CN108107731B - Automobile stability control method based on tire nonlinear characteristics - Google Patents

Automobile stability control method based on tire nonlinear characteristics Download PDF

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CN108107731B
CN108107731B CN201711362483.XA CN201711362483A CN108107731B CN 108107731 B CN108107731 B CN 108107731B CN 201711362483 A CN201711362483 A CN 201711362483A CN 108107731 B CN108107731 B CN 108107731B
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automobile
tire
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angle
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CN108107731A (en
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李绍松
王国栋
卢晓晖
于志新
张邦成
郑顺航
李增
吴晓东
宁方虎
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Changchun University of Technology
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

The method is characterized by comprising a reference model, a tire lateral force and cornering stiffness processor, an MPC controller, a braking force distribution module and a Carsim automobile model. The reference model is used for determining the expected yaw rate and the centroid slip angle of the automobile; a tire lateral force and cornering stiffness processor for determining a cornering angle, a lateral force and a cornering stiffness of the tire; the CarSim automobile model is used for outputting the actual motion state information of the automobile; the MPC controller selects a prediction model according to the cornering stiffness of the tire, and optimally solves the additional turning angle and the compensation yaw moment of the front wheel of the automobile; the additional turning angle of the front wheel and the turning angle of the front wheel generated by the steering input of the driver are superposed and then directly output to the CarSim automobile model, the compensation yaw moment is output to the braking force distribution module, the braking moments of the four wheels are determined by the braking force distribution module and are output to the CarSim automobile model, and the stability control is realized.

Description

Automobile stability control method based on tire nonlinear characteristics
The technical field is as follows:
the invention relates to the field of automobile stability control, in particular to an automobile stability control method based on tire nonlinear characteristics.
Background art:
with the continuous development of the dynamic control of the automobile chassis, the integrated control becomes the development direction in the future, and the combination of the active front wheel steering and the direct yaw moment to realize the stability of the automobile is widely researched. At present, control methods related to the field of automobile stability control mainly include robust control, neural network control, Model Predictive Control (MPC) and other methods, wherein the Model predictive control can better handle multi-target tasks and system constraints, and is widely applied to the field of automobile stability control.
MPC can be classified into linear MPC and non-linear MPC depending on the prediction model used and the optimization method. The linear MPC is widely used due to its small calculation burden and high calculation speed, however, the linear MPC cannot represent the tire cornering characteristics in the nonlinear region, and the nonlinear MPC capable of representing the nonlinear dynamic characteristics of the automobile is too heavy in calculation burden and poor in real-time performance, and is difficult to be applied to practice. According to the thesis [ Chenjie, Liliang, Song Jian ] automobile stability control research [ J ] automobile engineering,2016, 38(3):308-316 ] based on LTV-MPC, a linear time-varying MPC method is adopted, and the automobile stability control of the limit working condition is realized through limiting the target yaw angular speed, so that the calculation burden of the system is reduced. However, the limitation of the magnitude of the target yaw rate depends on the accurate estimation of the vehicle speed and the road surface adhesion coefficient, and the employed linear time-varying MPC method cannot embody the non-linear variation characteristics of the tire lateral force and the tire slip angle when the tire lateral force is saturated. The paper [ choice M, choice S b. MPC for achieving stability with respect to lateral force and active front influencing the preceding active applications [ J ] Proceedings of the organization of mechanical engineering Part D Journal of automotive engineering 2016,230(4) ], based on the linear time varying MPC method, when the tire side deviation angle exceeds a designed threshold value, the optimization solution of the MPC is corrected by the difference between the tire side deviation angle and the threshold value, achieving stability control after tire side force saturation, but this method does not embody the non-linear variation characteristic of the tire side force (absolute value) decreasing with the increase of the tire side deviation angle. A paper [ Cairano S D, Tseng H E, Bernardini D, et al. Steering Vehicle Control by switched mode Predictive Control [ J ]. IFAC Proceedings Volumes,2010,43(7):1-6 ] designs a switching controller according to the motion state of an automobile, and considers the change characteristic that the lateral force (absolute value) of the tire is reduced along with the increase of the lateral deflection angle of the tire under the limit working condition, but the method adopts a tire Model which is still linear and cannot represent the nonlinear dynamic characteristic of the automobile.
The invention content is as follows:
the method aims to solve the problems of narrow controller stability range and low control precision caused by the fact that the existing linear MPC control method cannot comprehensively represent the nonlinear characteristics of the tire. The invention provides an automobile stability control method based on tire nonlinear characteristics, which can automatically switch a prediction model according to a tire cornering stiffness value, convert a nonlinear prediction control problem into a linear prediction control problem by adopting a linear time-varying method, reduce the calculation burden of a system while representing the nonlinear dynamic characteristics of an automobile, and ensure the yaw stability of the automobile under a limit working condition.
