Longitudinal and lateral stability control method based on phase plane analysis

Abstract

The application relates to a longitudinal-lateral stability control method based on phase plane analysis, which comprises the following steps: constructing a vehicle-road model based on the kinematic relation between a vehicle and a target path and a vehicle model; obtaining road environment information and vehicle state information, establishing a phase plane with an instability energy ratio and a change rate of the instability energy ratio, setting a stability judgment criterion, and judging the vehicle working condition based on phase plane analysis; when the vehicle is in different working conditions, MPC control is carried out through corresponding path tracking controllers: in a stable working condition, a path tracking controller one based on the vehicle-path model MPC control is designed with the total lateral force of the front wheels of the vehicle as the control quantity; in an instability working condition, the parameters of the path tracking controller one are adjusted with the additional yaw moment of the vehicle to obtain a path tracking controller two. The application provides a reasonable decision method for different working conditions, and effectively improves the longitudinal-lateral stability and tracking performance of the vehicle.

Description

Technical Field

[0001] This invention relates to the field of intelligent transportation technology, and in particular to a longitudinal and lateral stability control method based on phase plane analysis. Background Technology

[0002] Four-wheel independent drive electric vehicles, with their superior dynamic performance, will become an excellent platform for intelligent vehicles. Distributed four-wheel drive electric vehicles can independently adjust the output torque of each wheel, thus achieving optimal power and handling stability.

[0003] Currently, the parameters commonly used to characterize the driving stability of vehicles are yaw rate and sideslip angle. However, unlike yaw rate, the sideslip angle cannot be directly measured. Existing decision-making methods are mostly based on empirically defined operating conditions, and the controller cannot fully utilize the vehicle's yaw stability. How to design a more reasonable decision-making method and make the most of the dynamic performance of four-wheel independent drive electric vehicles is the problem that this application aims to solve. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a longitudinal and lateral stability control method based on phase plane analysis. The technical objective is to provide a reasonable decision-making method for different operating conditions and improve vehicle dynamic performance.

[0005] The technical solution adopted in this invention is as follows:

[0006] This application provides a longitudinal and transverse stability control method based on phase plane analysis, including:

[0007] A vehicle-road model is constructed based on the kinematic relationship between the vehicle and the target path, and the vehicle model used to describe the lateral and yaw motions of the vehicle.

[0008] Obtain road environment information and vehicle status information, based on instability energy ratio R rate of change of instability energy ratio Establish a phase plane for the parameters, and determine the vehicle's operating condition based on the phase plane analysis. When equation (1) is satisfied, the vehicle is considered to be in a stable operating condition; otherwise, it is considered to be in an unstable operating condition.

[0009] (1)

[0010] in, in, E 1 , E 2 These are the vehicle's longitudinal kinetic energy and instability kinetic energy, respectively. These are the vehicle's longitudinal velocity, lateral velocity, and yaw rate, respectively. These are the vehicle's moment of inertia and mass, respectively. These are constants related to the operating conditions;

[0011] When the vehicle is under different operating conditions, MPC control is performed through the corresponding path tracking controller:

[0012] Under stable operating conditions, the total lateral force of the vehicle's front wheels is considered. F yf To design a path tracking controller based on the vehicle-path model MPC control for the control input, its state-space model is as follows:

[0013] (2)

[0014] In equation (2), the state vector Control quantity Output vector , A 1. B 1 represents the time-varying coefficient matrix. C 3 To select the matrix;

[0015] Under unstable operating conditions, the additional yaw moment of the vehicle... By adjusting the parameters of the first path tracking controller, a second path tracking controller is obtained, whose state-space model is as follows:

[0016] (3)

[0017] In equation (3), the state vector Control quantity Output vector , A 2. B 2 represents the time-varying coefficient matrix. C 4 To select the matrix;

[0018] In equations (2) and (3), These are the lateral deviation and heading deviation between the vehicle and the target path, respectively. k For discrete time the first k time;

[0019] The further technical solution is as follows:

[0020] The constants related to operating conditions The method for determining it is as follows:

[0021] make ,in, β The sideslip angle is the vehicle's center of gravity.

[0022] make ,when When =0, we get ,when R When =0, we get ,in, These are the maximum sideslip angle and maximum yaw rate under stable operating conditions, respectively.

[0023] The objective function of the MPC control is:

[0024]

[0025] in, are non-negative slack variables; Q, R, W represent weighting matrices; These are the sampling time, prediction time domain, and control time domain, respectively.

