A Stability Control Method for Electric Vehicles Based on Steady-State Lateral Acceleration Gain

Abstract

A method for electric vehicle stability control based on steady-state lateral acceleration gain is disclosed. This method includes 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 used to calculate the desired yaw rate and the ideal steering ratio yaw rate, respectively. The vehicle module outputs the actual state quantities of the vehicle, including longitudinal vehicle speed, yaw rate, and steering wheel angle. The feedback control module and the feedforward control module determine the feedback yaw moment and the feedforward yaw moment, respectively, and their sum determines the total yaw moment. The rear-wheel differential yaw moment distribution module distributes the total yaw moment according to the vehicle's steady-state characteristic category and transmits it to the vehicle module for control, thereby improving the vehicle's lateral stability and handling performance.

Description

Technical Field

[0001] This invention belongs to the field of vehicle stability control, and more specifically, it is a method for electric vehicle stability control based on steady-state lateral acceleration gain. Background Technology

[0002] With the rapid development of electric vehicle technology, electric drive systems offer more flexible and precise control over vehicle power and steering. Compared to traditional internal combustion engine vehicles, electric vehicles possess unique distributed drive characteristics. Particularly in distributed drive electric vehicles, the independent control of each wheel by the motor allows for more precise distribution of driving force, demonstrating significant potential in improving vehicle dynamics and handling stability, thus becoming an important trend in the automotive industry. Among these, rear-wheel differential control, as a crucial component of distributed drive, can provide additional yaw torque without relying on front-wheel steering, playing a vital role in enhancing overall vehicle handling capabilities.

[0003] In automotive design, handling and stability are key performance indicators affecting vehicle safety and driving experience. Especially under extreme conditions such as high-speed cornering and emergency obstacle avoidance, achieving high-responsive handling adjustments while maintaining stability becomes crucial. Vehicle stability control strategies based on Model Predictive Control (MPC) have been extensively studied. Patent CN108107732B proposes a joint control method combining active front-wheel steering and direct yaw moment. By constructing a linear time-varying MPC controller and embedding a tire nonlinear modeling structure, it achieves dynamic optimization adjustment of yaw rate. This method has some effect on improving vehicle stability under extreme conditions, but its control objective dimension is relatively singular. The control actuator still relies on traditional front-wheel mechanical steering and four-wheel braking systems, lacking modeling of the vehicle's ideal steering characteristics and failing to introduce a feedforward compensation mechanism to enhance dynamic response capabilities.

[0004] Furthermore, patent CN108107731B addresses the control accuracy issue in the tire's nonlinear region by proposing an MPC control architecture that switches the prediction model based on lateral stiffness judgment, enhancing the control system's modeling capability across different lateral stiffness ranges. This method expands the adaptability of tire modeling and introduces the center-of-gravity sideslip angle as an auxiliary control objective, resulting in some improvement in yaw control accuracy. However, its control strategy is still based on a closed-loop feedback control architecture, and the control actuators remain limited to traditional braking and steering mechanisms. It does not construct a feedforward and feedback coordination channel for dynamic operating conditions and does not add corresponding system characteristics from the feedforward control level. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes an electric vehicle stability control method based on steady-state lateral acceleration gain, employing a strategy that combines feedforward control and feedback control. Feedforward control can quickly respond to ideal steering demands, optimizing vehicle power output and response time, thereby improving handling smoothness; feedback control ensures vehicle stability under various complex operating conditions, providing more flexible and safer handling performance.

[0006] First, this invention comprehensively considers the vehicle's steady-state response characteristics and designs the ideal transmission ratio yaw rate based on the steady-state gain of lateral acceleration. On this basis, a rear-wheel differential steering assist model is established to determine the feedforward yaw torque required to achieve ideal steering characteristics, thereby realizing feedforward compensation control of the vehicle. Second, a steady-state yaw reference model is established to calculate the desired yaw rate, and a lateral stability feedback controller based on model predictive control (MPC) is designed. This controller solves for the feedback yaw torque, enabling tracking of the desired yaw rate and the center-of-gravity sideslip angle. Finally, according to the vehicle's steady-state response type, the generated total yaw torque is rationally distributed to the hub motors on the drive wheels, improving the vehicle's stability and handling.

