CN109050658B - Model predictive control-based automobile active front wheel steering self-adaptive adjustment method - Google Patents

Model predictive control-based automobile active front wheel steering self-adaptive adjustment method Download PDF

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CN109050658B
CN109050658B CN201810735029.2A CN201810735029A CN109050658B CN 109050658 B CN109050658 B CN 109050658B CN 201810735029 A CN201810735029 A CN 201810735029A CN 109050658 B CN109050658 B CN 109050658B
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automobile
tire
model
lateral force
front wheel
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CN109050658A (en
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李绍松
王国栋
张邦成
于志新
崔高健
卢晓辉
高嵩
韩玲
李政
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Changchun University of Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
    • B62D—MOTOR VEHICLES; TRAILERS
    • B62D6/00—Arrangements for automatically controlling steering depending on driving conditions sensed and responded to, e.g. control circuits
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W30/00—Purposes of road vehicle drive control systems not related to the control of a particular sub-unit, e.g. of systems using conjoint control of vehicle sub-units, or advanced driver assistance systems for ensuring comfort, stability and safety or drive control systems for propelling or retarding the vehicle
    • B60W30/02—Control of vehicle driving stability
    • B60W30/045—Improving turning performance

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  • Transportation (AREA)
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  • Chemical & Material Sciences (AREA)
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  • Steering Control In Accordance With Driving Conditions (AREA)
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Abstract

The model predictive control-based automobile active front wheel steering self-adaptive adjustment method is characterized by comprising a reference model, a tire data processor, an MPC controller and a CarSim automobile model; the reference model is used to determine a desired yaw rate of the vehicle; the tire data processor is used for determining a slip angle, a lateral force and a lateral force gradient 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; and the MPC controller optimally solves the additional turning angle of the front wheel of the automobile according to the expected yaw velocity of the automobile and the actual motion state information of the automobile, outputs the additional turning angle to the CarSim automobile model, and controls the automobile to realize yaw stability control.

