Electric vehicle stability control method based on steady-state lateral acceleration gain

Abstract

The invention discloses an electric vehicle stability control method based on steady-state lateral acceleration gain. The method comprises a steady-state yaw reference model, a steady-state lateral acceleration gain model, a feedback control module, a feedforward control module, a rear wheel differential yaw moment distribution module and a vehicle module. The steady-state yaw reference model and the steady-state lateral acceleration gain model are respectively used for calculating an expected yaw velocity and an ideal steering transmission ratio yaw velocity; the vehicle module is used for outputting actual state quantities of the vehicle, including longitudinal vehicle speed, yaw velocity and steering wheel angle; the feedback control module and the feed-forward control module determine feedback yawing moment and feed-forward yawing moment respectively, the feedback yawing moment and the feed-forward yawing moment are added to determine total yawing moment, and the rear wheel differential yawing moment distribution module distributes the total yawing moment according to steady-state characteristic categories of a vehicle and transmits the total yawing moment to the vehicle module for control. Therefore, the lateral stability and the maneuvering performance of the automobile are improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of automobile stability control, and more specifically to an electric vehicle stability control method based on steady-state lateral acceleration gain. BACKGROUND

[0002] With the rapid development of electric vehicle technology, the electric drive system provides more flexible and accurate control means for vehicle power control and steering control. Compared with traditional internal combustion engine vehicles, electric vehicles have unique distributed drive characteristics. In particular, in distributed drive electric vehicles, through independent control of each wheel by the motor, driving force can be more accurately allocated, thereby significantly improving vehicle dynamic performance and handling stability, and becoming an important trend in the development of the automobile industry. Among them, rear wheel differential control as an important part of distributed drive can provide additional yaw moment without relying on front wheel steering, and has important significance in improving vehicle handling capability.

[0003] In automobile design, handling and stability are key performance indicators that affect vehicle driving safety and driving experience, especially in high-speed steering, emergency obstacle avoidance and other extreme conditions. How to ensure stability while achieving high response handling adjustment has become a key issue. Vehicle stability control strategies based on model predictive control (MPC) have been widely studied. Patent CN108107732B proposes a combined control method combining active front wheel steering and direct yaw moment, which realizes dynamic optimization adjustment of yaw rate by constructing a linear time-varying MPC controller and embedding a tire nonlinear modeling structure. This method has certain effect in improving the stability of vehicles in extreme conditions, but its control target dimension is relatively single, and the control execution mechanism still relies on traditional front wheel mechanical steering and four-wheel braking system, lacks modeling of ideal steering characteristics of vehicles, and does not introduce a feedforward compensation mechanism to enhance dynamic response capability.

[0004] In addition, patent CN108107731B proposes an MPC control architecture that switches the prediction model through side stiffness to enhance the modeling capability of the control system in different side stiffness intervals. This method expands the adaptability of tire modeling and introduces the center of mass side slip angle as an auxiliary control target, which has certain improvement in yaw control accuracy. However, its control strategy is still based on a closed-loop feedback control architecture, and the control execution mechanism is still limited to traditional braking and steering mechanisms, without constructing a feedforward and feedback collaborative channel for dynamic conditions, and without increasing the corresponding characteristics of the system from the feedforward control level. SUMMARY

[0005] To solve the above problems, the application provides an electric vehicle stability control method based on steady-state lateral acceleration gain, which adopts a strategy combining feedforward control and feedback control. The feedforward control can quickly respond to ideal steering demand, optimize the power output and response time of the vehicle, and thus improve the stability of operation; the feedback control ensures the stability of the vehicle under various complex working conditions, and provides more flexible and safe operation performance.

[0006] Firstly, the application comprehensively considers the steady-state response characteristics of the vehicle, and designs the ideal transmission ratio yaw rate of the vehicle based on the steady-state gain of lateral acceleration. On this basis, a rear wheel differential steering auxiliary model is established to determine the feedforward yaw moment required to achieve the ideal steering characteristics, and then the feedforward compensation control of the vehicle is realized. Secondly, a steady-state yaw reference model is established to calculate the expected yaw rate, and a lateral stability feedback controller based on model predictive control (MPC) is designed, which solves the feedback yaw moment to realize the tracking of the expected yaw rate and the mass side slip angle. Finally, according to the steady-state response type of the vehicle, the total yaw moment generated is reasonably distributed to the hub motors on the driving wheels, so as to improve the stability and maneuverability of the vehicle.