[0007] The technical solution adopted by this invention to solve the technical problem is as follows:

[0008] A method for electric vehicle stability control based on steady-state lateral acceleration gain is disclosed. This method includes 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 used to calculate the desired yaw rate and the ideal steering ratio yaw rate, respectively. The vehicle module outputs the actual state quantities of the vehicle, including longitudinal vehicle speed, yaw rate, and steering wheel angle. The feedback control module and the feedforward control module determine the feedback yaw moment and the feedforward yaw moment, respectively, and their sum determines the total yaw moment. The rear-wheel differential yaw moment distribution module distributes the total yaw moment according to the vehicle's steady-state characteristic category and transmits it to the vehicle module for control, thereby improving the vehicle's lateral stability and handling performance.

[0009] The method includes the following steps:

[0010] Step 1: Design the steady-state yaw reference model:

[0011] This module is used to determine the desired yaw rate. Its expression is as follows:

[0012] (1)

[0013] In the formula, For the overall vehicle weight; It is the longitudinal speed of the car; and These are the distances from the car's center of gravity to the front and rear axles, respectively. and These are the lateral stiffness of the front and rear tires of the car, respectively. The front wheel mechanical steering has a fixed gear ratio; This refers to 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 basic expression for is as follows:

[0017] (2)

[0018] In the formula, It is the longitudinal speed of the car; and These are the distances from the car's center of gravity to the front and rear axles, respectively. It is the lateral acceleration gain; It is the minimum transmission ratio; It is the velocity threshold constant; It is a stability factor.

[0019] Step 2.2: To make the transmission ratio characteristics more continuous and smooth during speed changes, the S-function is used to fit the basic expression, resulting in the fitted expression, as shown in the following formula:

[0020] (3)

[0021] Step 2.3: Taking into account the steering wheel angle, add the influence coefficient of the transmission ratio with the steering wheel angle. To obtain the ideal steering ratio The expression has been revised; the specific expression is as follows:

[0022] (4)

[0023] In the formula, , , All are fitted parameters; is the coefficient of influence of the transmission ratio on the steering wheel angle; e is the base of the natural logarithm; Steering wheel angle; It is the longitudinal speed of the car; Let be the longitudinal speed constant of the vehicle.

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

[0025] (5)

[0026] In the formula, For the ideal front wheel steering angle.

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

[0028] (6)

[0029] In the formula, For the overall vehicle weight; and These are the distances from the car's center of gravity to the front and rear axles, respectively. and These are the lateral stiffness of the front and rear tires of the car, 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 equations for the model predictive control algorithm:

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

[0034] (7)

[0035] In the formula, This refers to the lateral speed of the car. and These are the lateral forces of the front and rear tires, respectively. It is the yaw moment of inertia about the vertical axis of the car's center of mass; It is the yaw rate of the car; This refers to the yaw moment of the car.

[0036] The differential equation for a two-degree-of-freedom vehicle can be expressed as follows:

[0037] (8)

[0038] In the formula, It is the sideslip angle of the car's center of gravity; It is the yaw rate of the car; It's the front wheel steering angle.

[0039] Equation (8) can be written in the form of a standard state-space equation:

[0040] (9)

[0041] in, ; ; ; ;

[0042] In the formula, For the overall vehicle weight; This refers to the lateral speed of the car. The longitudinal speed of the car; and These are the distances from the car's center of gravity to the front and rear axles, respectively. It is the yaw moment of inertia about the vertical axis of the car's center of mass; It is the sideslip angle of the car's center of gravity; It is the yaw rate of the car; and These are the lateral stiffness of the front and rear tires of the car, respectively.

[0043] The continuous-time state-space model shown in equation (9) is transformed into a discrete-time model that can be implemented in a digital control system. This invention employs a zero-order hold method to discretize the system. Let the system sampling period be... In this invention, the time constant is 0.01s. Under the condition that the input remains unchanged, the discrete-time form of the system can be written as:

[0044] (10)

[0045] In the formula, where This is the state vector at the current sampling time; For control input; For disturbance input; Let be 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] Therefore, the incremental discrete prediction model can be obtained as follows:

[0049] (11)

[0050] in, ;

[0051] In the formula, This is the current sampling time; For the first The increment of the state variable at each step; To control the increment of variables; This is the state variable at the current moment; Predict the output for the current time step; This is the predicted output from the previous time step.