The technical scheme adopted by the invention for solving the technical problem is as follows:
a vehicle stability control method based on tire nonlinear characteristics is characterized by comprising a reference model, a tire lateral force and lateral deflection stiffness processor, an MPC controller, a braking force distribution module and a Carsim vehicle model; the reference model is used for determining the expected yaw rate and the centroid slip angle of the automobile; a tire lateral force and cornering stiffness processor for determining a cornering angle, a lateral force and a cornering stiffness of the tire; the CarSim automobile model is used for outputting actual motion state information of an automobile, wherein the actual motion state information comprises automobile longitudinal speed, yaw velocity, mass center slip angle and road adhesion coefficient; the MPC controller selects a prediction model according to the tire cornering stiffness, and optimally solves the additional corner of the front wheel and the compensation yawing moment of the automobile by combining the expected yaw velocity of the automobile, the centroid cornering angle and the actual motion state information of the automobile; the additional turning angle of the front wheel is superposed with the turning angle of the front wheel generated by the steering input of a driver and then directly output to the CarSim automobile model, the compensation yaw moment is output to the braking force distribution module, the braking moments of four wheels are determined by the braking force distribution module and output to the CarSim automobile model, and the stability control is realized;
the method comprises the following steps:
step 1, establishing a reference model, and determining an expected automobile yaw angular velocity and a centroid slip angle, wherein the process comprises the following substeps:
step 1.1, a linear two-degree-of-freedom automobile model is used as a reference model, and the expression of a motion differential equation is as follows:
Figure GDA0001721817000000021
Figure GDA0001721817000000022
wherein β is the mass center slip angle of the automobile, gamma is the yaw rate of the automobile, I zIs the yaw moment of inertia around the vertical axis of the center of mass of the automobile; u shape xIs the vehicle longitudinal speed; l fAnd l rThe distances from the center of mass of the automobile to the front axle and the rear axle respectively; c fAnd C rThe cornering stiffness of the front and rear tires of the automobile respectively; delta f,driIs the front wheel steering angle generated by the driver steering input;
step 1.2, converting the formula (1a) into a transfer function, wherein the form is as follows:
Figure GDA0001721817000000023
to achieve the desired closed loop effect, the desired yaw rate of the vehicle is obtained based on equation (2):
Figure GDA0001721817000000031
wherein: gamma ray refIs the desired yaw rate of the vehicle; w is a nIs the natural frequency of the system, ξ is the system damping, G ω(s) is the transfer function gain; w is a d＝k 1w n,ξ d＝k 2ξ,G kω(s)＝k 3G ω(s)；k 1、k 2、k 3Is a parameter for improving the phase delay and the response speed of the system;
step 1.3, setting the expected centroid slip angle as:
β ref＝0 (4)
step 2, designing a tire lateral force and cornering stiffness processor, wherein the process comprises the following sub-steps:
step 2.1, designing a tire side deflection angle calculation module, and calculating the side deflection angles of the front and rear wheel tires according to the following formula:
wherein α fAnd α rRespectively are the slip angles of the front and rear tires of the automobile; delta fThe method is characterized in that the method is finally applied to the front wheel corner of the automobile, namely the superposition of the front wheel corner generated by the optimized solved front wheel additional corner and the steering input of a driver;
2.2, designing a tire lateral force and cornering stiffness calculation module, and acquiring a relation curve of the lateral force of the front wheel tire and the sidewall deviation angle of the front wheel tire under different road adhesion coefficients based on a Pacejka tire model in order to acquire the nonlinear characteristic of the front wheel tire to obtain a three-dimensional graph of the sidewall deviation characteristic of the front wheel tire; obtaining a relation curve of the lateral force of the front wheel tire to the sidewall deflection angle derivative of the front wheel tire under different road adhesion coefficients to obtain a three-dimensional graph of the sidewall deflection rigidity characteristic of the front wheel tire; the tire lateral force and lateral deflection rigidity processor respectively inputs the actual front wheel tire lateral deflection angle and the road surface attachment coefficient at the current moment into a front wheel tire lateral deflection characteristic three-dimensional graph and a front wheel tire lateral deflection rigidity characteristic three-dimensional graph, respectively obtains the front wheel tire lateral force and the front wheel tire lateral deflection rigidity at the current moment through a linear interpolation method, and outputs the front wheel tire lateral force and the front wheel tire lateral deflection rigidity to the MPC controller; updating the lateral force and lateral deflection rigidity data of the front wheel tire once by the tire lateral force and lateral deflection rigidity processor in each control period;
wherein: the Pacejka tire model is as follows:
Figure GDA0001721817000000033
wherein: f yIs the tire lateral force, α is the tire slip angle, B,c, D and E depend on the wheel vertical load F z；a 0＝1.75；a 1＝0；a 2＝1000；a 3＝1289；a 4＝7.11；a 5＝0.0053；a 6＝0.1925
Step 3, designing an MPC controller, wherein the process comprises the following substeps:
step 3.1, establishing a prediction model, including a prediction model A and a prediction model B, wherein the process comprises the following substeps:
step 3.1.1, establishing a prediction model A, wherein a motion differential equation is as follows:
Figure GDA0001721817000000041
Figure GDA0001721817000000042
wherein: m zIs to compensate for yaw moment;
writing the prediction equation into a state space equation for designing a prediction equation, which is concretely as follows:
Figure GDA0001721817000000043
wherein:
Figure GDA0001721817000000044
step 3.1.2, establishing a prediction model B, wherein the motion differential equation is as follows:
considering that when the sidewall deflection angle of a front wheel tire is large in actual running of an automobile, the lateral force of the front wheel tire and the sidewall deflection angle of the front wheel tire present a nonlinear change relationship, when the sidewall deflection rigidity of the front wheel tire is less than 0, the lateral force of the front wheel tire is reduced along with the increase of the sidewall deflection angle of the front wheel tire, and in order to represent the nonlinear change characteristic between the lateral force of the front wheel tire and the sidewall deflection angle of the front wheel tire, the expression of the sidewall lateral force of the front wheel tire is constructed as follows:
Figure GDA0001721817000000046
wherein:
Figure GDA0001721817000000047
wherein:
Figure GDA0001721817000000048
is the residual lateral force of the front wheel tire;
Figure GDA0001721817000000049
the lateral force of the front wheel tire is obtained by a linear interpolation method based on a three-dimensional graph of the sidewall deviation characteristic of the front wheel tire;
Figure GDA00017218170000000410
the cornering stiffness of the front wheel tire is obtained by a linear interpolation method based on a three-dimensional graph of the cornering stiffness characteristic of the front wheel tire;
Figure GDA00017218170000000411
is the sidewall deflection angle of the front wheel at the current moment;
considering that the side deflection angle of the rear wheel tire is small in actual running of an automobile, the side deflection force of the rear wheel tire is linearly increased along with the increase of the side deflection angle of the rear wheel tire, and the side deflection rigidity of the rear wheel tire is a fixed value, the expression of the side deflection force of the rear wheel tire is constructed as follows:
F y,r＝C r·α r, (11)
wherein: c rIs the cornering stiffness of the rear wheel tire, α rIs the slip angle of the rear wheel tire;
the motion differential equation of the finally obtained prediction model B is as follows:
Figure GDA0001721817000000051
writing the prediction equation into a state space equation for designing a prediction equation, which is concretely as follows:
Figure GDA0001721817000000052
wherein:
Figure GDA0001721817000000053
Figure GDA0001721817000000054
3.1.3, designing the switching door conditions of the prediction model A and the prediction model B, wherein when the sidewall deflection rigidity value of the current wheel is larger than zero, the MPC controller uses the prediction model A; when the sidewall deflection rigidity value of the current wheel is smaller than zero, the MPC controller uses a prediction model B; in each control period, the tire lateral force and cornering stiffness processor updates the lateral force and cornering stiffness data of the front wheel tires once and outputs the data to the MPC controller, and the MPC controller selects a prediction model according to the cornering stiffness and optimizes and solves the additional corner and the compensation yaw moment of the front wheels at the next moment;
step 3.1.4, establishing a prediction equation for predicting the future output of the system; in order to realize the tracking control of the yaw rate and the centroid slip angle of the automobile, a prediction model A and a prediction model B of a continuous time system are converted into an incremental model of a discrete time system:
Figure GDA0001721817000000055
wherein: sample time k int (T/T) s) T is simulation time, T sIs the simulation step length;
Figure GDA0001721817000000056
Figure GDA0001721817000000057
i＝1,2；C＝1；
step 3.2, designing an optimization target and constraint conditions, wherein the process comprises the following substeps:
step 3.2.1, using the expected yaw angular velocity and the centroid slip angle of the automobile and the two norms of the actual yaw angular velocity and the centroid slip angle error of the automobile as tracking performance indexes to reflect the track tracking characteristics of the automobile, wherein the expression is as follows:
wherein: gamma ray refIs the desired yaw rate of the vehicle, gamma is the actual yaw rate of the vehicle, β refIs the expected automobile centroid slip angle, β is the actual automobile centroid slip angle, P is the predicted time domain, k represents the current time, Q 1、Q 2Is a weighting factor;
step 3.2.2, using the two-norm of the control quantity change rate as a steering and braking smooth index, reflecting the steering and braking smooth characteristics in the tracking process, and establishing a discrete quadratic steering and braking smooth index as follows:
Figure GDA0001721817000000062
wherein: m is a control time domain; delta delta fIs an additional front wheel angle, Δ M zCompensating the change amount of the yaw moment; k represents the current time; s 1、S 2Is a weighting factor;
step 3.2.3, setting physical constraints of the actuator to meet the requirements of the actuator:
and limiting the upper limit and the lower limit of the control quantity and the variable quantity thereof by using a linear inequality to obtain the physical constraint of the steering actuator, wherein the mathematical expression is as follows:
Figure GDA0001721817000000063
step 3.3, solving the system prediction output, wherein the process comprises the following substeps:
3.3.1, converting the tracking performance index in the step 3.2.1 and the steering and braking smoothness index in the step 3.2.2 into a single index by using a linear weighting method, and constructing an automobile stability multi-target optimization control problem, wherein the problem needs to meet the physical constraint of a steering actuator, and the input and output of the problem accord with a prediction model:
Figure GDA0001721817000000064
subject to
i) Prediction model A or prediction model B
ii) the constraint condition is formula (17)
3.3.2, calling a QP algorithm in the controller, solving a multi-objective optimization control problem (18) and obtaining an optimal open-loop control sequence delta u as follows:
selecting a first group of elements delta u (0) in the optimal open loop control sequence at the current moment for feedback, wherein delta fAfter linearly overlapping with a front wheel steering angle input by a driver, directly outputting the front wheel steering angle to a CarSim automobile model; Δ M ZAnd the braking torque is output to a braking force distribution module, the braking torque of four wheels is determined through the braking force distribution module, and the braking torque is output to a CarSim automobile model, so that the yaw moment control is finally realized.