[0007] The technical scheme adopted by the application to solve the technical problems is as follows:

[0008] An electric vehicle stability control method based on steady-state lateral acceleration gain, the method comprising a steady-state yaw reference model, a steady-state lateral acceleration gain model, a feedback control module, a feedforward control module, a rear wheel differential yaw moment distribution module and a vehicle module; the steady-state yaw reference model and the steady-state lateral acceleration gain model are respectively used to calculate the expected yaw rate and the ideal steering transmission ratio yaw rate; the vehicle module is used to output the actual state quantity of the vehicle, including the longitudinal vehicle speed, the yaw rate and the steering wheel angle; the feedback control module and the feedforward control module are respectively used to determine the feedback yaw moment and the feedforward yaw moment, and the sum of the two determines the total yaw moment; the rear wheel differential yaw moment distribution module distributes the total yaw moment according to the steady-state characteristic category of the vehicle and transmits it to the vehicle module for control, so as to improve the lateral stability and maneuverability of the vehicle.

[0009] The method comprises the following steps:

[0010] Step 1, design a steady-state yaw reference model:

[0011] This module is used to determine the expected yaw rate , and the expression is as follows:

[0012] (1)

[0013] In the formula, is the mass of the whole vehicle. is the vehicle longitudinal speed; and are the distances from the vehicle mass center to the front and rear axles, respectively; and are the tire cornering stiffness of the front and rear wheels, respectively; is the front wheel mechanical steering fixed transmission ratio; is the steering wheel angle.

[0014] Step 2, design the steady-state lateral acceleration gain module:

[0015] The module design includes the following sub-steps:

[0016] Step 2.1, construct the ideal transmission ratio based on the steady-state lateral acceleration gain model The specific formula is as follows:

[0017] (2)

[0018] In the formula, is the vehicle longitudinal speed; and are the distances from the vehicle mass center to the front and rear axles, respectively; is the lateral acceleration gain; is the minimum transmission ratio; is the speed threshold constant; is the stability factor.

[0019] Step 2.2, to make the transmission ratio characteristics more continuous and smooth during speed changes, use the S function to fit the basic expression, get the fitting expression, the specific formula is as follows:

[0020] (3)

[0021] Step 2.3, considering the steering wheel angle, add the transmission ratio with steering wheel angle influence coefficient , get the ideal steering transmission ratio correction expression, the specific expression is as follows:

[0022] (4)

[0023] In the formula, , , are all fitting parameters; is the transmission ratio with steering wheel angle influence coefficient; e is the base of natural logarithm; is the steering wheel angle; is the vehicle longitudinal speed; is the vehicle longitudinal speed constant.

[0024] Step 2.4, Calculate the ideal front wheel steering angle :

[0025] (5)

[0026] where, is the ideal front wheel steering angle.

[0027] Step 2.5, Calculate the ideal steering ratio generated by the steady-state lateral acceleration gain model yaw rate :

[0028] (6)

[0029] where, is the total vehicle mass; and are the distances from the vehicle center of mass to the front and rear axles, respectively; and are the lateral stiffness of the front and rear tires, respectively.

[0030] Step 3, Design the feedback control module:

[0031] This module is designed based on the model predictive control algorithm; its design includes the following sub-steps:

[0032] Step 3.1, Establish the incremental discrete state space equation for the model predictive control algorithm:

[0033] Establish a two-degree-of-freedom vehicle dynamics model:

[0034] (7)

[0035] where, is the lateral velocity of the vehicle; and are the lateral forces of the front and rear tires, respectively; is the yaw moment of inertia around the vertical axis of the vehicle center of mass; is the yaw rate of the vehicle; is the yaw moment of the vehicle.

[0036] The two-degree-of-freedom vehicle differential equation expression can be obtained as follows:

[0037] (8)

[0038] where, is the vehicle center of mass side slip angle; is the yaw rate of the vehicle; is the front wheel steering angle.

