Distributed driving ideal yaw target setting and stability control method

Abstract

The invention discloses a distributed driving ideal yaw target setting and stability control method, which comprises the following steps of: establishing a whole vehicle dynamics model suitable for controller design, inputting related parameters through a vehicle, combining front and rear wheel side slip angle phase planes, carrying out region division of a stable state, and carrying out target setting and stability control on the whole vehicle dynamics model. According to the method, maneuverability and stability analysis and setting are carried out on the yaw velocity, the yaw velocity is fused, steady state control and feed-forward control are generated through the first step and the second step of a three-step method, then feedback control is carried out through an LQR controller, finally, the three quantities are superposed to obtain the needed additional yaw moment, reasonable distribution control is carried out based on the additional yaw moment, and the control precision is improved. The method aims at minimizing the distribution error and reducing the tire load utilization rate, adopts a multi-target optimization torque distribution strategy to distribute the four-wheel torque, and controls the four-wheel torque of the vehicle so as to achieve the purpose of distributed driving control.

Description

Technical Field

[0001] The present invention belongs to the technical field of vehicle stability control, and particularly relates to an ideal yaw target setting and stability control method for distributed drive. Background Art

[0002] With the evolution of vehicle drive modes, four-wheel drive electric vehicles have been continuously developed. For four-wheel independently driven electric vehicles, the torques and rotational speeds of the four wheels can be independently controlled, and thus more precise vehicle dynamics control can be achieved to improve vehicle handling stability. Torque vector control usually takes the ideal yaw angular velocity as the main control target. Therefore, reasonable target setting is particularly important. At present, the ideal yaw target is mostly obtained by multiplying the steering wheel angle by the steady-state yaw gain and is constrained according to the road surface adhesion coefficient. Although this method can improve vehicle handling stability, there are still some problems. More importantly, it is difficult to quantify the improvement effect of torque vector control on the handling stability of distributed drive vehicles, especially in the control algorithm development stage, and it is impossible to timely evaluate the rationality of the ideal yaw target design and the effectiveness of the torque vector control method. Therefore, designing an effective method for setting the ideal target of distributed drive control and performing stability control has become the research focus. Summary of the Invention

[0003] To solve the above technical problems, the present invention provides an ideal yaw target setting and stability control method for distributed drive, including the following steps:

[0004] Step 1: Establish a vehicle dynamics model applicable to controller design;

[0005] The dynamic equations describing the lateral motion and yaw motion of a two-degree-of-freedom vehicle are as follows:

[0006] In the formula, are the lateral reaction forces of the ground on the front and rear wheels, is the distance from the front axle to the center of mass, is the distance from the rear axle to the center of mass, is the front wheel angle, is the additional yaw moment, is the vehicle yaw angular velocity, is the center of mass sideslip angle, is the vehicle moment of inertia, is the longitudinal velocity of the center of mass, is the vehicle mass;

[0007] The tire sideslip characteristics are in the linear region and are expressed as:

[0008] In the formula, is the equivalent sideslip stiffness of the front axle, is the equivalent cornering stiffness of the rear axle, are the cornering angles of the front and rear wheels, expressed as:

[0009]

[0010] Step 2: By inputting relevant vehicle parameters and combining the phase plane of the front and rear wheel cornering angles, perform the division of the steady-state region, define the vehicle stability index, and normalize the result of the region division to characterize the vehicle's steady state;

[0011] Further, the specific steps are as follows:

[0012] Determine the saddle point positions in the phase plane of the front and rear wheel cornering angles. The left and right saddle point coordinates are expressed in the following form:

[0013]

[0014] Among them, are the coordinates of the left saddle point in the phase plane and the coordinates of the right saddle point in the phase plane, are the abscissa of the left saddle point, the ordinate of the left saddle point, the abscissa of the right saddle point, and the ordinate of the right saddle point respectively;

[0015] The yaw rate corresponding to the left saddle point and the yaw rate corresponding to the right saddle point and the sideslip angle of the center of mass corresponding to the left saddle point and the sideslip angle of the center of mass corresponding to the right saddle point are expressed as:

[0016]

[0017]

[0018] Among them, is the road surface adhesion coefficient, is the acceleration due to gravity, is the longitudinal acceleration, represents the tire cornering angle corresponding to the maximum lateral force, that is:

[0019]

[0020] In the formula, respectively represent different fitting parameters of the phase plane, and the specific expressions are as follows:

[0021]

[0022]

[0023]

[0024]

[0025] Among them, is the parameter to be identified.

[0026] The left and right saddle point coordinate data under different vehicle speeds, front wheel steering angles, road adhesion coefficients, and longitudinal accelerations can be fitted through the Matlab toolbox to obtain the left and right saddle point coordinates and as:

[0027]

[0028]

[0029] Combined with the above tire cornering characteristics, the front and rear wheel cornering angle phase plane is divided into a stable region and an unstable region. The region centered at the origin with a radius of represents the stable region, where , where represents the absolute value of the front wheel cornering angle corresponding to the ordinate in the normalized tire cornering characteristic curve of the front wheel;

[0030] The expression for the radius of the unstable region is as follows:

[0031]

[0032] where is the saddle point coordinate closest to the origin.

[0033] Define the vehicle stability index to characterize the stable state of the vehicle:

[0034] If :

[0035]

[0036] If :

[0037]

[0038] Among them, represents the distance from the actual state of the front and rear wheel cornering angles of the current vehicle to the origin, and its calculation formula is as follows:

[0039]

[0040] Step 3: Set the ideal yaw rate;

[0041] The setting of the ideal yaw rate is divided into the setting of the ideal yaw rate for maneuverability and the ideal yaw rate for stability, and the yaw rate is fused in combination with the stability index, so that the ideal yaw rate has different expressions in different stable state intervals.