[0052] Step 3.2: Calculate the predicted output. Based on model predictive control theory, the prediction time domain is taken as... Control time domain is The predicted output at time k can be obtained as follows:

[0053] (12)

[0054] Among them, the predicted output matrix Control input increment matrix Reference output sequence matrix ;

[0055] In the formula, , These are the desired yaw rate and the desired sideslip angle, respectively. It is the identity matrix. ; ; .

[0056] Step 3.3: Design optimization objectives and constraints:

[0057] The L2 norm of the deviation between the expected yaw rate and the predicted yaw rate in the time domain is used as the yaw rate tracking performance index, and its expression is as follows:

[0058] (13)

[0059] In the formula, It is a weighting factor for yaw rate tracking performance; It is the expected yaw rate; It is the actual yaw rate; For prediction in the time domain.

[0060] The L2 norm of the deviation between the expected centroid sideslip angle and the predicted centroid sideslip angle in the time domain is used as the centroid sideslip angle tracking performance index, and its expression is as follows:

[0061] (14)

[0062] In the formula, It is a weighting factor for yaw rate tracking performance; It is the expected centroid sideslip angle; It is the actual centroid sideslip angle.

[0063] The L2 norm of the change in control quantity is used as the smoothing index for the control quantity, and its expression is as follows:

[0064] (15)

[0065] In the formula, It is a weighting factor for changes in control input; It is the increase in yaw moment; It controls the time domain.

[0066] Set physical constraints for the actuator to meet its requirements:

[0067] (16)

[0068] in, It is the control variable, namely the increment of the yaw moment. ; It is the upper limit of the yaw moment increment; It is the lower limit of the yaw moment increment; It is the upper limit of the change in yaw moment increment; It is the lower limit of the change in the yaw moment increment.

[0069] Step 3.4: Solve for the system control input:

[0070] Using the linear weighting method, the tracking performance index described in equations (13) and (14) and the control quantity smoothing index described in equation (15) are transformed into a single index, 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 shown in equation (17) to obtain the optimal open-loop control sequence. for:

[0073] (18)

[0074] In the formula, It is a weighting factor for yaw rate tracking performance; It is the expected centroid sideslip angle; It is the actual centroid sideslip angle; It predicts the time domain; It is a weighting factor for yaw rate tracking performance; Desired yaw rate; It is the actual yaw rate; It is a weighting factor for changes in control input; It is the increase in yaw moment; It controls the time domain.

[0075] The first element of the optimal open-loop control sequence at the current moment is selected for feedback, and linearly superimposed with the previous moment to obtain the yaw moment feedback value. The output is sent 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 in steady state, ,at this time ,Right now :

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

[0079] in, For the overall vehicle weight; It is the longitudinal speed of the car; and These are the distances from the car's center of gravity to the front and rear axles, respectively. and These are the lateral stiffness of the front and rear tires of the car, respectively. It's the front wheel steering angle.

[0080] Will Substituting into equation (9), it can be derived that when a feedforward yaw moment exists... hour:

[0081] (19)

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

[0083] In the formula, It is the yaw moment of inertia about the vertical axis of the car's center of mass; The yaw rate is calculated from the steady-state lateral acceleration gain model.

[0084] When there is no feedforward yaw moment hour:

[0085] (20)

[0086] From the above two equations, the steady-state yaw moment feedforward value can be obtained:

[0087] (twenty one)

[0088] In the formula, = ; = ;

[0089] in, The ideal transmission ratio yaw rate is calculated from the steady-state lateral acceleration gain model. It is the expected yaw rate.