[0039] Write equation (8) in the form of a standard state space equation:

[0040] (9)

[0041] wherein, ; ; ; ;

[0042] wherein, is the total vehicle mass; is the lateral velocity of the vehicle; is the longitudinal velocity of the vehicle; and are the distances from the vehicle mass center to the front and rear axles, respectively; is the yaw moment of inertia about the vertical axis through the vehicle mass center; is the side slip angle of the vehicle mass center; is the yaw rate of the vehicle; and are the lateral stiffness of the front and rear tires of the vehicle, respectively.

[0043] The continuous-time state-space model shown in equation (9) is converted into a discrete-time model that can be implemented in a digital control system. The present application uses the zero-order hold method to discretize the system. Let the sampling period of the system be , the present application will use 0.01s, under the condition that the input remains unchanged, the discrete-time form of the system can be written as:

[0044] (10)

[0045] wherein, wherein is the state vector at the current sampling time; is the control input; is the disturbance input; is the state transition matrix of the system; the integral term is the input response matrix.

[0046] To further simplify the expression, the discrete system matrix is defined as follows:

[0047] ;

[0048] From this, the incremental discrete prediction model is obtained as follows:

[0049] (11)

[0050] wherein, ;

[0051] wherein, is the current sampling time; is the State variable increment of step State variable increment of step State variable of current time Predicted output of current time Predicted output of last time

[0052] Step 3.2, Calculate predicted output, according to model predictive control theory, take prediction horizon as , control horizon as , can get predicted output at current time k as:

[0053] (12)

[0054] Where, predicted output matrix ; control input increment matrix ; reference output sequence matrix ;

[0055] In the formula, , respectively as expected yaw rate and expected side slip angle, is an identity matrix, ; ; .

[0056] Step 3.3, design optimization target and constraint condition:

[0057] Use the two norm of the deviation of expected yaw rate and yaw rate in prediction horizon as yaw rate tracking performance index, its expression as follows:

[0058] (13)

[0059] In the formula, is the weighted factor of yaw rate tracking performance; is expected yaw rate; is actual yaw rate; is prediction horizon.

[0060] Use the two norm of the deviation of expected side slip angle and side slip angle in prediction horizon as side slip angle tracking performance index, its expression as follows:

[0061] (14)

[0062] In the formula, is the weighted factor of yaw rate tracking performance; is expected side slip angle; is actual side slip angle.

[0063] The two-norm of the control amount variation is used as the control amount smoothing index, and its expression is as follows:

[0064] (15)

[0065] In the formula, is a weighting factor for the control input variation; is the yaw moment increment; is the control time domain.

[0066] The actuator physical constraints are set to meet the actuator requirements:

[0067] (16)

[0068] In the formula, is the control variable, i.e., the yaw moment increment ; is the upper limit of the yaw moment increment; is the lower limit of the yaw moment increment; is the upper limit of the yaw moment increment variation; is the lower limit of the yaw moment increment variation.

[0069] Step 3.4, solve the system control input:

[0070] The tracking performance index described in formula (13) and formula (14) and the control amount smoothing index described in formula (15) are converted into a single index using the linear weighting method, and a multi-objective optimization control problem is constructed:

[0071] (17)

[0072] In the controller, a quadratic programming algorithm is used to solve the multi-objective optimization control problem as shown in formula (17) to obtain the optimal open-loop control sequence :

[0073] (18)

[0074] In the formula, is a weighting factor for the yaw angle velocity tracking performance; is the expected center side slip angle; is the actual center side slip angle; is the prediction time domain; is a weighting factor for the yaw angle velocity tracking performance; is the expected yaw angle velocity; is the actual yaw angle velocity; is a weighting factor for the control input variation; is the yaw moment increment; is the control time domain.

[0075] The first element of the optimal open-loop control sequence at the current time is selected for feedback, and the yaw moment feedback value is obtained by linear superposition with the previous time , which is output to the rear wheel differential yaw moment distribution module.

[0076] Step 4, design the feedforward control module:

[0077] Given the standard state space equation (9), when the system is stable, At this time , that is :

[0078] In the formula, ; = ; = ;

[0079] Where, is the mass of the vehicle; is the longitudinal speed of the vehicle; and are the distances from the vehicle mass center to the front and rear axles, respectively; and are the lateral stiffness of the front and rear tires of the vehicle, respectively; is the front wheel steering angle.

[0080] Substituting into equation (9) can derive when there is a feedforward yaw moment :

[0081] (19)

[0082] In the formula, = = ; = ;

[0083] In the formula, is the yaw moment of inertia around the vertical axis of the vehicle mass center; is the yaw rate calculated by the steady-state lateral acceleration gain model.