The invention has the beneficial effects that: the method uses a linear time-varying method to convert the nonlinear predictive control problem into a linear predictive control problem, fully utilizes the nonlinear tire cornering characteristic, reduces the calculation burden of the system, improves the yaw stability of the automobile, and enlarges the yaw stability control domain of the automobile; the two sets of prediction models used by the method share one set of prediction control algorithm, so that the design of the controller is simplified.
Drawings
Fig. 1 is a schematic diagram of the control system structure of the present invention.
FIG. 2 is a schematic view of a linear two-degree-of-freedom automobile model.
FIG. 3 is a three-dimensional graph of sidewall deflection characteristics for a front wheel tire.
FIG. 4 is a three-dimensional graph of sidewall deflection stiffness characteristics of a front wheel tire.
FIG. 5 is a schematic diagram of a predictive model switching door condition.
Fig. 6 is a brake force distribution diagram.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
Fig. 1 is a schematic structural diagram of a system of a vehicle stability control method based on tire nonlinear characteristics, and the system mainly comprises a reference model 1, a tire lateral force and cornering stiffness processor 2, an MPC controller 3, a braking force distribution module 4 and a Carsim vehicle model 5. The reference model 1 is used to determine the desired yaw rate and centroid slip angle of the vehicle; the tire lateral force and cornering stiffness processor 2 is used for determining a cornering angle, a lateral force and a cornering stiffness of the tire; the CarSim automobile model 5 is used for outputting the actual motion state information of the automobile, including the longitudinal speed, the yaw rate, the mass center slip angle and the road adhesion coefficient of the automobile; the MPC controller 3 selects a prediction model according to the tire cornering stiffness, optimally solves the additional corner of the front wheel of the automobile and the compensation yawing moment by combining the expected yaw velocity, the mass center cornering angle and the actual motion state information of the automobile, directly outputs the additional corner of the front wheel and the front wheel rotation angle generated by the steering input of a driver to the CarSim automobile model 5 after being superposed, outputs the compensation yawing moment to the braking force distribution module 4, determines the braking moments of four wheels through the braking force distribution module 4, and outputs the braking moments to the CarSim automobile model 5, thereby realizing the stability control.
The method of the present invention is specifically described below with a certain vehicle model of the CarSim vehicle simulation software as a platform, and the main parameters are shown in table 1:
TABLE 1 simulation of the principal parameters of a vehicle
The establishment of the reference model 1 comprises three parts: 1.1, establishing a linear two-degree-of-freedom automobile model; 1.2 determining a desired yaw rate of the vehicle; 1.3, determining a desired automobile mass center slip angle;
in section 1.1, a linear two-degree-of-freedom automobile model is shown in fig. 2, and the motion differential equation expression is as follows:
Figure GDA0001721817000000083
wherein β is the mass center slip angle of the automobile, gamma is the yaw rate of the automobile, I zIs the yaw moment of inertia around the vertical axis of the center of mass of the automobile; u shape xIs the vehicle longitudinal speed; l fAnd l rThe distances from the mass center of the automobile to the front axle and the front axle respectively; c fAnd C rRespectively the cornering stiffness of the front and rear tires of the vehicle. Delta f,driIs the front wheel steering angle generated by the driver's steering input.
In section 1.2, equation (1a) is converted to a transfer function of the form:
Figure GDA0001721817000000084
to achieve the desired closed loop effect, the desired yaw rate of the vehicle is obtained based on equation (2):
Figure GDA0001721817000000091
wherein: gamma ray refIs the desired yaw rate; w is a nIs the natural frequency of the system, ξ is the system damping, G ω(s) is the transfer function gain; w is a d＝k 1w n,ξ d＝k 2ξ,G kω(s)＝k 3G ω(s)；k 1、k 2、k 3Is a parameter for improving the phase delay and response speed of the system. w is a n、ξ、G ω(s)、K ωThe calculation process of (2) is as follows:
Figure GDA0001721817000000092
Figure GDA0001721817000000093
Figure GDA0001721817000000094
in section 1.3, the desired centroid slip angle is set to:
β ref＝0 (4)
the design of the tire lateral force and cornering stiffness processor 2 comprises two parts: 2.1 designing a tire slip angle calculation module; 2.2 designing a tire lateral force and cornering stiffness calculation module;
in part 2.1, the front and rear tire sidewall angles are calculated by:
Figure GDA0001721817000000095
wherein α fAnd α rRespectively are the slip angles of the front and rear tires of the automobile; delta fThe front wheel corner which is finally acted on the automobile, namely the front wheel additional corner which is optimally solved, and the front wheel corner which is generated by the steering input of the driver are superposed.