Description

Model predictive control-based automobile active front wheel steering self-adaptive adjustment method
The technical field is as follows:
the invention relates to the field of automobile yaw stability control, in particular to an automobile active front wheel steering adaptive adjustment method based on model prediction control.
Background art:
with the increasing importance of people on the driving safety of automobiles, the Active safety system of automobiles is rapidly developed, wherein an Active Front Steering (AFS) technology is widely applied as an effective yaw stability control system. At present, the Control methods adopted by the AFS mainly include PID Control, sliding mode variable structure Control, Model Predictive Control (MPC), and the like, wherein the Model Predictive Control can better handle multi-objective tasks and system constraints, and is widely applied in 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 dynamics characteristics of the automobile is too heavy in calculation burden and poor in real-time performance, and is difficult to be applied to practice. Therefore, many scholars begin to perform linearization on the lateral force of the tire, and propose a MPC control method with time varying linearity. An automobile stability control research based on LTV-MPC [ J ] automobile engineering,2016, 38(3):308-316 ] is realized by adopting a linear time-varying MPC method, and simultaneously, the nonlinear characteristic and the calculation burden of a system are considered. However, the method for the linearization treatment of the tire lateral force in the paper is too simple, cannot represent the actual change of the tire lateral force, and has an unsatisfactory control effect of the controller under the extreme working condition; in addition, the prediction model adopted by the paper is kept unchanged in the prediction time domain, and cannot represent the actual variation trend of the automobile in the rolling prediction process. The paper [ Choi M, Choi S B.MPC for vehicle lateral stability and lateral restraining and characterizing procedures [ J ] Proceedings of the organization of Mechanical Engineers Part D Journal of automatic Engineering,2016,230(4) ] gives a control strategy when the tire lateral force reaches saturation based on a linearized tire model, and realizes the vehicle stability control under the extreme conditions. However, the prediction model designed by the paper is also kept unchanged in the prediction time domain, and the prediction model cannot accurately represent the actual motion of the automobile in the rolling prediction process under the extreme working condition, so that the control effect of the controller is poor.
The invention content is as follows:
the method aims to solve the problem that the existing linear time-varying MPC method cannot reflect the non-linear dynamic characteristics of an automobile in a prediction model in a rolling prediction process, so that the AFS system is poor in control effect under the limit working condition. The invention provides an automobile active front wheel steering self-adaptive adjustment method based on model predictive control, which adopts a linear time-varying method to convert a nonlinear predictive control problem into a linear predictive control problem, automatically adjusts a predictive model according to the change trend of a tire lateral force in a rolling prediction process, reduces the calculation burden of a system, can accurately represent the nonlinear dynamic characteristics of an automobile, ensures the stability of an AFS controller under the limit working condition, and realizes the stability control of the automobile.
The technical scheme adopted by the invention for solving the technical problem is as follows:
the model predictive control-based automobile active front wheel steering self-adaptive adjustment method is characterized by comprising a reference model, a tire data processor, an MPC controller and a CarSim automobile model; the reference model is used to determine a desired yaw rate of the vehicle; the tire data processor is used for determining a slip angle, a lateral force and a lateral force gradient 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 optimally solves the additional turning angle of the front wheel of the automobile according to the expected yaw velocity of the automobile and the actual motion state information of the automobile, outputs the additional turning angle to the CarSim automobile model and controls the automobile to realize yaw stability control;
the method comprises the following steps:
step 1, establishing a reference model, and determining an expected automobile yaw angular velocity, 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 BDA0001721802410000021
wherein βIs the automobile centroid slip angle; gamma is the yaw rate of the vehicle; i iszIs the horizontal swinging moment inertia around the vertical axis of the mass center of the automobile; u shapexIs the vehicle longitudinal speed; lfAnd lrThe distances from the center of mass of the automobile to the front axle and the rear axle respectively; cfAnd CrThe cornering stiffness of the front and rear tires of the automobile respectively;f,driis the front wheel steering angle generated by the driver steering input;
step 1.2, converting a motion differential equation of the linear two-degree-of-freedom automobile model into a transfer function in the following form:
Figure BDA0001721802410000022
to achieve the desired closed loop effect, the desired yaw rate of the vehicle is obtained based on equation (2):
Figure BDA0001721802410000023
wherein: gamma rayrefIs the desired yaw rate of the vehicle; w is anIs the natural frequency of the system, ξ is the system damping, Gω(s) is the transfer function gain; w is ad＝k1wn,ξd＝k2ξ,Gkω(s)＝k3Gω(s)；k1、k2、k3Is a parameter for improving the phase delay and the response speed of the system;
step 2, designing a tire data processor, wherein the process comprises the following substeps:
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 BDA0001721802410000031
wherein αfAnd αrRespectively are the slip angles of the front and rear tires of the automobile;fis the front wheel corner of the car;