[0084] When there is no feedforward yaw moment :

[0085] (20)

[0086] From the above two formulas, the steady-state yaw moment feedforward value is obtained:

[0087] (21)

[0088] wherein, = ; = ;

[0089] wherein, is the ideal drive ratio yaw rate calculated by the steady-state lateral acceleration gain model; is the desired yaw rate.

[0090] Step 5, rear wheel differential yaw moment distribution module design:

[0091] The rear wheel differential yaw moment distribution module includes 5.1 wheel braking torque calculation and 5.2 yaw moment distribution strategy, wherein the wheel braking torque calculation is used to convert the yaw moment into the braking torque of the rear wheel, and the yaw moment distribution strategy determines the specific braking wheel through the steering characteristics of the vehicle. The specific steps are as follows:

[0092] Step 5.1, the specific formula of the wheel braking torque calculation is as follows:

[0093] (22)

[0094] wherein, is the braking torque; is the wheel track of the rear wheel of the vehicle; is the distance from the mass center of the vehicle to the rear axle; is the rolling radius of the wheel.

[0095] Step 5.2, the yaw moment distribution strategy determines the specific braking wheel through the steering characteristics of the vehicle, and the steering characteristics of the vehicle include three steering characteristics of understeering, oversteering and neutral steering. The stability factor will be determined, and the specific formula of the stability factor is as follows:

[0096] (23)

[0097] wherein, is the total mass of the vehicle; and are the distances from the mass center of the vehicle to the front and rear axles, respectively; and are the cornering stiffnesses of the front and rear tires of the vehicle, respectively.

[0098] When in formula (23), the stability factor At this time, the vehicle is understeering characteristic, and the problem of large turning radius is prone to occur. At this time, if the vehicle turns left, the wheel braking torque calculated by formula (22) is distributed to the left rear wheel, and the yaw moment is generated by braking the left rear wheel; at this time, if the vehicle turns right, the wheel braking torque calculated by formula (22) is distributed to the right rear wheel, and the yaw moment is generated by braking the right rear wheel, so as to ensure the steering stability of the vehicle.

[0099] When , the stability factor At this time, the vehicle is oversteering characteristic, that is, the steering response is too fast, and there is a risk of tail instability. At this time, if the vehicle turns right, the wheel braking torque calculated by formula (22) is distributed to the left rear wheel, and the yaw moment is generated by braking the left rear wheel; at this time, if the vehicle turns left, the wheel braking torque calculated by formula (22) is distributed to the right rear wheel, and the yaw moment is generated by braking the right rear wheel, so as to ensure the steering stability of the vehicle.

[0100] When , the stability factor The vehicle is in neutral steering characteristic. However, in actual driving, due to factors such as lateral load transfer and road adhesion condition change, the vehicle may deviate from the neutral steering characteristic and develop towards the oversteering characteristic or the understeering characteristic. Among them, the oversteering characteristic is more likely to cause the vehicle to lose stability, especially when driving at high speed or changing lanes in an emergency, which may cause the vehicle to rotate or slide, seriously threatening the driving safety. Therefore, in order to ensure the stability of the vehicle, the wheel braking torque will be distributed according to the oversteering characteristic, which will not be described here. BRIEF DESCRIPTION OF DRAWINGS

[0101] Figure 1 is a control system structure schematic diagram of the present application.

[0102] Figure 2 is a linear two-degree-of-freedom automobile model schematic diagram. DETAILED DESCRIPTION

[0103] The present application will be described in detail below in combination with the drawings and examples.