[0042] Furthermore, the setting of the maneuverability yaw rate is as follows:

[0043] Front wheel steering angle Expressed as:

[0044]

[0045] In the formula, is the wheelbase, is the turning radius, is the set target understeer degree, is the lateral acceleration, is the Ackermann steering angle, is the dynamic steering angle;

[0046] The relationship between the dynamic steering angle and the lateral acceleration is expressed as follows:

[0047]

[0048] Among them, are three adjustable parameters; is the set target understeer degree, is the set limit value of the lateral acceleration in the linear region, is the set target maximum lateral acceleration;

[0049] Express the lateral acceleration in the following form:

[0050]

[0051]

[0052] By reasonably setting , the maneuverability yaw rate under steady-state conditions is obtained, and its specific expression is as follows:

[0053]

[0054] The setting of the three parameters is as follows:

[0055] (1) Set ( The understeer degree of the base vehicle) can increase the steady-state yaw rate gain, making the vehicle's steering response more sensitive, thereby improving steering accuracy and enhancing handling performance;

[0056] (2) Set ( The lateral acceleration limit value of the linear region of the base vehicle) can expand the linear region of the vehicle's steering characteristics, enabling the vehicle to maintain good handling at a larger range of lateral accelerations, and thus providing a smoother and more predictable driving experience for the driver;

[0057] (3) Set ( The maximum lateral acceleration of the base vehicle) can increase the maximum lateral acceleration that the vehicle can achieve, keeping the vehicle stable under extreme conditions, reducing the risk of sideslip and spin-out, and thus improving driving safety.

[0058] Perform a Laplace transform on the vehicle's linear two-degree-of-freedom differential equation, and rearrange the terms to obtain the required transfer function. Combining the transfer function, the final ideal yaw rate target for handling is expressed in the following form:

[0059]

[0060] Among them, is the transfer function of the yaw rate expected value filter, is the complex frequency variable in the Laplace transform, is the natural frequency; is the damping ratio; is the time constant.

[0061] Furthermore, the stability yaw rate is set as follows:

[0062] Tire lateral force is a non-linear function that varies continuously with the tire sideslip angle, and the expression is as follows:

[0063]

[0064] Among them, respectively represent the front and rear wheels, are the front and rear wheel sideslip angles;

[0065] Perform a first-order Taylor expansion on the above non-linear function near the operating point to obtain a linear expression:

[0066]

[0067] Let:

[0068]

[0069] When the operating point is at the origin, it is the zero stiffness in the tire lateral force curve, which is the cornering stiffness. When the operating point is not at the origin, it is the tangent stiffness of the tire at the operating point .

[0070] The nonlinear two-degree-of-freedom vehicle dynamics equation is expressed as:

[0071]

[0072] The equilibrium point of the vehicle dynamics system is the state point that satisfies ;

[0073] Using the first Lyapunov method, the stability of this nonlinear vehicle dynamics system at the equilibrium point is judged, and the designed ideal front and rear wheel cornering characteristics are shown in the following formula:

[0074]

[0075]

[0076] In the formula, are the front and rear wheel lateral forces obtained by simplifying the tire cornering characteristics to set the ideal yaw rate of stability. are the cornering angles at the boundary between the linear region and the transition region and the cornering angle at the boundary between the transition region and the saturation region respectively. is the front wheel cornering angle, is the rear wheel cornering angle.

[0077] Integrating the two-degree-of-freedom vehicle model, the yaw rate of stability under stable conditions is obtained:

[0078]

[0079] In the formula, is the limit of the steady-state yaw rate, .

[0080] The final ideal yaw rate target of stability is expressed as follows:

[0081]

[0082] Among them, represents the natural frequency; represents the damping ratio; represents the time constant. By reasonably setting , the transient response characteristics of the ideal yaw rate for stability can be characterized.

[0083] Furthermore, the vehicle stability index obtained in the second step is used to fuse the target of the ideal yaw rate for maneuverability and the target of the ideal yaw rate for stability, and the final ideal yaw rate target is obtained; the fused ideal yaw rate target is expressed in the following form:

[0084]

[0085] where is the target of the ideal yaw rate for maneuverability, is the target of the ideal yaw rate for stability, is the vehicle stability index, is the fused ideal yaw rate target.

[0086] Step 4: Generate the steady-state control and feedforward control from the first and second steps of the three-step method, then perform feedback control by the LQR controller, and finally superimpose these three quantities to obtain the required additional yaw moment;

[0087] The steady-state control and feedforward control are designed as follows:

[0088] According to the two-degree-of-freedom vehicle model, let , the steady-state control quantity of the three-step method satisfies the following relationship:

[0089]

[0090] The desired steady-state control input of the three-step method is obtained:

[0091] On the basis of the steady-state control, considering the dynamic change of the system ideal yaw rate target , a reference feedforward control quantity is introduced, and the control input is expanded to:

[0092]

[0093] Substitute the above formula into the two-degree-of-freedom vehicle model and substitute the expression of , and we get:

[0094]

[0095] Let , and the feedforward control quantity is obtained as:

[0096] The LQR feedback controller is designed as follows:

[0097] Considering the additional yaw moment control quantity The linear two-degree-of-freedom vehicle dynamics state-space equation is as follows:

[0098]

[0099] Among them, the state vector includes the actual sideslip angle of the center of mass and the yaw angular velocity is the front wheel steering angle, and the additional yaw moment control quantity makes the state vector track its ideal value; is the system matrix, is the control matrix, is the input matrix;

[0100] Design the state feedback matrix The optimal control rate is: where is the error vector; Define the ideal state vector: Then there is ;

[0101] Combine the steady-state control and feedforward control based on the three-step method with the feedback control based on LQR to form the final additional yaw moment:

[0102]

[0103] Among them, and are the steady-state and dynamic feedforward control quantities based on the three-step method respectively, is the feedback control quantity based on LQR.

[0104] In the feedback control based on LQR, by adjusting the parameters in the weight matrix Q, the tracking degrees of the system for the two control objectives of the ideal yaw angular velocity and the ideal sideslip angle of the center of mass are balanced, and the comprehensive control performance of the vehicle under different driving conditions is optimized based on the stability index The adaptive weight;

[0105] The weight matrix The weight of the sideslip angle error of the center of mass and the weight of the yaw angular velocity error in are designed as functions of the stability index

[0106]

[0107] Among them, is a parameter, which is obtained through optimization.