[0090] Step 5: Design of the rear wheel differential yaw moment distribution module:

[0091] The rear wheel differential yaw moment distribution module consists of two parts: 5.1 wheel braking moment calculation and 5.2 yaw moment distribution strategy. The wheel braking moment calculation converts the yaw moment into the braking moment of the rear wheels, while the yaw moment distribution strategy determines the specific braking wheels based on the vehicle's steering characteristics. The specific steps are as follows:

[0092] The specific formula for calculating the wheel braking torque in step 5.1 is as follows:

[0093] (twenty two)

[0094] In the formula, It is the braking torque; It refers to the rear wheel track of the car; It is the distance from the car's center of gravity to the rear axle; It is the rolling radius of the wheel.

[0095] Step 5.2 The yaw moment distribution strategy determines the specific braking wheels based on the vehicle's steering characteristics, which include understeer, oversteer, and neutral steering. This is determined by a stability factor. To determine the stability factor The specific formula is as follows:

[0096] (twenty three)

[0097] in, For the overall vehicle weight; and These are the distances from the car's center of gravity to the front and rear axles, respectively. and These are the lateral stiffness of the front and rear tires of the car, respectively.

[0098] When in formula (23) When, stability factor At this time, the vehicle has understeer characteristics and is prone to problems with a large turning radius. At this time, if the vehicle turns left, the wheel braking torque calculated by formula (22) is distributed to the left rear wheel, and a yaw torque 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 a yaw torque is generated by braking the right rear wheel, so as to ensure the steering stability of the vehicle.

[0099] when When, stability factor At this time, the vehicle exhibits oversteering characteristics, meaning that the steering response is too fast, posing a risk of rear instability. If the vehicle turns right, the wheel braking torque calculated by formula (22) is distributed to the left rear wheel, generating a yaw torque by braking the left rear wheel; if the vehicle turns left, the wheel braking torque calculated by formula (22) is distributed to the right rear wheel, generating a yaw torque by braking the right rear wheel, in order to ensure the vehicle's steering stability.

[0100] when When, stability factor The vehicle initially exhibits neutral steering characteristics. However, in actual driving, factors such as lateral load transfer and changes in road surface adhesion conditions can cause the vehicle to deviate from these characteristics, developing towards oversteer or understeer. Oversteer, in particular, is more likely to cause rear-end instability, especially during high-speed cornering or emergency lane changes, potentially leading to vehicle spin or skidding, severely threatening driving safety. Therefore, to ensure vehicle stability, wheel braking torque will be distributed according to oversteer characteristics, which will not be elaborated upon here. Attached Figure Description

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

[0102] Figure 2 This is a schematic diagram of a linear two-degree-of-freedom car model. Detailed Implementation

[0103] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0104] Figure 1This is a schematic diagram of the system structure of an electric vehicle stability control method based on steady-state lateral acceleration gain according to the present invention. The system mainly includes 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. Steady-state yaw reference model 1 and steady-state lateral acceleration gain model 2 are used to calculate the desired yaw rate and the ideal steering ratio yaw rate, respectively. Vehicle module 6 outputs the actual state quantities of the vehicle, including longitudinal speed, yaw rate, and steering wheel angle. Feedback control module 3 optimizes and solves the yaw torque feedback value required to achieve vehicle lateral stability based on the desired yaw rate and the actual yaw rate state information of the vehicle using model predictive control algorithm. Feedforward control module 4 solves for the yaw torque feedforward value based on the ideal steering ratio yaw rate calculated by steady-state lateral acceleration gain model 2 and the desired yaw rate calculated by steady-state yaw reference model 1, improving the vehicle's handling. Rear wheel differential yaw torque distribution module 5 receives the total yaw torque generated by feedforward control module 4 and feedback control module 3 and distributes it reasonably according to the steady-state characteristic category. The distributed torque of each wheel is output to vehicle module 6 for vehicle stability control, thereby improving the vehicle's lateral stability and handling performance.