[0104] Figure 1The system structure schematic diagram of the electric vehicle stability control method based on the steady-state lateral acceleration gain is a system structure schematic diagram of the electric vehicle stability control method based on the steady-state lateral acceleration gain, and the system mainly comprises a steady-state yaw reference model 1, a steady-state lateral acceleration gain model 2, a feedback control module 3, a feedforward control module 4, a rear wheel differential yaw moment distribution module 5 and a vehicle module 6. The steady-state yaw reference model 1 and the steady-state lateral acceleration gain model 2 are respectively used for calculating a desired yaw rate and an ideal steering transmission ratio yaw rate; the vehicle module 6 is used for outputting actual state quantities of the automobile, including a longitudinal vehicle speed, a yaw rate and a steering wheel angle; the feedback control module 3 is used for solving a yaw moment feedback value required for realizing lateral stability of the vehicle according to the desired yaw rate and actual yaw rate state information of the automobile based on a model predictive control algorithm optimization; the feedforward control module 4 is used for solving a yaw moment feedforward value according to the ideal steering transmission ratio yaw rate calculated by the steady-state lateral acceleration gain model 2 and the desired yaw rate calculated by the steady-state yaw reference model 1, so as to improve the handling of the automobile; the rear wheel differential yaw moment distribution module 5 receives a total yaw moment generated by the feedforward control module 4 and the feedback control module 3 and reasonably distributes the total yaw moment according to a steady-state characteristic category, and outputs each wheel moment obtained after the distribution to the vehicle module 6 for automobile stability control, so as to improve the lateral stability and handling performance of the automobile.

[0105] To verify the effectiveness and engineering feasibility of the control strategy, a high-precision vehicle dynamics model is introduced to carry out system modeling and control effect verification. In the specific implementation method, a CarSim 2020 vehicle model is used as a core simulation platform, combined with high-speed steering, emergency obstacle avoidance and other typical extreme working conditions to build a whole vehicle lateral dynamics system, and through the joint simulation architecture of CarSim and Simulink, the comprehensive evaluation of the yaw rate tracking accuracy, the control effect of the mass side slip angle and the rear wheel yaw moment directional distribution logic is realized, which is the key verification basis before the subsequent real vehicle experiment. The following takes a certain distributed drive electric vehicle in the CarSim automobile simulation software as an example to specifically explain the method of the application, and the main parameters of the Carsim automobile are as follows:

[0106] The mass of the automobile m is 1231 ; the distance a from the mass center of the automobile to the front axle is 1.04 m; the distance b from the mass center of the automobile to the front axle is 1.56 m; the yaw moment of inertia around the vertical axis of the mass center of the automobile is 2031.4 ; the wheel track d of the automobile is 1.481 m; and the effective rolling radius r of the wheel is 0.31 m.

[0107] In step 1, the steady-state yaw reference model 1 is designed:

[0108] This module is used for determining the desired yaw rate , and the expression is as follows:

[0109] (24)

[0110] where, is the total vehicle mass; is the vehicle longitudinal speed; and are the distances from the vehicle mass center to the front and rear axles, respectively and are the tire cornering stiffness of the front and rear wheels, respectively; is the front wheel mechanical steering fixed transmission ratio; is the steering wheel angle.

[0111] The steady-state lateral acceleration gain model 2 is designed in step 2:

[0112] It includes the following five parts: step 2.1, constructing the basic expression of the ideal steering transmission ratio according to the steady-state lateral acceleration gain model; step 2.2, determining the fitting expression of the ideal steering transmission ratio ; step 2.3, determining the correction expression of the ideal steering transmission ratio ; step 2.4, calculating the ideal front wheel steering angle ; and step 2.5, calculating the ideal steering transmission ratio yaw rate .

[0113] In step 2.1, the basic expression of the ideal steering transmission ratio is constructed according to the steady-state lateral acceleration gain model:

[0114] (25)

[0115] where, is the lateral acceleration gain value 7.51; is the stability factor; is the minimum transmission ratio value 9.6; is the speed threshold constant value 30 .

[0116] In step 2.2, the fitting expression of the ideal steering transmission ratio is determined:

[0117] Considering that the transmission ratio should not have a sudden change in the process of speed change for more continuity and smoothness, the S function is selected to fit the curve of formula (25), and the fitting expression is obtained, and the specific expression is selected as follows:

[0118] (26)

[0119] The ideal transmission ratio is determined in step 2.3 The correction expression is:

[0120] The steering wheel angle is considered and a gain coefficient influenced by the steering wheel angle is added In this design, the maximum transmission ratio is obtained when the fixed yaw rate gain is 0.3 The ideal steering transmission ratio is obtained by replacing the value of coefficient A2 The correction expression is:

[0121] (27)

[0122] In the formula, , , are fitting parameters; is a transmission ratio coefficient influenced by the steering wheel angle; e is the base of natural logarithm; is the steering wheel angle; is the longitudinal speed of the vehicle; is the constant of the longitudinal speed of the vehicle.