[0108] When When the vehicle state is in the stable region, the ideal yaw rate control target is only composed of the ideal yaw rate target for maneuverability; when When the vehicle state enters the unstable region, the ideal yaw rate control target gradually incorporates the ideal yaw rate target for stability.

[0109] Step Five: Based on the additional yaw moment obtained in Step Four , aiming to minimize the distribution error and reduce the tire load utilization rate, a multi-objective optimization torque distribution strategy is adopted to distribute the four-wheel torque and control the four-wheel torques of the vehicle.

[0110] Furthermore, the steps for minimizing the distribution error include:

[0111] Let the desired generalized resultant force vector composed of the desired total driving force and the additional yaw moment be:

[0112]

[0113] where is the vehicle's desired additional yaw moment output by the upper-layer additional yaw moment decision controller, is the total driving force desired by the driver, and its calculation expression is as follows:

[0114]

[0115] where is the wheel rolling radius, is the total demand torque of the driver calculated by the driver demand torque analysis module based on the pedal opening signal;

[0116] When the vehicle is driving normally, since the front wheel angle is small, let , the dynamic equation of the system is expressed as:

[0117]

[0118] where is the longitudinal force of the left front wheel, is the longitudinal force of the left rear wheel, is the longitudinal force of the left rear wheel, is the longitudinal force of the right rear wheel, are the track widths of the front and rear axles of the vehicle respectively;

[0119] Define the lower-layer control quantity as:

[0120]

[0121] Then rewrite the dynamic equation as:

[0122]

[0123] Among them, represents the generalized resultant force acting on the vehicle's center of mass, including the total driving force and the additional yaw moment of the whole vehicle ; the matrix is the efficiency matrix, defined as follows:

[0124]

[0125] Based on the above analysis, the first objective function is defined to minimize the distribution error, and the formula is:

[0126]

[0127] Among them, is the error weight matrix, which is used to describe the priorities of the system for the additional yaw moment demand of the whole vehicle and the driver's longitudinal driving force demand.

[0128] The steps of reducing the tire load utilization rate are as follows:

[0129] The tire load utilization rate refers to the ratio of the tire force to the maximum adhesion force that the ground can provide, and is defined as:

[0130]

[0131] Among them, respectively represent the longitudinal, lateral and vertical forces of the tire, is the adhesion coefficient between each wheel and the road surface;

[0132] The second objective function is defined to minimize the tire load utilization rate of each wheel, and the formula is:

[0133]

[0134] Among them, is the tire load utilization rate weight matrix, defined as:

[0135]

[0136] Considering the actuator constraints and the tire adhesion limit constraints, the longitudinal forces of each wheel of the vehicle must satisfy:

[0137]

[0138] Among them, is the tire radius, is the maximum torque of each motor;

[0139] The optimization distribution problem of the lower - layer driving force is expressed as:

[0140]

[0141] Wherein, is the weighting factor; the above - mentioned optimization problem is solved by the active - set method, and finally the torque control amounts of the four motors of the distributed - drive vehicle are obtained : .

[0142] Advantages of the present invention:

[0143] The present invention provides an ideal yaw target setting and stability control method suitable for distributed drive. The driver operates the steering wheel, and inputs the steering wheel angle into the vehicle stability analysis and ideal target setting module. This module combines the corresponding parameters of the vehicle, calculates the vehicle stability index and ideal target through calculation, and inputs the parameters into the three - step feed - forward and LQR feedback controller. This controller inputs the calculated additional yaw moment into the controlled vehicle, and adopts a multi - objective optimization torque distribution strategy. Combining with the torque distribution module, the torques corresponding to the four wheels are input into the controlled vehicle to achieve the purpose of distributed drive control. Brief Description of the Drawings

[0144] Figure 1 is a schematic diagram of the overall flow of the control method of the present invention.

[0145] Figure 2 is a schematic diagram of the standard two - degree - of - freedom vehicle model for controller design in the present invention.

[0146] Figure 3 is a schematic diagram of the stable region division of the front - and - rear wheel sideslip angles in the phase plane in the present invention.

[0147] Figure 4 is a schematic diagram of the lateral forces of the front and rear tires under the pure sideslip condition in the present invention.

[0148] Figure 5 is a schematic diagram of the curve of the additional front - wheel steering angle and the lateral acceleration in the present invention.

[0149] Figure 6 is a schematic diagram of the calculation of the ideal yaw angular velocity target for stability in the present invention. Detailed Embodiment

[0150] The following further describes the present invention with reference to the drawings. As Figure 1 shown, the detailed embodiment of an ideal yaw target setting and stability control method for distributed drive provided by the present invention is as follows:

[0151] Step 1: Establish a vehicle dynamics model suitable for controller design;

[0152] As Figure 2 shown, due to the computing power limitation of the controller and the requirements for the accuracy of the vehicle model, the standard two-degree-of-freedom vehicle model is adopted in the present invention. Through the dynamic analysis of this model, the dynamic equations describing the lateral motion and yaw motion of the two-degree-of-freedom vehicle are obtained as follows:

[0153]

[0154] In the formula, are the lateral reaction forces of the ground on the front and rear wheels, is the distance from the front axle to the center of mass, is the distance from the rear axle to the center of mass, is the front wheel steering angle, is the additional yaw moment, is the vehicle yaw angular velocity, is the sideslip angle of the center of mass, is the moment of inertia of the whole vehicle, is the longitudinal velocity of the center of mass, is the mass of the whole vehicle.

