. Therefore, the first term of the objective function can be written as:

[0196] J = f T Hf(54);

[0197] where H is the weight matrix used to adjust the distribution ratio of the longitudinal forces of each tire. Constrained by the road surface adhesion limit, the resultant force of the longitudinal force and the lateral force of the tire will not exceed the maximum adhesion force μf z . When the longitudinal force is large, the proportion of the longitudinal force in the maximum adhesion force is large, leaving less reserve for the lateral force, providing a smaller margin for vehicle stability control, which is not conducive to vehicle stability control. A smaller longitudinal force can prevent wheel slip and wear, and at the same time improve the reliability of control. Therefore, another term is added to the objective function and written as:

[0198] J = f T Hf + ρf(55);

[0199] where

[0200] c i is the weighting coefficient used to adjust the weight of the longitudinal force load rate of each tire; To sum up, the torque distribution problem can be summarized as the following quadratic programming optimal control problem:

[0201]

[0202] where ε M is the error coefficient, that is, when the longitudinal force is near the yaw moment of the vehicle at M and satisfies the road surface adhesion constraint and the torque output constraint, find the longitudinal force value that minimizes the objective function J; Finally, the obtained longitudinal force is converted into the wheel torque output: T i = Rf xi (58).

[0203] The optimal control allocation algorithm based on quadratic programming is specifically as follows: For a quadratic programming problem with equality constraints, the Lagrange method can be applied to solve it, and the lower-layer torque allocation is a quadratic programming problem with inequality constraints, and its common solution algorithms include the interior point method, the trust region reflection method, and the active set method, etc.

[0204] Such as Figure 8As shown, the present invention uses the active set algorithm to solve the quadratic programming problem with inequality constraints, which has high computational efficiency and can obtain the result within fewer iterations. The active set algorithm solves the quadratic programming problem with inequality constraints by transforming the inequality constraints into equality constraints. For the quadratic programming problem with only equality constraints:

[0205]

[0206] Apply the Lagrange method to solve, and the optimal solution is:

[0207]

[0208] where Q = G -1 -G -1 A T (AG -1 A T ) -1 AG -1 , R = G -1 A T (AG -1 A T ) -1 , U = -(AG -1 A T ) -1 ;

[0209] For the quadratic programming problem with inequality constraints:

[0210]

[0211] For a feasible solution, its corresponding active set is the subset of the inequality constraints with equalities and the set of all equality constraints; in each iteration of the solution, select some inequality constraints from the inequality constraints, and form the execution set of this iteration with all equality constraints, and then solve the quadratic programming sub-problem corresponding to this execution set; according to the solution result, change the composition of the inequality constraints in the execution set, and finally obtain the optimal solution of the original quadratic programming problem. The specific algorithm process is as follows:

[0212] At the beginning of the calculation, there is a feasible solution x 0 , and its corresponding execution set is W 0 ; for each iteration, let the current solution be x k , and the execution set is W k ; if x k satisfies the KKT condition, that is, the descent gradient of x k is 0 and λ k has no negative components, then x k is the optimal solution and the solution ends; otherwise, solve the quadratic programming sub-problem corresponding to W k ;

[0213] The sub - problem is described as follows: Expand the objective function at the feasible solution x k to obtain:

[0214]

[0215] The corresponding quadratic programming sub - problem is:

[0216]

[0217] Apply the Lagrange method to solve for the iteration step p k , then the new iterative feasible point is:

[0218] x k+1 = x k + α k p k (63);

[0219] Among them, when α k = 1, the execution set remains unchanged. Otherwise, if x k advances by p k , x k+1 will exceed the feasible region. Take the intersection point of the next advancing direction of x k and the feasible region as x k+1 , and add the touched constraint to the execution set. If the solved p k = 0, then x k is already the optimal solution of the quadratic programming sub - problem. If x k does not satisfy the KKT conditions of the original quadratic programming problem, that is, the Lagrange multiplier λ k corresponding to the optimal solution of the sub - problem has negative components, indicating that there is at least one inequality constraint in the execution set W k such that when x k moves towards the feasible side of this inequality constraint, the value of the objective function decreases. Let x k+1 = x k , and remove the inequality constraint corresponding to the smallest negative component of λ k+1 in the new execution set W k , and iterate in this way.

[0220] S4. Conduct vehicle electronic stability controller simulation and analysis. The vehicle electronic stability controller simulation includes anti - rollover condition simulation, trajectory tracking condition simulation, and anti - folding condition simulation. Among them, the anti - rollover condition simulation and analysis are used to verify the anti - rollover effect of the controller. The working condition for this is a sinusoidal input of the steering wheel angle. The vehicle maintains a certain speed under the control of the driver model and inputs the steering wheel angle according to a sine wave. The relationship between the steering wheel angle and time is as Figure 9 shown, and the peak value of the steering wheel angle is 250°, and the frequency is 0.2 Hz.