[0123] The ideal front wheel angle is calculated in step 2.4 :

[0124] (28)

[0125] In the formula, is the ideal front wheel angle.

[0126] The ideal transmission ratio yaw rate generated by the steady-state lateral acceleration gain model is calculated in step 2.5 :

[0127] (29)

[0128] In the formula, is the mass of the vehicle; and are the distances from the mass center of the vehicle to the front and rear axles, respectively; and are the lateral stiffness of the front and rear tires of the vehicle, respectively.

[0129] The feedback control module 3 is designed in step 3:

[0130] The design of this module includes the following four parts: step 3.1, establishing an incremental discrete state space equation for the model predictive control algorithm; step 3.2, calculating the predicted output; step 3.3, designing the optimization target and constraint conditions; step 3.4, solving the system control input.

[0131] The incremental discrete state space equation for the model predictive control algorithm is established in step 3.1, and the state space equation is as shown in the formula (32). Figure 2 The vehicle dynamics equation is established by using the linear two-degree-of-freedom vehicle model as shown in the formula (31).

[0132] (30)

[0133] In the formula, y is the lateral velocity of the vehicle; is the lateral force of the front tire; is the lateral force of the rear tire; is the yaw moment of inertia around the vertical axis of the mass center of the vehicle; is the yaw angular velocity of the vehicle. The two-degree-of-freedom vehicle differential equation expression can be obtained as shown in the formula (32).

[0134]

[0135] (31)

[0136] In the formula, δ is the side slip angle of the mass center of the vehicle; is the yaw angular velocity of the vehicle; is the front wheel steering angle. The formula (31) is written in the form of a standard state space equation as shown in the formula (32).

[0137]

[0138] (32)

[0139] In the formula, ; ; ;

[0140] The continuous time state space model shown in the formula (32) is converted into a discrete time model that can be implemented in a digital control system. The system is discretized by using the zero-order hold method. Assuming that the sampling period of the system is T, the present application uses 0.01s. Under the condition that the input remains unchanged, the discrete time form of the system can be written as shown in the formula (33). (33)

[0141] In the formula, x(k) is the state vector at the current sampling time; is the control input; is the disturbance input; is the state transition matrix of the system; and the integral term is the input response matrix. For further simplification of the expression, the discrete system matrix is defined as shown in the formula (34).

[0142] ​​​

[0143] The incremental discrete prediction model is as follows:

[0144] (34)

[0145] where, ;

[0146] where, is the current sampling time; is the state variable increment of the step; is the control variable increment; is the current state variable; is the current predicted output; is the previous predicted output.

[0147] In step 3.2, the predicted output is calculated. According to the model predictive control theory, the prediction horizon is and the control horizon is The predicted output at the current time k is:

[0148] (35)

[0149] where, the predicted output matrix , the control input increment matrix , and the reference output sequence matrix ;

[0150] where, , are the expected yaw rate and expected side slip angle, respectively, is the identity matrix, ; ; .

[0151] In step 3.3, the optimization objective and constraint conditions are designed, including three aspects: design of lateral stability performance index, design of control quantity smoothing index, and setting of actuator physical constraints.

[0152] The two-norm of the deviation between the expected yaw rate and the yaw rate in the prediction horizon is used as the yaw rate tracking performance index, and its expression is as follows:

[0153] (36)

[0154] where, is the weighting factor of the yaw rate tracking performance; is the expected yaw rate; is the actual yaw rate; is the prediction horizon.

[0155] The two-norm of the deviation of the desired yaw center side slip angle from the predicted yaw center side slip angle in the prediction horizon is used as the yaw center side slip angle tracking performance index, which is expressed as follows:

[0156] (37)

[0157] In the formula, is a weighting factor of the yaw rate tracking performance; is the desired yaw center side slip angle; is the actual yaw center side slip angle.

[0158] The two-norm of the control variable variation is used as the control variable smoothness index, which is expressed as follows:

[0159] (38)

[0160] In the formula, is a weighting factor of the control input variation; is the yaw moment increment, is the control horizon.

[0161] The actuator physical constraints are set to meet the actuator requirements:

[0162] (39)

[0163] In the formula, is the control variable, i.e., the yaw moment increment ; is the upper limit of the yaw moment increment; is the lower limit of the yaw moment increment; is the upper limit of the yaw moment increment variation; is the lower limit of the yaw moment increment variation.