[0155] Considering that the front wheel steering angle is small, so the sideslip angles of the front and rear wheels are small, and the side-slip characteristics of the tires are in the linear region, then there are:

[0156] In the formula, is the equivalent cornering stiffness of the front axle, is the equivalent cornering stiffness of the rear axle, are the sideslip angles of the front and rear wheels, expressed as:

[0157]

[0158] Step 2: Through the vehicle input related parameters, combined with the sideslip angle phase plane of the front and rear wheels, conduct the regional division of the steady state, and normalize the results of the regional division;

[0159] Furthermore, the specific steps are as follows:

[0160] Determine the saddle point positions in the sideslip angle phase plane of the front and rear wheels. The left and right saddle point coordinates are expressed in the following forms:

[0161]

[0162] Among them, are the coordinates of the left saddle point of the phase plane and the coordinates of the right saddle point of the phase plane respectively, are the abscissa of the left saddle point, the ordinate of the left saddle point, the abscissa of the right saddle point, and the ordinate of the right saddle point respectively;

[0163] The actual positions of the left and right saddle points are determined by the two-dimensional coordinates formed by the front and rear wheel slip angles, and the front and rear wheel slip angles are related to the yaw rate and the center-of-mass slip angle; the yaw rate corresponding to the left saddle point and the yaw rate corresponding to the right saddle point and the center-of-mass slip angle corresponding to the left saddle point and the center-of-mass slip angle corresponding to the right saddle point are expressed as:

[0164]

[0165]

[0166] wherein, is the road surface adhesion coefficient, is the gravitational acceleration, is the longitudinal acceleration, represents the tire slip angle corresponding to the maximum lateral force, which is affected by the road surface adhesion, and the two are approximately linearly related, that is:

[0167] In the formula, respectively represent different fitting parameters of the phase plane, and the specific expressions are as follows:

[0168]

[0169]

[0170]

[0171]

[0172] wherein, is the parameter to be identified.

[0173] The left and right saddle point coordinate data under different vehicle speeds, front wheel steering angles, road surface adhesion coefficients, and longitudinal accelerations can be fitted through the Matlab toolbox to obtain the left and right saddle point coordinates as:

[0174]

[0175]

[0176] The present invention divides the phase plane of the front and rear wheel slip angles into a stable region and an unstable region in combination with the above-mentioned tire slip characteristics, and both regions are centered on the origin; as Figure 3 shown, the green circular region centered on the origin with a radius of represents the stable region, wherein , wherein is expressed as in the normalized tire slip characteristic curve of the front wheel, the ordinate The absolute value of the corresponding front wheel sideslip angle.

[0177] The red circular area is defined as the unstable area, and its radius expression is as follows:

[0178]

[0179] where are the coordinates of the saddle point closest to the origin.

[0180] Define the stability index to characterize the stable state of the vehicle:

[0181] If :

[0182]

[0183] If :

[0184]

[0185] where represents the distance from the actual state of the front and rear wheel sideslip angles of the current vehicle to the origin, and its calculation formula is as follows:

[0186]

[0187] Step 3: Set the ideal yaw rate;

[0188] The setting of the ideal yaw rate is divided into the setting of the maneuverability ideal yaw rate and the stability ideal yaw rate, and the yaw rate is fused in combination with the stability index, so that the ideal yaw rate has different expressions in different stable state intervals.

[0189] The setting of the maneuverability yaw rate is as follows:

[0190] The front wheel steering angle is expressed as:

[0191] In the formula, is the wheelbase, is the turning radius, is the set target understeer degree, is the lateral acceleration, is the Ackermann steering angle, is the dynamic steering angle;

[0192] The relationship between the dynamic steering angle and the lateral acceleration is expressed as follows:

[0193]

[0194] where are three adjustable parameters; is the set lateral acceleration limit value in the linear region, is the set target maximum lateral acceleration;

[0195] Let be expressed in the following form:

[0196]

[0197]

[0198] By reasonably setting , the handling yaw rate under steady-state conditions can be obtained, and its specific expression is as follows:

[0199]

[0200] By setting these three parameters, the following design goals can be achieved:

[0201] (1) Setting ( is the understeer degree of the base vehicle) can increase the steady-state yaw rate gain, making the vehicle's steering response more sensitive, thereby improving steering accuracy and enhancing handling performance;

[0202] (2) Setting ( is the lateral acceleration limit value in the linear region of the base vehicle) can expand the linear region of the vehicle's steering characteristics, enabling the vehicle to maintain good handling at a larger range of lateral accelerations, and thus providing a smoother and more predictable driving experience for the driver;

[0203] (3) Setting ( is the maximum lateral acceleration of the base vehicle) can increase the maximum lateral acceleration that the vehicle can achieve, keeping the vehicle stable under extreme conditions, reducing the risk of sideslip and spin, and thus improving driving safety.

[0204] Taking the Laplace transform of the vehicle's linear two-degree-of-freedom differential equation and rearranging the terms, the required transfer function can be obtained. Combining with the transfer function, the final ideal handling yaw rate target is expressed in the following form:

[0205]

[0206] where, is the transfer function of the yaw rate expected value filter, is the complex frequency variable in the Laplace transform, is the natural frequency; is the damping ratio; is the time constant. By reasonably setting , the transient response characteristics of the operational ideal yaw rate can be characterized.

[0207] The stability yaw rate is set as follows:

[0208] The stability ideal yaw rate target functions to ensure vehicle stability and avoid oversteering of the vehicle, which may cause danger. The tire side force curves of the front and rear wheels in the pure slip angle state are as Figure 4 shown. The tire side force is a non-linear function that continuously changes with the tire slip angle. The tire side force has the following expression:

[0209]

[0210] where respectively represent the front and rear wheels, are the slip angles of the front and rear wheels;

[0211] Perform a first-order Taylor expansion of the above non-linear function near the operating point to obtain a linear approximation expression:

[0212] Let:

[0213] When the operating point is at the origin, is the zero stiffness in the tire side force curve, that is, the cornering stiffness, as shown by Line1 in Figure 4 ; as shown by Line2 in Figure 4 , when the operating point is not at the origin, is the tangent stiffness of the tire at the operating point .