[0221] Compare the vehicle state variables in the cases of no electronic stability controller, PID controller, and MRAC controller to verify the rollover prevention effect of the electronic stability controller. When the semi-trailer is fully loaded and driving on a high-adhesion road surface, the main instability form is rollover. Therefore, during the simulation, the semi-trailer is fully loaded, the road adhesion coefficient is 0.8, and the vehicle speed is maintained at 65 km / h. The simulation results are as Figure 10 shown. In the absence of an electronic stability controller, the roll angle of the semi-trailer body increases rapidly and rollover occurs, making the simulation impossible to proceed. Both the PID controller and the MRAC controller can limit the roll angle of the body to prevent the vehicle from rolling over, and the limiting effect of the MRAC is better than that of the PID. In terms of the control of the vehicle's sideslip angle at the center of mass, in the initial stage, the MRAC performs better than the PID on the semi-trailer and can limit the sideslip angle at the center of mass to a smaller range. Subsequently, the two are basically the same; in terms of the performance on the tractor, in the initial stage, the limiting effect of the MRAC on the sideslip angle at the center of mass is stronger than that of the PID. Subsequently, the limiting effect of the PID is better than that of the MRAC. However, it should be noted that the phase of the sideslip angle at the center of mass of the PID lags significantly behind the input of the steering wheel angle, while the lag of the MRAC is not obvious. The lag brought by the controller may have an adverse impact on the driver's operation and reduce the vehicle's handling quality. Therefore, the MRAC electronic stability controller proposed in the present invention has a better effect than the traditional PID controller.

[0222] The simulation and analysis of the trajectory tracking working condition, and the working condition for evaluating the trajectory tracking performance of the controller is the J-turn. The driver maintains a certain vehicle speed to track the target path. The target path is as Figure 11 shown, consisting of a straight section and an arc with a central angle of 120°, and the radius of the arc is 45 meters. During the simulation, the semi-trailer is fully loaded, the road adhesion coefficient is 0.2, and the vehicle speed is maintained at 30 km / h. The simulation results are as Figure 12 shown.

[0223] Due to the understeering characteristics of the vehicle, on a low-adhesion road surface, a vehicle without an electronic stability control system cannot track the target path and runs out of the lane. Both the PID and the MRAC can enable the vehicle to track the target path well. In terms of the control of the yaw rate, the MRAC has a better control effect, and there is only a lag for the semi-trailer; the control effect of the PID meets the requirements, but there is a steady-state error compared with the reference value. In terms of the output of the wheel torque, for the tractor, the wheel torque output by the MRAC is equivalent to that of the PID, but no brakes are used, which can reduce wear and extend the brake life; for the semi-trailer, although the peak value of the torque output by the MRAC is greater than that of the PID, the output torque drops to a lower level after the vehicle state is stable, while the PID always remains at a high value. Therefore, under the condition of similar control effects, the average torque output of the MRAC is smaller, which can reduce brake wear and extend its life.

[0224] To verify the adaptive ability of MRAC, simulations were carried out again with the semi-trailer unloaded and other conditions remaining unchanged, and the control effects of PID and MRAC were compared. The simulation results are as Figure 13 shown. The simulation results show that when the vehicle parameters change significantly, the original PID parameters will deteriorate the control effect and even make the vehicle unstable; while MRAC can adaptively adjust the controller parameters to ensure a good control effect even when the vehicle parameters change significantly.

[0225] Anti-fold condition simulation: When the tractor-semitrailer turns on a low-adhesion road surface and brakes at the same time, it is prone to folding instability. The specific conditions of the simulation are as follows: The semi-trailer is fully loaded, the road adhesion coefficient is 0.2, the initial vehicle speed is 40 km / h, starting from 1 second, braking with a deceleration of -0.74 m / s^2, and at the same time, the steering wheel starts to linearly rotate 180° within 1 second starting from 2 seconds and keeps the final steering angle unchanged. The simulation results are as Figure 14 shown. Without control, the articulation angle of the vehicle will increase rapidly, the sideslip angle and yaw rate of the tractor's center of mass will get out of control, and the vehicle will fold. Under the action of the electronic stability controller, all state variables of the vehicle are limited within a reasonable range, avoiding the occurrence of folding.