[0164] The solution of the system control input in step 3.4 includes two parts: constructing a multi-objective optimization control problem and solving the multi-objective optimization control problem.

[0165] The tracking performance index described in formula (36) and formula (37) and the control variable smoothness index described in formula (38) are converted into a single index by using a linear weighting method to construct a multi-objective optimization control problem:

[0166] (40)

[0167] In the controller, a quadratic programming algorithm is used to solve the multi-objective optimization control problem as shown in formula (40) to obtain the optimal open-loop control sequence as follows:

[0168] (41)

[0169] The first element of the optimal open-loop control sequence at the current time is selected for feedback, and the yaw moment feedback value is obtained by linear superposition with the previous time , which is output to the rear wheel differential yaw moment distribution module 5.

[0170] The feedforward control module 4 is designed in step 4:

[0171] This module is used to calculate the yaw moment feedforward value required to achieve the steady-state lateral acceleration gain response characteristic.

[0172] Given the standard state-space equation (32), when the system is stable, At this time , that is ;

[0173] In the formula, ; = = ;

[0174] Where, is the mass of the vehicle; is the longitudinal speed of the vehicle; and are the distances from the vehicle's center of mass to the front and rear axles, respectively; and are the lateral stiffness of the front and rear tires of the vehicle, respectively; is the actual yaw rate; is the actual center of mass side slip angle; is the front wheel steering angle.

[0175] Substituting into equation (32) can derive that when there is a feedforward yaw moment :

[0176] (42)

[0177] In the formula, = = = ;

[0178] Where, is the yaw moment of inertia around the vertical axis of the vehicle's center of mass; is the ideal transmission ratio yaw rate calculated by the steady-state lateral acceleration gain model.

[0179] When there is no yaw moment feedforward value :

[0180] (43)

[0181] The yaw moment feedforward value at steady state can be obtained from the above two equations:

[0182] (44)

[0183] where, is the ideal transmission ratio yaw rate calculated from the steady-state lateral acceleration gain model; is the desired yaw rate.

[0184] The rear wheel differential yaw moment distribution module is designed in step 5:

[0185] The rear wheel differential yaw moment distribution module includes two parts: 5.1 wheel braking torque calculation and 5.2 yaw moment distribution strategy, wherein the wheel braking torque calculation is used to convert the yaw moment into the braking torque of the rear wheel, and the yaw moment distribution strategy determines the specific braking wheel through the steering characteristics of the vehicle. The specific steps are as follows:

[0186] The wheel braking torque calculation in step 5.1 is specifically as follows:

[0187] (45)

[0188] where, is the braking torque; is the wheel track of the rear wheel of the vehicle; is the distance from the center of mass of the vehicle to the rear axle; is the rolling radius of the wheel.

[0189] The yaw moment distribution strategy in step 5.2 determines the specific braking wheel through the steering characteristics of the vehicle, which includes three steering characteristics: understeering, oversteering and neutral steering. The stability factor will be determined, and the specific formula of the stability factor is as follows:

[0190] (46)

[0191] where, is the total mass of the vehicle; and are the distances from the center of mass of the vehicle to the front and rear axles, respectively; and are the cornering stiffnesses of the front and rear tires of the vehicle, respectively.

[0192] In specific implementation, when in formula (23), the stability factor At this time, the vehicle is understeering characteristic, and the problem of large turning radius is prone to occur. At this time, if the vehicle turns left, the wheel braking torque calculated by formula (22) is distributed to the left rear wheel to generate a yaw moment by braking the left rear wheel; at this time, if the vehicle turns right, the wheel braking torque calculated by formula (22) is distributed to the right rear wheel to generate a yaw moment by braking the right rear wheel, so as to ensure the steering stability of the vehicle.

[0193] When , the stability factor At this time, the vehicle is oversteering characteristic, that is, the steering response is too fast, and there is a risk of tail instability. At this time, if the vehicle turns right, the wheel braking torque calculated by formula (22) is distributed to the left rear wheel to generate a yaw moment by braking the left rear wheel; at this time, if the vehicle turns left, the wheel braking torque calculated by formula (22) is distributed to the right rear wheel to generate a yaw moment by braking the right rear wheel, so as to ensure the steering stability of the vehicle.