[0214] The non-linear two-degree-of-freedom vehicle dynamics equation is expressed as:

[0215]

[0216] The equilibrium point of the vehicle dynamics system is the state point that satisfies; using the first Lyapunov method, judge the stability of this non-linear vehicle dynamics system at the equilibrium point . First, linearize the non-linear vehicle dynamics system at the equilibrium point to obtain the Jacobian matrix of the system, that is, the first-order partial derivative matrix of the system equation with respect to the state variables , and its expression is:

[0217]

[0218] Among them, are the tangent stiffnesses of the front and rear wheels at the equilibrium point respectively.

[0219] If all the eigenvalues of the Jacobian matrix have negative real parts, the original non-linear vehicle dynamics system is stable at this equilibrium point, and this stability condition is expressed as:

[0220]

[0221] Among them, are the tangent stiffnesses of the front and rear wheels at the equilibrium point respectively, are the trace and determinant of the Jacobian matrix respectively, is the wheelbase of the vehicle, is the moment of inertia of the vehicle about the z-axis, is the total vehicle mass, is the vehicle speed.

[0222] The stability of the system at the equilibrium point includes the following four cases:

[0223] Case 1 The sideslip states of both the front and rear wheels are in the rising region of the tire lateral force curve, as Figure 4 shown, that is , and at this time is satisfied; when , is satisfied, the system is stable at the equilibrium point, and at this time the vehicle has understeering characteristics or neutral steering characteristics ; when , the vehicle has oversteering characteristics, and at this time the stability condition for is:

[0224]

[0225] Among them, is the critical vehicle speed.

[0226] Case 2 The sideslip state of the front wheel is in the falling region of the tire lateral force curve, and the sideslip state of the rear wheel is in the rising region of the tire lateral force curve, that is ; usually the tangent slope in the falling region is smaller, that is , so is satisfied; the stability condition for is:

[0227]

[0228] When the front wheel is working in the falling region, the rear wheel usually works in the non-linear region, that is Very small and relatively small, so this situation can ensure the system stability; in addition, since , compared with Case 1, in this situation is larger, and the understeering characteristic of the vehicle is stronger.

[0229] In Case 3, the front wheel sideslip state is in the rising region of the tire lateral force curve, and the rear wheel sideslip state is in the falling region of the tire lateral force curve, that is ; at this time , indicating that the system has two eigenvalues with opposite signs, and the system state cannot maintain stability near this point, and this equilibrium point is a saddle point.

[0230] In Case 4, the front and rear wheel sideslip states are both in the falling region of the tire lateral force curve, that is ; at this time, it satisfies , the system has two positive eigenvalues, and the system state will diverge along the corresponding direction near this point, and this equilibrium point is an unstable point.

[0231] It can be seen from the above analysis that the stability of the vehicle is mainly affected by the tire sideslip state, and the key factor leading to vehicle instability is that the rear wheel sideslip characteristic enters the falling region. Based on the above analysis, if an ideal front and rear wheel sideslip characteristic that ensures the vehicle always has stability is to be designed, the following conditions need to be met:

[0232] (1) The absolute value difference of the front and rear wheel sideslip angles in the linear region is greater than zero;

[0233] (2) The standardized tire sideslip characteristic curves of the front and rear wheels should avoid crossing;

[0234] (3) The rear wheel lateral force should avoid saturation, and the front wheel lateral force should gradually tend to saturation as the sideslip angle increases, but does not decrease, and finally tends to a certain value.

[0235] The ideal front and rear wheel sideslip characteristics designed according to the above requirements are shown in the following formula:

[0236]

[0237]

[0238] In the formula, are the front and rear wheel lateral forces obtained by simplifying the tire sideslip characteristic to set the ideal yaw rate for stability, are respectively the sideslip angles at the boundary between the linear region and the transition region and the sideslip angles at the boundary between the transition region and the saturation region, is the front wheel sideslip angle, is the rear wheel sideslip angle.

[0239] This design effectively avoids the problem of vehicle instability caused by the rear wheels entering the descending region in the side slip state. At the same time, the understeering characteristics exhibited by this design have a linear segment, a transition segment, and a saturation segment, which are similar to the steering characteristics of an actual vehicle. A vehicle with such ideal front and rear wheel side slip characteristics can maintain the maximum lateral acceleration achievable by the front wheels.

[0240] As Figure 5 shown, under the condition of road surface adhesion coefficient μ = 1.0, the steering characteristics of the basic vehicle and the steering characteristics expressed by the two designed ideal yaw targets are presented. The design idea of the stability ideal yaw rate target is as follows:

[0241] (1) When , the designed is close, so that the finally fused yaw rate target remains , ensuring the improvement effect of vehicle maneuverability.

[0242] (2) When , increase the understeer degree of the vehicle to make it close to the steering characteristics of the basic vehicle, but not exceed the understeer degree of the basic vehicle. This can not only ensure the stability of the vehicle but also guarantee a certain improvement effect on maneuverability.

[0243] (3) When , the target maximum lateral acceleration is reached. At this time, the lateral force of the front wheels based on which the design is carried out no longer changes. If the lateral force of the rear wheels continues to increase, will decrease, avoiding vehicle instability caused by the saturation of the rear wheel lateral force.

[0244] The calculation block diagram of the stability yaw rate target is as Figure 6 shown. Integrating the two-degree-of-freedom vehicle model, the stability yaw rate under stable conditions is obtained:

[0245]

[0246] In the formula, is the limit of the steady-state yaw rate, .

[0247] In order to characterize the transient characteristics of the stability yaw rate target, a response transfer function is established for it. The final expression of the stability ideal yaw rate target is as follows:

[0248]

[0249] Among them, [[ID= represents the damping ratio; represents the time constant. By reasonably setting , the transient response characteristics of the ideal yaw rate for stability can be characterized.

[0250] Using the vehicle stability index obtained in the second step, the ideal yaw rate target for maneuverability and the ideal yaw rate target for stability are fused to obtain the final ideal yaw rate target. The fused ideal yaw rate target is expressed in the following form:

[0251]

[0252] where is the ideal yaw rate target for maneuverability, is the ideal yaw rate target for stability, is the vehicle stability index, is the fused ideal yaw rate target.

[0253] Step Four: Design the controller for three-step feedforward and LQR feedback.