[0105] To verify the effectiveness and engineering feasibility of the proposed control strategy, this invention introduces a high-precision vehicle dynamics model to conduct system modeling and control effect verification. Specifically, the CarSim 2020 vehicle model is used as the core simulation platform. A vehicle lateral dynamics system is constructed based on typical extreme conditions such as high-speed steering and emergency obstacle avoidance. Through a joint simulation architecture of CarSim and Simulink, a comprehensive evaluation of the yaw rate tracking accuracy, the center of gravity sideslip angle control effect, and the rear wheel yaw moment orientation distribution logic is achieved, serving as a key verification basis before subsequent real-vehicle experiments. The method of this invention is further illustrated below using a distributed drive electric vehicle in the CarSim automotive simulation software as an example. The main parameters of the CarSim vehicle are as follows:

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

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

[0108] This module is used to determine the desired yaw rate. Its expression is as follows:

[0109] (twenty four)

[0110] In the formula, For the overall vehicle weight; It is the longitudinal speed of the car; and These are the distances from the car's center of gravity to the front and rear axles, respectively. and These are the lateral stiffness of the front and rear tires of the car, respectively. The front wheel mechanical steering has a fixed gear ratio; This refers to the steering wheel angle.

[0111] In step 2, the steady-state lateral acceleration gain model 2 is designed:

[0112] It includes the following five parts: Step 2.1, Constructing the ideal steering ratio based on the steady-state lateral acceleration gain model. The basic expression; Step 2.2, determine the ideal steering gear ratio. The fitting expression; Step 2.3: Determine the ideal steering ratio. The corrected expression; Step 2.4, calculate the ideal front wheel steering angle. Step 2.5: Calculate the ideal steering ratio yaw rate. .

[0113] In step 2.1, the ideal steering gear ratio is constructed based on the steady-state lateral acceleration gain model. Basic expression:

[0114] (25)

[0115] In the formula, The lateral acceleration gain is set to 7.51; It is a stability factor; The minimum transmission ratio is 9.6; The velocity threshold constant is 30. .

[0116] Determine the ideal steering gear ratio in step 2.2 The fitted expression:

[0117] Considering that the transmission ratio is more continuous and smooth during speed change and should not have abrupt changes, the S-function is selected to fit the curve of equation (25) to obtain the fitting expression. The specific expression is as follows:

[0118] (26)

[0119] Determine the ideal transmission ratio in step 2.3 Corrected expression:

[0120] Taking into account the steering wheel angle, a gain-steering-angle influence coefficient is added. In this design, the maximum transmission ratio is determined when the yaw rate gain is fixed at 0.3. By substituting the value of coefficient A2, the ideal steering gear ratio is obtained. Corrected expression:

[0121] (27)

[0122] In the formula, , , All are fitted parameters; is the coefficient of influence of the transmission ratio on the steering wheel angle; e is the base of the natural logarithm; Steering wheel angle; It is the longitudinal speed of the car; Let be the longitudinal speed constant of the vehicle.

[0123] Calculate the ideal front wheel steering angle in step 2.4 :

[0124] (28)

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

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

[0127] (29)

[0128] In the formula, For the overall vehicle weight; and These are the distances from the car's center of gravity to the front and rear axles, respectively. and These are the lateral stiffness of the front and rear tires of the car, respectively.

[0129] In step 3, the feedback control module 3 is designed:

[0130] The design of this module includes the following four parts: Step 3.1, establishing the incremental discrete state-space equations for the model predictive control algorithm; Step 3.2, calculating the predicted output; Step 3.3, designing the optimization objective and constraints; Step 3.4, solving for the system control input.

[0131] In step 3.1, the incremental discrete state-space equations for the model predictive control algorithm are established, so as to... Figure 2 The linear two-degree-of-freedom car model shown establishes the vehicle dynamics equations:

[0132] (30)

[0133] In the formula, This refers to the lateral speed of the car. and These are the lateral forces of the front and rear tires, respectively. It is the yaw moment of inertia about the vertical axis of the car's center of mass; It is the yaw rate of the car.

[0134] The differential equation for a two-degree-of-freedom vehicle can be expressed as follows:

[0135] (31)

[0136] In the formula, It is the sideslip angle of the car's center of gravity; It is the yaw rate of the car; It's the front wheel steering angle.