[0194] When , the stability factor The vehicle is in neutral steering characteristic. However, in actual driving, due to factors such as lateral load transfer and change of road adhesion conditions, the vehicle may deviate from the neutral steering characteristic and develop towards oversteering characteristic or understeering characteristic. Among them, the oversteering characteristic is more likely to cause the vehicle to lose stability, especially when driving at high speed or changing lanes in an emergency, which may cause the vehicle to rotate or slide, seriously threatening the safety of driving. Therefore, in order to ensure the stability of the vehicle, the wheel braking torque will be distributed according to the oversteering characteristic, which will not be described here.

[0195] In summary: the application proposes a stability control method for electric vehicles based on steady-state lateral acceleration gain, which calculates the ideal steering characteristic parameters through the steady-state lateral acceleration gain model, determines the expected control target by combining the steady-state yaw reference model, and realizes the cooperative regulation of front feed and feedback yaw moment. Compared with the traditional MPC control method which only relies on feedback, this method introduces the steady-state lateral acceleration gain to design the ideal transmission ratio, which can match the steering demand at different speeds in advance, and at the same time, through the directional distribution strategy of rear wheel yaw moment, it can accurately adapt to understeering, oversteering and other working conditions, avoiding the universality defects of traditional distribution methods. It can effectively improve the vehicle yaw angular velocity tracking accuracy and the control effect of the center of mass side slip angle, enhance the stability and maneuverability of the distributed drive electric vehicle in extreme conditions, and has good application prospect in the field of vehicle stability control.

Claims

1. A steady-state lateral acceleration gain-based electric vehicle stability control method, characterized by, The application comprises the following modules: steady-state yaw reference model, steady-state lateral acceleration gain model, feedback control module, feedforward control module, rear wheel differential yaw torque distribution module and vehicle module; wherein the steady-state yaw reference model and the steady-state lateral acceleration gain model respectively calculate the expected yaw rate and the ideal transmission ratio yaw rate; the vehicle module is used to output the actual state quantity of the automobile, including the longitudinal vehicle speed, the yaw rate and the steering wheel angle; the feedforward control module and the feedback control module respectively determine the feedforward yaw torque and the feedback yaw torque, and output them to the rear wheel differential yaw torque distribution module for distribution and to the vehicle module for vehicle stability control; the steady-state lateral acceleration gain model is specifically designed as follows: The steady-state lateral acceleration gain model is designed to determine the ideal transmission ratio yaw rate, and the process is as follows: Step 2.1 Building ideal steering ratio by steady-state lateral acceleration gain model The basic expression of the above is given by the following formula: wherein is the vehicle longitudinal speed; and are the distances from the vehicle mass center to the front and rear axles, respectively; is the lateral acceleration gain; is the minimum transmission ratio; is the speed threshold constant; is the stability factor; In order to make the transmission ratio characteristic more continuous and smooth during the speed change process, the S function is used to fit the basic expression to obtain the fitting expression, and the specific formula is as follows: Step 2.3: Considering the steering wheel angle, the transmission ratio is added with the steering wheel angle influence coefficient , to obtain the ideal steering transmission ratio The correction expression is as follows: wherein , , are fitting parameters; is the transmission ratio influence coefficient with respect to the steering wheel angle; e is the base of the natural logarithm; is the vehicle longitudinal speed constant; is the steering wheel angle; Step 2.4 Calculation of ideal front wheel steering angle : The specific formula is as follows: Step 2.5 Calculate the ideal transmission ratio yaw rate generated by the steady-state lateral acceleration gain model The specific formula is as follows: In the formula, is the total vehicle mass; and are the cornering stiffness of the front and rear tires, respectively.

2. The steady-state lateral acceleration gain-based electric vehicle stability control method of claim 1, wherein, The feedforward control module is used to calculate the yaw torque feedforward value, and the specific formula is as follows: In the formula, = ; ; ; = ; wherein, is the total vehicle mass; is the vehicle longitudinal speed; and are the distances from the vehicle mass center to the front and rear axles, respectively; and are the tire cornering stiffnesses of the front and rear wheels, respectively; is the yaw rate calculated by the reference model; is the ideal transmission ratio yaw rate calculated by the steady state lateral acceleration gain model; is the yaw moment of inertia about the vertical axis through the vehicle mass center.

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