[0254] The feedforward design is as follows:

[0255] According to the two-degree-of-freedom vehicle model, let , the three-step steady-state control quantity satisfies the following relationship:

[0256]

[0257] The desired three-step steady-state control input is obtained:

[0258] Based on the steady-state control, considering the dynamic change of the ideal yaw rate target of the system, the reference feedforward control quantity is introduced, and the control input is expanded to:

[0259]

[0260] Substitute the above formula into the two-degree-of-freedom vehicle model and substitute the expression of, we get:

[0261] Let , the feedforward control quantity is obtained as:

[0262] The LQR feedback controller design is as follows:

[0263] Considering the additional yaw moment control quantity The linear two-degree-of-freedom vehicle dynamics state space equation is as follows:

[0264] Among them, the state vector includes the actual sideslip angle of the center of mass and the yaw rate is the front wheel steering angle, and the additional yaw moment control quantity makes the state vector track its ideal value; is the system matrix, is the control matrix, is the input matrix.

[0265] Design the state feedback matrix , and the optimal control rate is: , where is the error vector; define the ideal state vector: , then there is .

[0266] Combine the steady-state control and feedforward control based on the three-step method with the feedback control based on LQR to form the final additional yaw moment:

[0267] Among them, are the steady-state and dynamic feedforward control quantities based on the three-step method respectively, is the feedback control quantity based on LQR.

[0268] In the feedback control based on LQR, in fact, only by adjusting the parameters in the weight matrix Q can the tracking degree of the system for the two control objectives of the ideal yaw rate and the ideal sideslip angle of the center of mass be balanced. From the perspective of actual driving requirements, when the vehicle is in the stable region, improving the maneuverability should be given priority; while when the vehicle is approaching the unstable region, stability control should become the primary goal. For this reason, the present invention designs an adaptive weight based on the stability index to optimize the comprehensive control performance of the vehicle under different driving conditions.

[0269] The weight matrix The weight of the sideslip angle error of the center of mass and the weight of the yaw rate error in are designed as functions of the stability index

[0270]

[0271] Among them, are parameters, obtained through optimization, and take values of = 0.001, = 0.5, = 0.5, When = 0.8, the system control effect is better.

[0272] When , the vehicle state is in the stable region. At this time, the ideal yaw rate control target is only composed of the ideal yaw rate target for maneuverability, and the weight is close to zero, while is relatively large, making the torque vector control mainly focus on improving the maneuverability of the vehicle. When , the vehicle state enters the unstable region. At this time, the ideal yaw rate control target gradually integrates the ideal yaw rate target for stability, the weight increases, and the weight decreases, so that the torque vector control can effectively suppress the further deterioration of the vehicle state and significantly improve the driving safety. <{

[0273] Step Five: Based on the additional yaw moment obtained in Step Four, aiming to minimize the distribution error and reduce the tire load utilization rate, a multi-objective optimization torque distribution strategy is adopted to distribute the four-wheel torque and control the four-wheel torque of the vehicle.

[0274] For the lower-layer driving torque distribution problem of the torque vector control of distributed drive vehicles, the present invention adopts a multi-objective optimization torque distribution strategy to distribute the four-wheel torque. This strategy can ensure the stable margin of the wheels while making the torque control amount of each motor meet the upper-layer control target, thus achieving a better control effect.

[0275] The steps for minimizing the distribution error include:

[0276] Let the expected generalized resultant force vector composed of the expected total driving force and the additional yaw moment be:

[0277]

[0278] where is the expected additional yaw moment of the whole vehicle output by the upper-layer additional yaw moment decision controller, is the total driving force expected by the driver, and its calculation expression is as follows:

[0279]

[0280] where is the wheel rolling radius, is the total demand torque of the driver calculated by the driver demand torque analysis module according to the pedal opening signal;

[0281] When the vehicle is driving normally, since the front wheel angle is small, let , so the lateral force on the total driving force and the additional yaw moment of the whole vehicle The influence. At this time, the dynamic equation of the system is expressed as:

[0282]

[0283] Among them, is the longitudinal force of the left front wheel, is the longitudinal force of the left rear wheel, is the longitudinal force of the left rear wheel, is the longitudinal force of the right rear wheel, are the track widths of the front and rear axles of the vehicle respectively.

[0284] Define the lower-layer control variable as:

[0285] Then the dynamic equation is rewritten as:

[0286] Among them, represents the generalized resultant force acting on the vehicle's center of mass, including the total driving force and the additional yaw moment of the whole vehicle ; The matrix is the efficiency matrix, defined as follows:

[0287]

[0288] Based on the above analysis, define the first objective function to minimize the distribution error, and the formula is:

[0289] Among them, is the error weight matrix, which is used to describe the priorities of the system for the demand of the additional yaw moment of the whole vehicle and the driver's longitudinal driving force demand.

[0290] The steps of reducing the tire load utilization rate are as follows:

[0291] The tire load utilization rate refers to the ratio of the tire force to the maximum adhesion force that the ground can provide, and is defined as: ;

[0292] Among them, respectively represent the longitudinal, lateral and vertical forces of the tire, is the adhesion coefficient between each wheel and the road surface.

[0293] Reducing the tire load utilization rate can increase the tire adhesion margin, avoid the tire force reaching the adhesion limit, and thus improve the vehicle's stability. Since each in-wheel motor of the distributed drive vehicle directly controls the longitudinal force of the tire, and the lateral force is a constant term for the optimization problem and will not affect the optimal solution. Therefore, define the second objective function To minimize the tire load utilization rate of each wheel, the formula is: ;

[0294] where, is the tire load utilization rate weight matrix, defined as: ;

[0295] Considering the actuator constraints and tire adhesion limit constraints, the longitudinal forces of each wheel of the vehicle must satisfy:

[0296]

[0297] where, is the tire radius, is the maximum torque of each motor.

[0298] In summary, the lower-layer driving force optimization distribution problem is expressed as:

[0299]

[0300] where, is the weighting factor. Solve the above optimization problem by the active set method, and finally obtain the torque control quantities of the four motors of the distributed drive vehicle :

[0301] .