[0026] The constraints of the MPC control include vehicle stability constraints:

[0027] In the formula, ;

[0028] in, l r The distance from the vehicle's center of gravity to the rear axle. These are the coefficient of friction of the ground and the acceleration due to gravity, respectively. Indicates the rear wheel slip angle:

[0029] ,in, l f This is the distance from the vehicle's center of gravity to the front axle. L Wheelbase Rear wheel lateral stiffness;

[0030] It also includes control quantity constraints:

[0031] ,

[0032] in, These represent the control increments respectively. Absolute value and control quantity u The maximum limit of absolute value.

[0033] The longitudinal and transverse stability control method based on phase plane analysis further includes:

[0034] The additional yaw moment generated by the path tracking controller 2 Assigned to four tires:

[0035]

[0036] In the formula, These represent the torque changes for the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. , l r This is the distance from the vehicle's center of gravity to the rear axle. L Wheelbase l s It is half the track width. R This is the tire radius.

[0037] The kinematic relationship between the vehicle and the target path is as follows:

[0038]

[0039] in, This represents the heading angular velocity of the target path. For reference path at location s The curvature of the road at that location.

[0040] The vehicle model is a two-degree-of-freedom vehicle model.

[0041]

[0042] In the formula, m Indicates vehicle mass; Indicates the vehicle's moment of inertia; F yf This indicates the total lateral force on the front wheels; F yr This represents the total lateral force on the rear wheels; l f This indicates the distance from the vehicle's center of gravity to the front axle; l r This indicates the distance from the vehicle's center of gravity to the rear axle. This indicates the additional yaw moment of the vehicle.

[0043] The beneficial effects of this invention are as follows:

[0044] Based on phase plane analysis, this invention designs a vehicle longitudinal and lateral stability judgment criterion that includes multiple physical quantity indicators such as energy ratio and energy ratio change rate. Based on the judgment criterion, the vehicle operating conditions are judged. By designing a path tracking controller based on model predictive control (MPC), a force-driven switching MPC control strategy based on different operating conditions is proposed, which effectively improves the longitudinal and lateral stability and tracking performance of the vehicle, especially the stability of the vehicle under extreme operating conditions.

[0045] The stability determination criterion of this invention does not require the use of the vehicle's center of gravity sideslip angle, which has a wider range of applications and applicability. It can enable intelligent vehicles to drive stably under extreme conditions and has strong industrial applicability.

[0046] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. Attached Figure Description

[0047] Figure 1 This is a flowchart of the method of the present invention.

[0048] Figure 2 This is a kinematic relationship model between the vehicle and the target path in the method of the present invention.

[0049] Figure 3 This is the vehicle stability judgment criterion based on phase plane analysis in the method of the present invention. Detailed Implementation

[0050] The specific embodiments of the present invention are described below with reference to the accompanying drawings.

[0051] See Figure 1 This embodiment of a longitudinal and transverse stability control method based on phase plane analysis includes:

[0052] S1. Based on the kinematic relationship between the vehicle and the target path, and the vehicle model used to describe the lateral and yaw motions of the vehicle, a vehicle-road model is constructed. The construction process is as follows:

[0053] See Figure 2 A rectangular coordinate system is established with the forward direction of the vehicle body as the x-axis and the leftward direction of the vehicle body as the y-axis. A geodetic coordinate system XOY is also established. The kinematic relationship between the vehicle and the target path is as follows:

[0054]

[0055] In the formula, These are the lateral deviation and heading deviation between the vehicle and the target path, respectively. v y Indicates the lateral speed of the vehicle; This indicates the yaw rate of the vehicle. v x Indicates the longitudinal speed of the vehicle; Indicates the heading angular velocity of the target path; For reference path at location s The curvature of the road at that location.

[0056] A two-degree-of-freedom vehicle model is used to describe the vehicle's lateral and yaw motions, assuming the front wheel steering angle... For small angles, longitudinal speed v x The vehicle model remains unchanged as follows:

[0057]

[0058] In the formula, m Indicates vehicle mass; Indicates the vehicle's moment of inertia; F yf This indicates the total lateral force on the front wheels; F yr This represents the total lateral force on the rear wheels; l f This indicates the distance from the vehicle's center of gravity to the front axle; l r This indicates the distance from the vehicle's center of gravity to the rear axle. This indicates the additional yaw moment of the vehicle.