[0137] Equation (31) can be written in the form of a standard state-space equation:

[0138] (32)

[0139] in, ; ; ;

[0140] The continuous-time state-space model shown in equation (32) is transformed into a discrete-time model that can be implemented in a digital control system. This invention employs a zero-order hold method to discretize the system. Let the system sampling period be... In this invention, the time constant is 0.01s. Under the condition that the input remains unchanged, the discrete-time form of the system can be written as:

[0141] (33)

[0142] In the formula, where This is the state vector at the current sampling time; For control input; For disturbance input; Let be the state transition matrix of the system; the integral term is the input response matrix.

[0143] To further simplify the expression, the discrete system matrix is ​​defined as follows:

[0144]

[0145] Therefore, the incremental discrete prediction model can be obtained as follows:

[0146] (34)

[0147] in, ;

[0148] In the formula, This is the current sampling time; For the first The increment of the state variable at each step; To control the increment of variables; This is the state variable at the current moment; Predict the output for the current time step; This is the predicted output from the previous time step.

[0149] In step 3.2, the predicted output is calculated. According to model predictive control theory, the prediction time domain is taken as... Control time domain is The predicted output at time k can be obtained as follows:

[0150] (35)

[0151] Among them, the predicted output matrix Control input increment matrix Reference output sequence matrix ;

[0152] In the formula, , These are the desired yaw rate and the desired sideslip angle, respectively. It is the identity matrix. ; ; .

[0153] Step 3.3 involves designing optimization objectives and constraints, including three aspects: designing lateral stability performance indicators, designing control quantity smoothing indicators, and setting actuator physical constraints.

[0154] The L2 norm of the deviation between the expected yaw rate and the predicted yaw rate in the time domain is used as the yaw rate tracking performance index, and its expression is as follows:

[0155] (36)

[0156] In the formula, It is a weighting factor for yaw rate tracking performance; It is the expected yaw rate; It is the actual yaw rate; It is the prediction time domain.

[0157] The L2 norm of the deviation between the expected centroid sideslip angle and the predicted centroid sideslip angle in the time domain is used as the centroid sideslip angle tracking performance index, and its expression is as follows:

[0158] (37)

[0159] In the formula, It is a weighting factor for yaw rate tracking performance; It is the expected centroid sideslip angle; It is the actual centroid sideslip angle.

[0160] The L2 norm of the change in control quantity is used as the smoothing index for the control quantity, and its expression is as follows:

[0161] (38)

[0162] In the formula, It is a weighting factor for changes in control input; It is the increase in yaw moment. It controls the time domain.

[0163] Set physical constraints for the actuator to meet its requirements:

[0164] (39)

[0165] in, It is the control variable, namely the increment of the yaw moment. ; It is the upper limit of the yaw moment increment; It is the lower limit of the yaw moment increment; It is the upper limit of the increment of yaw moment; It is the lower limit of the change in the yaw moment increment.

[0166] The solution to the system control input in step 3.4 consists of two parts: constructing the multi-objective optimization control problem and solving the multi-objective optimization control problem.

[0167] Using the linear weighting method, the tracking performance index described in equations (36) and (37) and the control quantity smoothing index described in equation (38) are transformed into a single index, and a multi-objective optimization control problem is constructed:

[0168] (40)

[0169] In the controller, a quadratic programming algorithm is used to solve the multi-objective optimization control problem shown in equation (40) to obtain the optimal open-loop control sequence. for:

[0170] (41)

[0171] The first element of the optimal open-loop control sequence at the current moment is selected for feedback, and linearly superimposed with the previous moment to obtain the yaw moment feedback value. The output is sent to the rear wheel differential yaw moment distribution module 5.

[0172] In step 4, the feedforward control module 4 is designed:

[0173] This module is used to calculate the yaw moment feedforward value required to achieve the steady-state lateral acceleration gain response characteristics.

[0174] Given the standard state-space equation (32), when the system is in steady state, ,at this time ,Right now ;

[0175] In the formula, ; = = ;

[0176] in, For the overall vehicle weight; It is the longitudinal speed of the car; and These are the distances from the car's center of gravity to the front and rear axles, respectively. and These are the lateral stiffness of the front and rear tires of the car, respectively. It is the actual yaw rate; It is the actual centroid sideslip angle; It's the front wheel steering angle.