Claims

1. An ideal yaw target setting and stability control method for distributed drive, characterized in that: It includes the following steps: Step 1: Establish a vehicle dynamics model applicable to controller design; Step 2: Through vehicle input-related parameters, combined with the front and rear wheel sideslip angle phase plane, conduct a stable state region division, define a vehicle stability index, and normalize the result of the region division to characterize the vehicle's stable state; Step 3: Set the ideal yaw rate; the setting of the ideal yaw rate includes the setting of the maneuverability ideal yaw rate and the stability ideal yaw rate. Use the vehicle stability index obtained in Step 2 to fuse the maneuverability ideal yaw rate target and the stability ideal yaw rate target to obtain the final ideal yaw rate target; the fused ideal yaw rate target is expressed in the following form: ， Among them, is the target of the ideal yaw rate for maneuverability, is the target of the ideal yaw rate for stability, is the vehicle stability index, is the target of the ideal yaw rate after fusion; Step 4: Generate steady-state control and feedforward control from the first and second steps of the three-step method, then perform feedback control by the LQR controller, and finally superimpose these three quantities to obtain the required additional yaw moment; The steady-state control and feedforward control are designed as follows: According to the two-degree-of-freedom vehicle model, let , the steady-state control quantity of the three-step method satisfies the following relationship: ， Among them, is the vehicle yaw rate, is the lateral reaction force of the ground on the front and rear wheels, is the distance from the front axle to the center of mass, is the distance from the rear axle to the center of mass, is the steady-state feedforward control quantity, is the moment of inertia of the whole vehicle; Obtain the desired three-step steady-state control input: ; Based on the steady-state control, considering the dynamic change of the ideal yaw rate target of the system introduce the reference feedforward control quantity , and the control input is expanded to: ; is the additional yaw moment, is the dynamic feedforward control quantity; Substitute the above formula into the two-degree-of-freedom vehicle model and substitute the expression of to obtain: ; Let , the feedforward control quantity is obtained as follows: ; The LQR feedback controller is designed as follows: Consider the additional yaw moment control amount The linear two-degree-of-freedom vehicle dynamics state space equation is as follows: , Among them, the state vector includes the actual centroidal sideslip angle and the yaw rate is the front wheel steering angle, and the additional yaw moment control quantity makes the state vector track its ideal value; is the system matrix, is the control matrix, is the input matrix; Design state feedback matrix , the optimal control rate is: , where is the error vector; define the ideal state vector: , then there is ; Combine the steady-state control and feedforward control based on the three-step method with the feedback control based on LQR to form the final additional yaw moment: , Among them, are the steady-state and dynamic feedforward control quantities based on the three-step method, is the feedback control quantity based on LQR; Step 5: Based on the additional yaw moment finally obtained in Step 4 , aiming to minimize the distribution error and reduce the tire load utilization rate, a multi-objective optimization torque distribution strategy is adopted to distribute the torques of the four wheels and control the torques of the four wheels of the vehicle.

2. A method for setting an ideal yaw target and stability control of a distributed drive, according to claim 1, characterized in that: The vehicle dynamics model established in Step 1 is as follows: ， In the formula, is the lateral reaction force of the ground on the front and rear wheels, is the distance from the front axle to the center of mass, is the distance from the rear axle to the center of mass, is the front wheel steering angle, is the additional yaw moment, is the vehicle yaw rate, is the sideslip angle of the center of mass, is the vehicle moment of inertia, is the longitudinal speed of the center of mass, is the vehicle mass; The tire sideslip characteristics are in the linear region and are expressed as: ， In the formula, is the equivalent cornering stiffness of the front axle, is the equivalent cornering stiffness of the rear axle, , For the front and rear wheel sideslip angles, it is expressed as: 。 3. A method for setting an ideal yaw target and stability control of a distributed drive, according to claim 1, characterized in that: The specific steps of Step 2 are as follows: Determine the saddle point positions in the front and rear wheel sideslip angle phase plane, and the left and right saddle point coordinates are expressed in the following form: ， Among them, are respectively the coordinates of the left saddle point and the right saddle point in the phase plane, are respectively the abscissa of the left saddle point, the ordinate of the left saddle point, the abscissa of the right saddle point, and the ordinate of the right saddle point; The yaw rate corresponding to the left saddle point and the yaw rate corresponding to the right saddle point and the sideslip angle of the center of mass corresponding to the left saddle point and the sideslip angle of the center of mass corresponding to the right saddle point are expressed as: ， ， wherein, is the road surface adhesion coefficient, is the acceleration due to gravity, is the longitudinal acceleration, is the longitudinal speed of the center of mass, represents the tire sideslip angle corresponding to the maximum lateral force, i.e.: ; In the formula respectively represent different fitting parameters of the phase plane, and the specific expressions are as follows: ， Among them, is the parameter to be identified, is the front wheel steering angle; By fitting the left and right saddle point coordinate data under different vehicle speeds, front wheel angles, road surface adhesion coefficients, and longitudinal accelerations, the left and right saddle point coordinates are obtained as follows: ， Combined with the above tire cornering characteristics, the front and rear wheel cornering angle phase plane is divided into a stable region and an unstable region. The region centered at the origin with a radius of represents the stable region, where , where is expressed as the absolute value of the front wheel cornering angle corresponding to the ordinate in the normalized tire cornering characteristic curve of the front wheel; The expression of the unstable region radius is as follows: ， Among them is the saddle point coordinate closest to the origin; Define the vehicle stability index to characterize the stable state of the vehicle: If :[[]]END]] , If :[[]]END]] , Among them, represents the distance from the actual state of the sideslip angles of the front and rear wheels of the current vehicle to the origin, and its calculation formula is as follows: 。 4. A method for setting an ideal yaw target and stability control of a distributed drive according to claim 1, characterized in that: The maneuverability yaw rate setting described in Step 3 is as follows: Front wheel steering angle Expressed as: ， In the formula, is the wheelbase, is the turning radius, is the set target understeer degree, is the lateral acceleration, is the Ackermann steering angle, is the dynamic steering angle; The relationship between the dynamic steering angle and the lateral acceleration is expressed as follows: ， Among them, are three adjustable parameters; is the set target understeer degree, is the set linear region lateral acceleration limit value, is the set target maximum lateral acceleration; Express the lateral acceleration in the following form: ， By reasonable setting , the handling yaw rate under steady-state conditions can be obtained , and its specific expression is as follows: ， Laplace transform is performed on the linear two-degree-of-freedom differential equation of the vehicle, and after transposing and arranging, the required transfer function is obtained. Combining with the transfer function, the ideal yaw rate target of the handling performance is finally expressed in the following form: ， Among them, is the transfer function of the yaw rate desired value filter, is the complex frequency variable in the Laplace transform, is the natural frequency; is the damping ratio; is the time constant.