In part 2.2, in order to obtain the nonlinear characteristics of the front wheel tire, based on the Pacejka tire model, a relation curve of the lateral force of the front wheel tire and the sidewall deviation angle of the front wheel tire under different road adhesion coefficients is obtained, and a three-dimensional graph of the sidewall deviation characteristics of the front wheel tire is obtained, as shown in fig. 3; and obtaining a relation curve of the lateral force of the front wheel tire to the sidewall deflection angle derivative of the front wheel tire under different road adhesion coefficients to obtain a three-dimensional graph of the sidewall deflection rigidity characteristic of the front wheel tire, as shown in FIG. 4. The tire lateral force and lateral deflection rigidity processor 2 respectively inputs the actual front wheel tire lateral deflection angle and the road surface attachment coefficient at the current moment into the front wheel tire lateral deflection characteristic three-dimensional graph and the front wheel tire lateral deflection rigidity characteristic three-dimensional graph, respectively obtains the front wheel tire lateral force and the front wheel tire lateral deflection rigidity at the current moment through a linear interpolation method, and outputs the front wheel tire lateral force and the front wheel tire lateral deflection rigidity to the MPC controller 3. The tire lateral force and cornering stiffness processor 2 updates the front wheel tire lateral force and front wheel tire cornering stiffness data once per control cycle.
Wherein: the Pacejka tire model is as follows:
Figure GDA0001721817000000101
Figure GDA0001721817000000102
wherein: f yIs the tire side force, α is the tire slip angle, B, C, D and E depend on the wheel vertical load F z；a 0＝1.75；a 1＝0；a 2＝1000；a 3＝1289；a 4＝7.11；a 5＝0.0053；a 6＝0.1925
The design of the MPC controller 3 comprises three parts: 3.1, establishing a prediction model and a prediction equation 3.2 to design an optimization target and constraint conditions; 3.3 solving the system prediction output;
in section 3.1, the establishment of the prediction model and the prediction equation comprises four parts: 3.1.1 designing a prediction model A; 3.1.2 designing a prediction model B; 3.1.3 designing the switching door conditions of the prediction model A and the prediction model B; 3.1.4 establishing a prediction equation;
in section 3.1.1, the prediction model a adopts a linear two-degree-of-freedom automobile model, as shown in fig. 2, the motion differential equation is as follows:
Figure GDA0001721817000000103
wherein: m zIs to compensate for yaw moment;
writing the prediction equation into a state space equation for designing a prediction equation, which is concretely as follows:
wherein:
Figure GDA0001721817000000106
in section 3.1.2, the prediction model B adopts a linear two-degree-of-freedom automobile model, as shown in fig. 2, and the motion differential equation is as follows:
considering that a front wheel tire side deflection angle is large in actual running of an automobile, and a front wheel tire side force and the front wheel tire side deflection angle show a nonlinear change relationship, as shown in fig. 5, when the front wheel tire side deflection rigidity is less than 0, the front wheel tire side force is reduced along with the increase of the front wheel tire side deflection angle, and in order to represent the nonlinear change characteristic between the front wheel tire side force and the front wheel tire side deflection angle, a front wheel tire side force expression is constructed as follows:
wherein:
Figure GDA0001721817000000112
wherein:
Figure GDA0001721817000000113
is the residual lateral force of the front wheel tire, i.e., the intercept in equation (10), as shown in fig. 5;
Figure GDA0001721817000000114
based on the three-dimensional map of the sidewall deviation characteristic of the front wheel tire by a linear interpolation methodThe lateral force of the front wheel tire obtained;
Figure GDA0001721817000000115
the cornering stiffness of the front wheel tire is obtained by a linear interpolation method based on a three-dimensional graph of the cornering stiffness characteristic of the front wheel tire; is the tire sidewall deflection angle of the front wheel at the current moment.
Considering that the tire cornering angle of a rear wheel tire is small in actual driving of an automobile, the tire cornering characteristic is in a linear region, the tire cornering force of the rear wheel tire is linearly increased along with the increase of the tire cornering angle of the rear wheel tire, and the tire cornering stiffness of the rear wheel tire is a fixed value, the expression of the tire cornering force of the rear wheel tire is constructed as follows:
F y,r＝C r·α r, (11)
wherein: c rIs the cornering stiffness of the rear wheel tire, α rIs the slip angle of the rear wheel tire;
the motion differential equation expression of the finally obtained prediction model B is as follows:
Figure GDA0001721817000000117
writing the prediction equation into a state space equation for designing a prediction equation, which is concretely as follows:
Figure GDA0001721817000000118
wherein:
Figure GDA0001721817000000119
Figure GDA00017218170000001110
in section 3.1.3, the design of the gate switching conditions of the prediction model a and the prediction model B is as shown in fig. 5, the MPC controller 3 uses the prediction model a when the tire cornering stiffness value of the current wheel is greater than zero, and the MPC controller 3 uses the prediction model B when the tire cornering stiffness value of the current wheel is less than zero.
As shown in FIG. 5, the current tire sidewall deviation angle is
Figure GDA0001721817000000121
When the tire sidewall deviation characteristic of the front wheel is in a nonlinear region, the tire sidewall deviation rigidity value of the front wheel is smaller than zero, and the MPC controller 3 obtains the tire lateral force of the front wheel at the current moment from the tire lateral force and sidewall deviation rigidity processor 2 Sidewall deflection stiffness for front wheel tires
Figure GDA0001721817000000123
Calculating the residual lateral force of the front wheel tire Optimizing the additional corner and the compensation yaw moment of the front wheel at the current moment by using the prediction model B; at the next moment, the tire side deflection angle of the front wheel is changed, the tire side force and side deflection rigidity processor 2 obtains the data of the side force and the side deflection rigidity of the front wheel tire again and outputs the data to the MPC controller 3, and the MPC controller 3 selects a prediction model according to the side deflection rigidity of the front wheel tire, so that the additional corner and the compensation yaw moment of the front wheel at the next moment are optimized.