[0226] So far, the design of the electronic stability controller for the tractor-semitrailer is completed. The controller adopts a hierarchical structure. The upper-layer controller is responsible for outputting the additional yaw moment, and the lower-layer controller outputs the moments acting on each wheel according to the additional yaw moment output by the upper-layer controller. Aiming at the problem of large parameter changes of the semi-trailer under different working conditions, the upper-layer controller adopts model reference adaptive control. By adding an adaptive rate, the parameters of the reference model are dynamically adjusted, and the output is changed to make the performance of the actual model close to the reference model. The lower-layer controller uses optimal control to distribute torque, which can make full use of the tire load, reduce brake wear, and extend the service life.

[0227] Therefore, the present invention adopts the above-mentioned method for controlling the driving stability of a motor-driven tractor-semitrailer. First, the principle of model reference adaptive control is briefly introduced, and then the three states of the vehicle during the steering process and the principle of direct yaw moment control are introduced. Subsequently, according to the simplified model, the calculation methods of the safe area of the vehicle driving state and the reference values of the vehicle state variables are analyzed. Then, the boundary conditions and objective functions of the lower-layer torque distribution problem are defined, and the active set algorithm for solving the quadratic programming problem is introduced. Finally, simulations are carried out for the anti-rollover, path tracking, anti-fold and adaptive capabilities of the controller, and the control effects of MRAC and PID are compared. MRAC can effectively prevent the vehicle from rolling over, and its control effect is better than that of PID; and compared with PID, MRAC has the ability to adapt to the parameter changes of the semi-trailer and has stronger robustness than PID.

[0228] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent replacements, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for controlling driving stability of a motor-driven tractor-trailer, characterized in that: The following steps are involved: S1. Establish a three-degree-of-freedom dynamic model of the tractor-trailer; S2, a vehicle electronic stability controller adopting a hierarchical structure, comprising an upper controller and a lower controller, wherein an indirect model reference adaptive control (MRAC) method is adopted to design the upper controller; S3, design the lower controller based on the torque allocation algorithm of optimal control, and obtain the optimal solution of the original quadratic programming problem based on the optimal control allocation algorithm of quadratic programming; S4. Simulate and analyze the vehicle electronic stability controller.

2. A method for controlling driving stability of a motor-driven tractor-trailer according to claim 1, characterized in that: In S1, when establishing the three-degree-of-freedom dynamic model of the tractor-trailer, it is assumed that only the longitudinal, lateral and yaw motions of the tractor and the semitrailer are considered, and the motions of the train in the horizontal plane are not considered, and the vertical, pitch and roll motions are not considered. At the same time, the following assumptions are added: The road surface is horizontal; Changes in the vertical load on the tire do not affect the tire's cornering stiffness; The longitudinal velocity of the vehicle remains constant; The articulation angle between the tractor and the semi-trailer is within the range of -20° to 20°; Tire stiffness is linearly related to tire slip angle.

3. A method for controlling driving stability of a motor-driven tractor-trailer according to claim 2, characterized in that: In S1, based on the assumption that the change of the vertical load of the tire does not affect the tire's cornering stiffness, the tires on both sides of the same axle of the vehicle are simplified to one, and the vehicle is simplified to a single-track vehicle model. For the tractor, there is: Where m is the mass of the tractor, u is the longitudinal velocity of the tractor, is the rate of change of the sideslip angle of the tractor's center of mass, r is the yaw rate of the tractor, f1, f2, f3 are the lateral forces of the tractor's tires, and f h is the lateral force of the saddle on the tractor, I z is the moment of inertia of the tractor in the yaw direction, a, b, c are the longitudinal distances from each axle of the tractor to its center of mass, d h is the longitudinal distance from the saddle of the tractor to its center of mass, ΔM is the control input, and is the additional yaw moment acting on the tractor; For semi-trailers, there are: Among them, m t is the mass of the semitrailer, u t is the longitudinal speed of the semitrailer, is the rate of change of the semitrailer's center of mass sideslip angle, r t is the yaw rate of the semitrailer, f4, f5, f6 are the lateral forces of the semitrailer tires, Γ is the articulation angle between the tractor and the semitrailer, I zt is the moment of inertia of the semitrailer in the yaw direction, a t ,b t ,c t are the longitudinal distances from each axle of the semitrailer to its center of mass, d ht is the longitudinal distance from the semitrailer saddle to its center of mass, ΔM t is the control variable input, which is the additional yaw moment acting on the semi-trailer; There are the following kinematic constraints between the tractor and the semi-trailer: Based on the assumption that tire stiffness is linearly related to tire slip angle, the tire force on each axle is calculated as follows: Among them, k i is the linear cornering stiffness of each tire, δ is the tractor front wheel steering angle input; Combining equations (1)-(6), we can eliminate the force f acting on the saddle: h , and let cosΓ=1, we get the linear simplified tractor-trailer dynamic model: Among them, x is the state variable, M is the generalized mass matrix, and u is the control input, which has the following form: k 11 =(d h -a)k1+(d h +b)k2+(d h +c)k3 (11); k 33 =(d ht +a t )k4+(d ht +b t )k5+(d ht +c t )k6 (13); Multiply both sides of equation (7) by M -1 , we get the model of the state space expression, namely: Where A=M -1 K, B = M -1 L.