5. A method for setting an ideal yaw target and stability control of a distributed drive, according to claim 4, characterized in that: The settings of the three parameters are as follows: (1) Setting , is the understeer degree of the base vehicle; (2) Setting is the lateral acceleration limit value of the basic vehicle linear region; (3) Setting is the maximum lateral acceleration of the basic vehicle.

6. A method for setting an ideal yaw target and stability control of a distributed drive according to claim 1, characterized in that: The stability yaw rate setting described in Step 3 is as follows: Lateral force of tire is a non-linear function that varies continuously with the tire's side slip angle, and the expression is as follows: ， Among them, respectively represent the front and rear wheels, are the sideslip angles of the front and rear wheels; Perform a first-order Taylor expansion of the above non-linear function around the operating point to obtain a linear expression: ， Let: ， When the operating point is at the origin, it is the zero stiffness in the tire lateral force curve, that is, the cornering stiffness. When the operating point is not at the origin, it is the tangent stiffness of the tire at the operating point ; The nonlinear two-degree-of-freedom vehicle dynamics equation is expressed as: ， Equilibrium point of the vehicle dynamics system is the state point that satisfies ; Using the first Lyapunov method, the stability of the nonlinear vehicle dynamics system at the equilibrium point is judged, and the ideal front and rear wheel sideslip characteristics are designed as shown in the following formula: ， In the formula, are the lateral forces of the front and rear wheels obtained by simplifying the tire cornering characteristics for setting the ideal yaw rate of stability, are the cornering angles at the boundary between the linear region and the transition region and the cornering angle at the boundary between the transition region and the saturation region respectively, is the front wheel cornering angle, is the rear wheel cornering angle; Integrate the two-degree-of-freedom vehicle model to obtain the steady-state yaw rate : ， In the formula, is the steady-state yaw rate limit, ; Final stability ideal yaw rate target The expression is as follows: ， Among them, represents the natural frequency; represents the damping ratio; represents the time constant; By reasonably setting , the transient response characteristics of the ideal yaw rate for stability can be characterized.

7. A method for setting an ideal yaw target and stability control of a distributed drive, according to claim 1, characterized in that: In Step 4, in the feedback control based on LQR, by adjusting the parameters in the weight matrix Q, the tracking degrees of the system for the two control objectives of the ideal yaw rate and the ideal sideslip angle of the center of mass are balanced, and based on the adaptive weights of the stability index , the comprehensive control performance of the vehicle under different driving conditions is optimized; Weight matrix The weight of the centroid sideslip angle error And the weight of the yaw rate error Are designed as stability indicators Of the function, defined as follows: ， Among them, is a parameter obtained through optimization; When the vehicle state is in the stable region, the ideal yaw rate control target is only composed of the handling ideal yaw rate target at this time; when the vehicle state enters the unstable region, the ideal yaw rate control target gradually integrates the stability ideal yaw rate target.

8. A method for setting an ideal yaw target and stability control of a distributed drive, according to claim 1, characterized in that: The minimization of the distribution error described in Step 5 includes: Let the desired generalized resultant force vector composed of the desired total driving force and the additional yaw moment be as follows: ， wherein, is the vehicle's expected additional yaw moment output by the upper-layer additional yaw moment decision-making controller, is the total driving force expected by the driver, and its calculation expression is as follows: ， Among them, is the rolling radius of the wheel, is the total driver demand torque calculated by the driver demand torque analysis module based on the pedal opening signal; Let , the dynamic equation of the system is expressed as: ， Among them, is the longitudinal force of the left front wheel, is the longitudinal force of the left rear wheel, is the longitudinal force of the left rear wheel, is the longitudinal force of the right rear wheel, and are the track widths of the front and rear axles of the vehicle respectively; Define the lower-layer control quantity as follows: ; The kinetic equation is then rewritten as: , Among them, represents the generalized resultant force acting on the vehicle's center of mass, including the total driving force and the additional yaw moment of the whole vehicle ; the matrix is the efficiency matrix and is defined as follows: ， Define the first objective function to minimize the allocation error, with the formula: , Among them, is the error weight matrix, which is used to describe the priorities of the vehicle's additional yaw moment demand and the driver's longitudinal driving force demand of the system.

9. A method for setting an ideal yaw target and stability control of a distributed drive, according to claim 1, characterized in that: The reduction of the tire load utilization rate described in Step 5 includes: The tire load utilization rate refers to the ratio of the tire force to the maximum adhesion force that the ground can provide and is defined as: ， Among them, respectively represent the longitudinal, lateral and vertical forces of the tire, are the adhesion coefficients between each wheel and the road surface; Define the second objective function To minimize the tire load utilization rate of each wheel, the formula is: ， Among them, is the tire load utilization rate weight matrix, defined as: ； Considering the actuator constraint and the tire adhesion limit constraint, the longitudinal forces of each wheel of the vehicle must satisfy: ， Among them, is the tire radius, is the maximum torque of each motor; The lower-layer driving force optimization distribution problem is expressed as: ， Among them, is the weighting factor; the above optimization problem is solved by the active set method, and finally the torque control amounts of the four motors of the distributed drive vehicle are obtained : .

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