[0059] Assuming the front wheel slip angle α f and rear wheel slip angle α r If all angles are small, then the total lateral force on the front wheel is... F yf and the total lateral force of the rear wheels F yr Represented as: ,in:

[0060]

[0061] In the formula, C f Indicates the front wheel lateral stiffness; C r Indicates the rear wheel lateral stiffness; Indicates the steering angle of the vehicle's front wheels; β Indicates the sideslip angle of the vehicle's center of gravity, due to lateral velocity. v y Much smaller than longitudinal velocity v x , β It can be represented as β=v y / v x Therefore, we can conclude that:

[0062]

[0063] Combining (1) to (8), the vehicle-road model is represented as follows:

[0064]

[0065] In the formula, Represents the state vector; when the vehicle is in a stable operating condition, the control variable... When the vehicle is in an unstable operating condition, ; A ,B Both represent time-varying coefficient matrices; Indicates the output vector; C This represents the selection matrix.

[0066] S2. Obtain road environment information and vehicle status information, with the instability energy ratio R as the horizontal axis and the rate of change of the instability energy ratio as the vertical axis. Establish a phase plane for the vertical axis, and determine the vehicle's operating condition based on the phase plane analysis. When the stability judgment criterion of equation (11) is met, the vehicle is considered to be in a stable operating condition; otherwise, it is considered to be in an unstable operating condition.

[0067]

[0068] in, in, E 1 , E 2 These are the vehicle's longitudinal kinetic energy and instability kinetic energy, respectively. These are the vehicle's longitudinal velocity, lateral velocity, and yaw rate, respectively. These are the vehicle's moment of inertia and mass, respectively. For constants related to operating conditions, their determination method is as follows:

[0069] From the centroid side slip angle β Definition:

[0070] ;make ,when When =0, we get (12);

[0071] when R When =0, we get (13), among which, These represent the maximum sideslip angle and maximum yaw rate under stable operating conditions. Assume a vehicle longitudinal speed of 100 km / h and a ground friction coefficient of... μ= 0.55, gravitational acceleration is taken as 9.8 m / s². 2 Solve C 1 and C 2:

[0072]

[0073] The limiting sideslip angle of the center of mass under steady-state conditions is approximately 12°, and the yaw rate is approximately 22° / s. Substituting these values ​​into equations (12) and (13) yields the following solution: .

[0074] Stability judgment criteria such as Figure 3As shown, when the coordinates of the instability energy ratio and the rate of change of energy ratio fall between the two straight lines during vehicle operation, the vehicle is considered to be in a stable condition; otherwise, the vehicle is considered to have become unstable.

[0075] S3. When the vehicle is under different operating conditions, MPC control is performed through the corresponding path tracking controller:

[0076] Under stable operating conditions, the total lateral force of the vehicle's front wheels is considered. F yf To design a path tracking controller based on the vehicle-path model MPC control for the control quantity, specifically:

[0077] Define the prediction time domain N p and control time domain N c Then in the first k At time t, the state sequence, output sequence, and control sequence are represented as follows:

[0078]

[0079] Wherein, the state vector Control quantity Output vector , and The discrete-time state space is obtained by discretizing equation (9) using the forward Euler method, and is expressed as:

[0080] (16)

[0081] In equation (16), It is the identity matrix. T It is the sampling time. C 3 represents the selection matrix;

[0082] Under unstable operating conditions, the additional yaw moment of the vehicle... By adjusting the parameters of the first path tracking controller, a second path tracking controller is obtained. Specifically:

[0083] Due to vehicle instability, control measures need to be applied to the vehicle, indirectly controlling the energy ratio to stabilize it. Using the lateral force of the front wheels and the additional yaw moment as control variables, the discrete-time state-space representation is as follows:

[0084] (17)

[0085] In equation (17), the state vector Control quantity Output vector , It is the identity matrix.T It is the sampling time. C 4 represents the selection matrix.

[0086] Specifically, the objective function of the MPC control is:

[0087]

[0088] in, These are non-negative slack variables used to ensure that the optimization problem has a solution; Q, R, and W represent weighting matrices. These represent the sampling time, prediction time domain, and control time domain, respectively. Considering control accuracy and computational efficiency, the sampling time... T =0.02s, N c =20, N p =30.

[0089] The constraints of the MPC control include vehicle stability constraints:

[0090]

[0091] In the formula, ;

[0092] in, l r The distance from the vehicle's center of gravity to the rear axle. These are the coefficient of friction of the ground and the acceleration due to gravity, respectively. This represents the rear wheel slip angle; considering tire saturation and maximum tire lateral force, and assuming that the effects of ground lateral force, front suspension inertial force, and centripetal acceleration force on the tire are 3... μmg From equation (17), we can obtain:

[0093]

[0094] in, l f This is the distance from the vehicle's center of gravity to the front axle. L Wheelbase Rear wheel lateral stiffness;

[0095] It also includes control quantity constraints:

[0096]

[0097] in, These represent the control increments respectively. Absolute value and control quantity u The maximum limit of absolute value.