[0177] Will Substituting into equation (32), it can be derived that when a feedforward yaw moment exists... hour:

[0178] (42)

[0179] In the formula, = = = ;

[0180] in, It is the yaw moment of inertia about the vertical axis of the car's center of mass; The ideal transmission ratio yaw rate is calculated from the steady-state lateral acceleration gain model.

[0181] When there is no yaw moment feedforward value hour:

[0182] (43)

[0183] From the above two equations, the steady-state yaw moment feedforward value can be obtained:

[0184] (44)

[0185] in, The ideal transmission ratio yaw rate is calculated from the steady-state lateral acceleration gain model. It is the expected yaw rate.

[0186] In step 5, the rear wheel differential yaw moment distribution module is designed:

[0187] The rear wheel differential yaw moment distribution module consists of two parts: 5.1 wheel braking moment calculation and 5.2 yaw moment distribution strategy. The wheel braking moment calculation converts the yaw moment into the braking moment of the rear wheels, while the yaw moment distribution strategy determines the specific braking wheels based on the vehicle's steering characteristics. The specific steps are as follows:

[0188] The specific formula for calculating the wheel braking torque in step 5.1 is as follows:

[0189] (45)

[0190] In the formula, It is the braking torque; It refers to the rear wheel track of the car; It is the distance from the car's center of gravity to the rear axle; It is the rolling radius of the wheel.

[0191] Step 5.2 The yaw moment distribution strategy determines the specific braking wheels based on the vehicle's steering characteristics, which include understeer, oversteer, and neutral steering. This is determined by a stability factor. To determine the stability factor The specific formula is as follows:

[0192] (46)

[0193] in, For the overall vehicle weight; and These are the distances from the car's center of gravity to the front and rear axles, respectively. and These are the lateral stiffness of the front and rear tires of the car, respectively.

[0194] In specific implementation, when formula (23) When, stability factor At this time, the vehicle has understeer characteristics and is prone to problems with a large turning radius. At this time, if the vehicle turns left, the wheel braking torque calculated by formula (22) is distributed to the left rear wheel, and a yaw torque 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 a yaw torque is generated by braking the right rear wheel, so as to ensure the steering stability of the vehicle.

[0195] when When, stability factor At this time, the vehicle exhibits oversteering characteristics, meaning that the steering response is too fast, posing a risk of rear instability. If the vehicle turns right, the wheel braking torque calculated by formula (22) is distributed to the left rear wheel, generating a yaw torque by braking the left rear wheel; if the vehicle turns left, the wheel braking torque calculated by formula (22) is distributed to the right rear wheel, generating a yaw torque by braking the right rear wheel, in order to ensure the vehicle's steering stability.

[0196] when When, stability factor The vehicle initially exhibits neutral steering characteristics. However, in actual driving, factors such as lateral load transfer and changes in road surface adhesion conditions can cause the vehicle to deviate from these characteristics, developing towards oversteer or understeer. Oversteer, in particular, is more likely to cause rear-end instability, especially during high-speed cornering or emergency lane changes, potentially leading to vehicle spin or skidding, severely threatening driving safety. Therefore, to ensure vehicle stability, wheel braking torque will be distributed according to oversteer characteristics, which will not be elaborated upon here.

[0197] In summary, this invention proposes a stability control method for electric vehicles based on steady-state lateral acceleration gain. It calculates ideal steering characteristic parameters using a steady-state lateral acceleration gain model and determines the desired control objective by combining it with a steady-state yaw reference model, achieving coordinated regulation of feedforward and feedback yaw moments. Compared to traditional MPC control methods that rely solely on feedback, this method introduces steady-state lateral acceleration gain to design an ideal transmission ratio, allowing for pre-matching of steering requirements at different vehicle speeds. Simultaneously, it precisely adapts to understeer and oversteer conditions through a rear-wheel yaw moment directional distribution strategy, avoiding the universality limitations of traditional distribution methods. This effectively improves the vehicle's yaw rate tracking accuracy and center-of-gravity sideslip angle control, enhancing the stability and handling of distributed drive electric vehicles under extreme conditions, and has promising application prospects in the field of automotive stability control.

Claims

1. A steady-state side 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.

Images