In section 3.1.4, to realize the tracking control of the yaw rate and the centroid slip angle of the vehicle, the prediction model a and the prediction model B of the continuous-time system are converted into incremental models of the discrete-time system:
Δx(k+1)＝A cΔx(k)+B cuΔu(k)+B cdΔd(k),
y(k)＝CΔx(k)+y(k-1). (14)
wherein: sample time k int (T/T) s) T is simulation time, T sIs the simulation step length; i＝1,2；C＝1。
the design of optimization objectives and constraints in section 3.2 includes three parts: 3.2.1 designing yaw angular velocity and centroid slip angle tracking performance indexes; 3.2.2 designing a steering and braking smoothness index; 3.2.3 setting actuator physical constraints;
in the section 3.2.1, the expected yaw rate and the centroid slip angle of the automobile and the two norms of the errors of the actual yaw rate and the centroid slip angle of the automobile are used as tracking performance indexes to reflect the track tracking characteristics of the automobile, and the expressions are as follows:
Figure GDA0001721817000000127
wherein: gamma ray refIs the desired yaw rate of the vehicle, gamma is the actual yaw rate of the vehicle, β refIs the expected automobile centroid slip angle, β is the actual automobile centroid slip angle, P is the predicted time domain, k represents the current time, Q 1、Q 2Is a weighting factor;
in the 3.2.2 part, the two-norm of the control quantity change rate is used as a steering and braking smooth index, the steering and braking smooth characteristics in the tracking process are reflected, and the discrete quadratic steering and braking smooth index is established as follows:
Figure GDA0001721817000000128
wherein: m is a control time domain; delta delta fIs an additional front wheel angle, Δ M zCompensating the change amount of the yaw moment; k represents the current time; s 1、S 2Is a weighting factor;
in section 3.2.3, the physical constraints of the steering actuator are obtained by limiting the upper and lower limits of the controlled variable and the variable thereof by using a linear inequality, and the mathematical expression of the physical constraints is as follows:
Figure GDA0001721817000000134
in section 3.3, the solution of the system prediction output includes two parts: 3.3.1 constructing a multi-target optimization control problem of the yaw stability of the automobile; 3.3.2 solving the multi-objective optimization control problem;
in the 3.3.1 part, the tracking performance index of the 3.2.1 part and the steering and braking smooth index of the 3.2.2 part are converted into a single index by using a linear weighting method, and an automobile stability multi-objective optimization control problem is constructed, wherein the problem needs to meet the physical constraint of a steering actuator, and the input and output conform to a prediction model:
Figure GDA0001721817000000131
subject to
i) Prediction model A or prediction model B
ii) the constraint condition is formula (17)
In the 3.3.2 part, a QP algorithm is called in a controller, a multi-objective optimization control problem (18) is solved, and an optimal open-loop control sequence delta u is obtained as follows:
Figure GDA0001721817000000132
selecting a first group of elements delta u (0) in the optimal open loop control sequence at the current moment for feedback, wherein delta fThe front wheel steering angle input by a driver is linearly superposed and then directly output to the CarSim automobile model 5, the delta Mz is output to the braking force distribution module, the braking torque of four wheels is determined by the braking force distribution module 4 and is output to the CarSim automobile model 5, and stability control is realized.
The design flow of the braking force distribution module 4 is as follows:
as shown in fig. 6, when the compensation yaw moment calculated by the MPC controller 3 is less than zero, if the sidewall deviation angle of the front wheel of the vehicle is less than the sidewall deviation angle of the rear wheel of the vehicle, the braking force distribution module 4 generates the compensation yaw moment by applying a braking force to the front right wheel, so as to correct the excessive steering of the vehicle; if the side deflection angle of the front wheel tire of the automobile is larger than that of the rear wheel tire, the braking force distribution module 4 applies braking force to the right rear wheel to generate a compensation yaw moment so as to correct understeer of the automobile;
when the compensation yaw moment calculated by the MPC controller 3 is larger than zero, if the side deviation angle of the front wheel of the automobile is smaller than the side deviation angle of the rear wheel, the braking force distribution module 4 generates the compensation yaw moment by applying braking force to the left front wheel, and corrects the excessive steering of the automobile. If the side deflection angle of the front wheel tire of the automobile is larger than that of the rear wheel tire, the braking force distribution module 4 applies braking force to the left rear wheel to generate compensation yaw moment so as to correct understeer of the automobile.
The braking force distribution strategy is specifically as follows:
Figure GDA0001721817000000144
wherein, F b1、F b2、F b3、F b4The braking force of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel is respectively; c half of the vehicle track.