[0098] Specifically, regarding the additional yaw moment generated by the path tracking controller 2 Distributed to the four tires, with the addition of yaw moment, the torque of the four wheels of the car can be expressed as:

[0099]

[0100] In the formula, These represent the torque changes for the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. , l r This is the distance from the vehicle's center of gravity to the rear axle. L Wheelbase l s It is half the track width. R This is the tire radius.

[0101] In summary, this application solves the technical problem that existing algorithms cannot effectively utilize vehicle yaw performance under extreme conditions. By using energy ratio and energy ratio change rate as stability decision indicators, a path tracking controller based on model predictive control (MPC) is designed, and a force-driven on-off MPC control strategy is proposed, improving the longitudinal and lateral stability of the vehicle under extreme conditions. It will be understood by those skilled in the art that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method of longitudinal-lateral stability control based on phase plane analysis, characterized by, Comprise: A vehicle-road model is constructed based on a kinematic relationship between the vehicle and the target path, and a vehicle model describing lateral and yaw motion of the vehicle; Obtain road environment information and vehicle state information, to instability energy ratio R , the rate of change of instability energy ratio Establish a phase plane for parameters, based on phase plane analysis, determine vehicle working conditions, when formula (1) is satisfied, it is considered that the vehicle is in stable working condition, otherwise it is considered to be in unstable working condition; （1）， wherein, wherein, E 1 , E 2 are the longitudinal kinetic energy and the instability kinetic energy of the vehicle, respectively, are the longitudinal velocity, the lateral velocity and the yaw angular velocity of the vehicle, respectively, are the moment of inertia and the mass of the vehicle, respectively; is a constant related to the working condition; When the vehicle is in different working conditions, the MPC control is performed by the corresponding path tracking controller: In the steady state, the total lateral force of the front wheels of the vehicle is F yf A path tracking controller one based on the vehicle-path model MPC control is designed for the control quantity, and a state space model thereof is: （2）， In formula (2), a state vector , a control variable , an output vector , A 1 , B 1 denotes a time-varying coefficient matrix, C 3 is a selection matrix; In the unstable working condition, the additional yaw moment of the vehicle Adjusting the parameters of the path tracking controller one, a path tracking controller two is obtained, and a state space model thereof is: （3）， In formula (3), a state vector , a control variable , an output vector , A 2 , B 2 denotes a time-varying coefficient matrix, C 4 is a selection matrix; in formula (2) and formula (3), are a lateral deviation and a heading deviation between the vehicle and the target path, respectively, k is a discrete-time first k moment; The objective function of the MPC control is: wherein are non-negative slack variables; Q, R, W represent weighting matrices;, are the sampling time, prediction horizon and control horizon, respectively; The constraints of the MPC control include vehicle stability constraints: wherein, ; wherein, l r the distance of the vehicle's center of mass to the rear axle, the ground friction coefficient and the gravitational acceleration, respectively, denotes the rear wheel side slip angle: wherein, l f is the distance from the vehicle center of mass to the front axle, L is the wheelbase, is the rear wheel cornering stiffness; further comprising a control quantity constraint: wherein, respectively represent the control quantity increment absolute value and control quantity u maximum limit value of the absolute value.

2. The phase-plane analysis-based longitudinal-lateral stability control method according to claim 1, characterized by, The The method for determining the constant related to the working condition is: Let wherein, β is the vehicle's mass center side slip angle; Let When = 0, we get When R = 0, we get where are the maximum sideslip angle and the maximum yaw rate of the steady state, respectively.

3. The phase-plane analysis-based longitudinal-lateral stability control method according to claim 1, characterized by, Further comprise: the additional yaw moment generated by the path following controller assigned to the four tires: ， In the formula, respectively, the torque variation amount of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, , l r is the distance from the vehicle center of mass to the rear axle, L is the wheelbase, l s is half of the track, R is the tire radius.

4. The phase-plane analysis-based longitudinal-lateral stability control method according to claim 1, characterized by, The kinematic relationship between the vehicle and the target path is: wherein, denotes the heading angular velocity of the target path, is the road curvature of the reference path at position s .

5. The phase-plane analysis-based longitudinal-lateral stability control method according to claim 4, characterized by, The vehicle model is a two-degree-of-freedom vehicle model: ， wherein m represents the vehicle mass; represents the vehicle moment of inertia; F yf represents the total front lateral force; F yr represents the total rear lateral force; l f represents the distance from the vehicle center of mass to the front axle; l r represents the distance from the vehicle center of mass to the rear axle, represents the vehicle additional yaw moment.

Images