4. A method for controlling driving stability of a motor-driven tractor-trailer according to claim 1, characterized in that: In S2, the indirect MRAC method estimates the output error between the system and the reference model, applies the adaptive law to adjust the estimated system parameters, and then adjusts the gains of the feedforward control and feedback control according to the parameters of the estimated system and the reference model; For the following controlled systems: Where x∈R n is the state variable of the system, u∈R m is the input of the system, A and Λ are the parameter matrices of the system and are unknown or slowly changing, B is known, assuming that the state variables and their derivatives of the system are bounded, and the control objective of the system is to control the state variable x to track the reference signal x m ; Assume the reference model is: Among them, x m ∈R n is the system reference state, r∈R m is the reference system control input, A m and B m is the reference system parameter; At this time, the control law is: in, Take the parameter adaptive law: Among them, Γ A and Γ Λ is the adaptive coefficient, which is used to adjust the effect of the adaptive rate, and P is the equation A m T P+PA m +Q=0 solution, Q is a positive definite matrix.

5. A method for controlling driving stability of a motor-driven tractor-trailer according to claim 4, characterized in that: In S2, before designing the upper-level controller, the vehicle state safety area and the reference state need to be determined. The vehicle state safety area is described by the vehicle speed and the curvature during steady-state turning, and the boundary of the vehicle state safety area is determined by the steering wheel angle constraint, the road adhesion constraint, and the vehicle rollover constraint. The reference state includes the reference yaw rate and the reference sideslip angle of the center of mass. The road adhesion constraint and rollover constraint to be satisfied are determined by integrating the vehicle state safety area to obtain the reference yaw rate. At the same time, the reference sideslip angle of the center of mass is set to be constant at 0 by integrating the vehicle path tracking performance, adhesion conditions and the phase lag of the sideslip angle of the center of mass at high speed.

6. A method for controlling driving stability of a motor-driven tractor-trailer according to claim 5, characterized in that: In S2, the vehicle electronic stability controller calculates the reference state quantity based on the driver's steering wheel angle input and the vehicle state. The linear quadratic tracker LQT calculates the input to the reference system based on the reference state quantity and the actual state quantity. The input of the reference system and the actual vehicle state quantity are passed through the model reference adaptive controller to obtain the input to the actual model, and finally the torque distributed to each axis is obtained through the lower-level controller.

7. A method for controlling driving stability of a motor-driven tractor-trailer according to claim 6, characterized in that: In S2, the linear quadratic tracker LQT is designed to calculate the input to the reference system based on the reference state quantity and the actual state quantity; For reference models y=Cx+Du, requiring the system output y to follow the expected output y r , and at the same time ensure that the energy consumption is small, the performance index function of the control is written as: Where, error e = y r -y, matrix Q, R are weight coefficients; The corresponding optimal control input is: u * (t)=-R -1 B T (Px(t)-g)(24); Where P is the Riccati equation A T P+PA-PBR -1 B T P+C T For the solution of QC=0, g is approximately obtained by the following formula: g≈(PBR -1 B T -A T ) -1 C T Qy r (25)。 8. The method for controlling driving stability of a motor-driven tractor-trailer according to claim 1, characterized in that: In S3, the torque distribution algorithm based on optimal control is specifically: The tractor drive shaft adopts a wheel hub motor. First, the maximum output yaw moment of the drive shaft is calculated. The maximum torque of the motor is obtained according to the output characteristic curve of the wheel hub motor and the wheel speed, and then the maximum output yaw moment of the drive shaft is obtained. The torque is distributed to each wheel, considering the tire adhesion limit constraint, the non-driven wheel longitudinal force constraint and the motor output torque constraint. The objective function is constructed with the goal of making the tire longitudinal force as small as possible, preventing wheel slippage and wear, and improving control reliability. The torque distribution problem is summarized as a quadratic programming optimal control problem.

9. A method for controlling driving stability of a motor-driven tractor-trailer according to claim 1, characterized in that: In S3, the optimal control allocation algorithm based on quadratic programming is specifically: The active set algorithm is used to solve the quadratic programming problem with inequality constraints. The inequality constraints are converted into equality constraints. The problem is solved iteratively. In each iteration, the KKT condition is determined based on the current solution and the execution set. If not, the corresponding quadratic programming subproblem is solved. The execution set and iterative feasible points are updated according to the solution results until the optimal solution of the original quadratic programming is obtained. Finally, the longitudinal force is converted into wheel torque output.

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