Claims (1)

1. A vehicle stability control method based on tire nonlinear characteristics is characterized by comprising a reference model, a tire lateral force and lateral deflection stiffness processor, an MPC controller, a braking force distribution module and a Carsim vehicle model; the reference model is used for determining the expected yaw rate and the centroid slip angle of the automobile; a tire lateral force and cornering stiffness processor for determining a cornering angle, a lateral force and a cornering stiffness of the tire; the CarSim automobile model is used for outputting actual motion state information of an automobile, wherein the actual motion state information comprises automobile longitudinal speed, yaw velocity, mass center slip angle and road adhesion coefficient; the MPC controller selects a prediction model according to the tire cornering stiffness, and optimally solves the additional corner of the front wheel and the compensation yawing moment of the automobile by combining the expected yaw velocity of the automobile, the centroid cornering angle and the actual motion state information of the automobile; the additional turning angle of the front wheel is superposed with the turning angle of the front wheel generated by the steering input of a driver and then directly output to the CarSim automobile model, the compensation yaw moment is output to the braking force distribution module, the braking moments of four wheels are determined by the braking force distribution module and output to the CarSim automobile model, and the stability control is realized;
the method comprises the following steps:
step 1, establishing a reference model, and determining an expected automobile yaw angular velocity and a centroid slip angle, wherein the process comprises the following substeps:
step 1.1, a linear two-degree-of-freedom automobile model is used as a reference model, and the expression of a motion differential equation is as follows:
Figure FDA0002242600580000011
Figure FDA0002242600580000012
wherein β is the mass center slip angle of the automobile, gamma is the yaw rate of the automobile, I zIs the yaw moment of inertia around the vertical axis of the center of mass of the automobile; m is the mass of the automobile; u shape xIs the vehicle longitudinal speed; l fAnd l rThe distances from the center of mass of the automobile to the front axle and the rear axle respectively; c fAnd C rThe cornering stiffness of the front and rear tires of the automobile respectively; delta f,driIs the front wheel steering angle generated by the driver steering input;
step 1.2, converting the formula (1a) into a transfer function, wherein the form is as follows:
to achieve the desired closed loop effect, the desired yaw rate of the vehicle is obtained based on equation (2):
wherein: gamma ray refIs the desired yaw rate of the vehicle; w is a nIs the natural frequency of the system, ξ is the system damping, G ω(s) is transferringA function gain; w is a d＝k 1w n,ξ d＝k 2ξ,G kω(s)＝k 3G ω(s)；k 1、k 2、k 3Is a parameter for improving the phase delay and the response speed of the system;
step 1.3, setting the expected centroid slip angle as:
β ref＝0 (4)
step 2, designing a tire lateral force and cornering stiffness processor, wherein the process comprises the following sub-steps:
step 2.1, designing a tire side deflection angle calculation module, and calculating the side deflection angles of the front and rear wheel tires according to the following formula:
Figure FDA0002242600580000021
wherein α fAnd α rRespectively are the slip angles of the front and rear tires of the automobile; delta fThe method is characterized in that the method is finally applied to the front wheel corner of the automobile, namely the superposition of the front wheel corner generated by the optimized solved front wheel additional corner and the steering input of a driver;
2.2, designing a tire lateral force and cornering stiffness calculation module, and acquiring a relation curve of the lateral force of the front wheel tire and the sidewall deviation angle of the front wheel tire under different road adhesion coefficients based on a Pacejka tire model in order to acquire the nonlinear characteristic of the front wheel tire to obtain a three-dimensional graph of the sidewall deviation characteristic of the front wheel tire; obtaining a relation curve of the lateral force of the front wheel tire to the sidewall deflection angle derivative of the front wheel tire under different road adhesion coefficients to obtain a three-dimensional graph of the sidewall deflection rigidity characteristic of the front wheel tire; the tire lateral force and lateral deflection rigidity processor respectively inputs the actual front wheel tire lateral deflection angle and the road surface attachment coefficient at the current moment into a front wheel tire lateral deflection characteristic three-dimensional graph and a front wheel tire lateral deflection rigidity characteristic three-dimensional graph, respectively obtains the front wheel tire lateral force and the front wheel tire lateral deflection rigidity at the current moment through a linear interpolation method, and outputs the front wheel tire lateral force and the front wheel tire lateral deflection rigidity to the MPC controller; updating the lateral force and lateral deflection rigidity data of the front wheel tire once by the tire lateral force and lateral deflection rigidity processor in each control period;
wherein: the Pacejka tire model is as follows:
Figure FDA0002242600580000022
wherein: f yIs the tire lateral force, α is the tire slip angle, μ is the road adhesion coefficient, B, C, D and E are dependent on the wheel vertical load F z；a 0＝1.75；a 1＝0；a 2＝1000；a 3＝1289；a 4＝7.11；a 5＝0.0053；a 6＝0.1925；
Step 3, designing an MPC controller, wherein the process comprises the following substeps:
step 3.1, establishing a prediction model, including a prediction model A and a prediction model B, wherein the process comprises the following substeps:
step 3.1.1, establishing a prediction model A, wherein a motion differential equation is as follows:
Figure FDA0002242600580000031
Figure FDA0002242600580000032
wherein: m zIs to compensate for yaw moment;
writing the prediction equation into a state space equation for designing a prediction equation, which is concretely as follows:
Figure FDA0002242600580000033
wherein:
Figure FDA0002242600580000034
step 3.1.2, establishing a prediction model B, wherein the motion differential equation is as follows:
considering that when the sidewall deflection angle of a front wheel tire is large in actual running of an automobile, the lateral force of the front wheel tire and the sidewall deflection angle of the front wheel tire present a nonlinear change relationship, when the sidewall deflection rigidity of the front wheel tire is less than 0, the lateral force of the front wheel tire is reduced along with the increase of the sidewall deflection angle of the front wheel tire, and in order to represent the nonlinear change characteristic between the lateral force of the front wheel tire and the sidewall deflection angle of the front wheel tire, the expression of the sidewall lateral force of the front wheel tire is constructed as follows:
wherein:
wherein:
Figure FDA0002242600580000038
is the residual lateral force of the front wheel tire;
Figure FDA0002242600580000039
the lateral force of the front wheel tire is obtained by a linear interpolation method based on a three-dimensional graph of the sidewall deviation characteristic of the front wheel tire;
Figure FDA00022426005800000310
the cornering stiffness of the front wheel tire is obtained by a linear interpolation method based on a three-dimensional graph of the cornering stiffness characteristic of the front wheel tire;
Figure FDA00022426005800000311
is the sidewall deflection angle of the front wheel at the current moment;
considering that the side deflection angle of the rear wheel tire is small in actual running of an automobile, the side deflection force of the rear wheel tire is linearly increased along with the increase of the side deflection angle of the rear wheel tire, and the side deflection rigidity of the rear wheel tire is a fixed value, the expression of the side deflection force of the rear wheel tire is constructed as follows:
F y,r＝C r·α r, (11)
wherein: c rIs the cornering stiffness of the rear wheel tire, α rIs the slip angle of the rear wheel tire;
the motion differential equation of the finally obtained prediction model B is as follows:
Figure FDA0002242600580000041
writing the prediction equation into a state space equation for designing a prediction equation, which is concretely as follows:
Figure FDA0002242600580000042
wherein:
x＝[γ,β] T；u＝[δ f,M Z] T；
Figure FDA0002242600580000043
Figure FDA0002242600580000044
3.1.3, designing the switching door conditions of the prediction model A and the prediction model B, wherein when the sidewall deflection rigidity value of the current wheel is larger than zero, the MPC controller uses the prediction model A; when the sidewall deflection rigidity value of the current wheel is smaller than zero, the MPC controller uses a prediction model B; in each control period, the tire lateral force and cornering stiffness processor updates the lateral force and cornering stiffness data of the front wheel tires once and outputs the data to the MPC controller, and the MPC controller selects a prediction model according to the cornering stiffness and optimizes and solves the additional corner and the compensation yaw moment of the front wheels at the next moment;
step 3.1.4, establishing a prediction equation for predicting the future output of the system; in order to realize the tracking control of the yaw rate and the centroid slip angle of the automobile, a prediction model A and a prediction model B of a continuous time system are converted into an incremental model of a discrete time system:
Figure FDA0002242600580000045
wherein: sample time k int (T/T) s) T is simulation time, T sIs the simulation step length;
Figure FDA0002242600580000046
Figure FDA0002242600580000047
i＝1,2；C＝1；
step 3.2, designing an optimization target and constraint conditions, wherein the process comprises the following substeps:
step 3.2.1, using the expected yaw angular velocity and the centroid slip angle of the automobile and the two norms of the actual yaw angular velocity and the centroid slip angle error of the automobile as tracking performance indexes to reflect the track tracking characteristics of the automobile, wherein the expression is as follows:
Figure FDA0002242600580000048
wherein: gamma ray refIs the desired yaw rate of the vehicle, gamma is the actual yaw rate of the vehicle, β refIs the expected automobile centroid slip angle, β is the actual automobile centroid slip angle, P is the predicted time domain, k represents the current time, Q 1、Q 2Is a weighting factor;
step 3.2.2, using the two-norm of the control quantity change rate as a steering and braking smooth index, reflecting the steering and braking smooth characteristics in the tracking process, and establishing a discrete quadratic steering and braking smooth index as follows:
Figure FDA0002242600580000051
wherein: m is a control time domain; delta delta fIs an additional front wheel angle, Δ M zCompensating the change amount of the yaw moment; k represents the current time; s 1、S 2Is a weighting factor;
step 3.2.3, setting physical constraints of the actuator to meet the requirements of the actuator:
and limiting the upper limit and the lower limit of the control quantity and the variable quantity thereof by using a linear inequality to obtain the physical constraint of the steering actuator, wherein the mathematical expression is as follows:
Figure FDA0002242600580000052
step 3.3, solving the system prediction output, wherein the process comprises the following substeps:
3.3.1, converting the tracking performance index in the step 3.2.1 and the steering and braking smoothness index in the step 3.2.2 into a single index by using a linear weighting method, and constructing an automobile stability multi-target optimization control problem, wherein the problem needs to meet the physical constraint of a steering actuator, and the input and output of the problem accord with a prediction model:
Figure FDA0002242600580000053
subject to
i) Prediction model A or prediction model B
ii) the constraint condition is formula (17)
3.3.2, calling a QP algorithm in the controller, solving a multi-objective optimization control problem (18) and obtaining an optimal open-loop control sequence delta u as follows:
Figure FDA0002242600580000054
selecting a first group of elements delta u (0) in the optimal open loop control sequence at the current moment for feedback, wherein delta fLinear superposition of front wheel steering angle with driver steering inputThen, directly outputting the data to a CarSim automobile model; Δ M ZAnd the braking torque is output to a braking force distribution module, the braking torque of four wheels is determined through the braking force distribution module, and the braking torque is output to a CarSim automobile model, so that the yaw moment control is finally realized.
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