2.2, designing a tire lateral force and tire lateral force gradient calculation module, and acquiring a relation curve of the tire lateral force and the tire lateral deflection angle under different road surface adhesion coefficients based on a Pacejka tire model in order to acquire the nonlinear characteristic of the tire to obtain a tire lateral deflection characteristic three-dimensional graph; obtaining a relation curve of tire lateral force to tire sidewall deflection angle derivatives under different road adhesion coefficients to obtain a tire lateral force gradient three-dimensional graph; the tire data processor respectively inputs the actual tire cornering angle and the road surface adhesion coefficient at the current moment into a tire cornering characteristic three-dimensional graph and a tire lateral force gradient three-dimensional graph, respectively obtains the tire lateral force and the tire lateral force gradient at the current moment through a linear interpolation method, and outputs the tire lateral force and the tire lateral force gradient to the MPC controller; updating the tire lateral force and the tire lateral force gradient value once by the tire data processor in each control cycle;
wherein: the Pacejka tire model is as follows:
Fy,j＝μDsin(Catan(Bαj-E(Bαj-αjtan(Bαj))))
Figure BDA0001721802410000032
wherein: j ═ f, r, representing the front and rear wheels; fy,jIs the tire lateral force, αjIs the tire slip angle; b, C, D and E depend on the wheel vertical load Fz；a0＝1.75；a1＝0；a2＝1000；a3＝1289；a4＝7.11；a5＝0.0053；a6＝0.1925；
Step 3, designing an MPC controller, wherein the process comprises the following substeps:
step 3.1, establishing a prediction model, wherein the process comprises the following substeps:
step 3.1.1, linearizing the tire model, wherein the expression is as follows:
Figure BDA0001721802410000033
wherein:
Figure BDA0001721802410000041
is at the current slip angle
Figure BDA0001721802410000042
A tire lateral force gradient value of (a);
Figure BDA0001721802410000043
is the residual lateral force of the tire, calculated by the following equation:
Figure BDA0001721802410000044
wherein:
Figure BDA0001721802410000045
the method is based on a tire lateral force three-dimensional graph obtained by a linear interpolation method;
Figure BDA0001721802410000046
the method is based on a tire cornering stiffness characteristic three-dimensional graph, and a tire lateral force gradient is obtained through a linear interpolation method;
Figure BDA0001721802410000047
is the actual tire slip angle at the current time;
based on equation (5), during rolling prediction, the tire lateral force expression is designed as follows:
Figure BDA0001721802410000048
wherein:
Figure BDA0001721802410000049
wherein: p is the prediction time domain; the superscript "k + i | k" indicates the predicted future i-th time at the current time k; rhok+i|kAnd ξk+i|kIs to adjust
Figure BDA00017218024100000410
And
Figure BDA00017218024100000411
a varying weight factor;
step 3.1.2, establishing a prediction model, wherein the motion differential equation expression of the prediction model is as follows:
Figure BDA00017218024100000412
substituting equation (7) into equation (9) yields a prediction model in the rolling prediction process as:
Figure BDA00017218024100000413
3.1.3, establishing a prediction equation for predicting the future output of the system, writing the equation (10) into a state space equation for designing the prediction equation, wherein the specific steps are as follows:
Figure BDA0001721802410000051
wherein:
x＝γ；u＝f；
Figure BDA0001721802410000052
Figure BDA0001721802410000053
Figure BDA0001721802410000054
Figure BDA0001721802410000055
in order to realize the tracking control of the yaw rate of the automobile, a prediction model of a continuous time system is converted into an incremental model of a discrete time system:
Figure BDA0001721802410000056
wherein: sample time k int (T/T)s) T is simulation time, TsIs the simulation step length;
Figure BDA0001721802410000057
Figure BDA0001721802410000058
step 3.2, designing an optimization target and constraint conditions, wherein the process comprises the following substeps:
step 3.2.1, using a two-norm of the error between the expected automobile yaw rate and the actual automobile yaw rate as a yaw rate tracking performance index to reflect the track tracking characteristic of the automobile, wherein the expression is as follows:
Figure BDA0001721802410000059
wherein: gamma rayrefIs the desired yaw rate of the vehicle; gamma is the actual vehicle yaw rate; p is the prediction time domain; k represents the current time; q is a weighting factor;
step 3.2.2, using the two-norm of the control quantity change rate as a steering smooth index to reflect the steering smooth characteristic in the yaw rate tracking process, wherein the control quantity u is the automobile front wheel corner, and the discrete quadratic steering smooth index is established as follows:
Figure BDA0001721802410000061
wherein: m is a control time domain; Δ u is the amount of change in the control amount; k represents the current time; s is a weighting factor;
step 3.2.3, setting physical constraints of the actuator to meet the requirements of the actuator:
the method comprises the following steps of utilizing a linear inequality to limit a front wheel steering angle and upper and lower limits of variable quantity of the front wheel steering angle to obtain physical constraints of a steering actuator, wherein the mathematical expression is as follows:
Figure BDA0001721802410000062
wherein:fminis the lower limit of the front wheel steering angle,fmaxis the upper limit of the front wheel steering angle △fminIs the lower limit of the amount of change in the steering angle of the front wheel △fmaxIs the upper limit of the front wheel steering angle variation;
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 smooth index in the step 3.2.2 into a single index by using a linear weighting method, and constructing a multi-target optimization control problem of the yaw stability of the automobile, wherein the problem is to meet the physical constraint of a steering actuator, and the input and output of the problem accord with a prediction model:
Figure BDA0001721802410000063
subject to
i) Prediction model
ii) the constraint is formula (15)
3.3.2, solving the multi-objective optimization control problem (16) in the controller by adopting a quadratic programming algorithm to obtain an optimal open-loop control sequence △fComprises the following steps:
Figure BDA0001721802410000064
selecting △ the first element in the optimal open-loop control sequence at the current timef(0) Feedback is carried out, and the front wheel rotation angle is obtained after linear superposition with the previous momentfAnd the yaw stability control is output to a CarSim automobile model to realize the yaw stability control of the automobile.
The invention has the beneficial effects that: the method converts the nonlinear predictive control problem into the linear predictive control problem by using a linear time-varying method, so that the calculation burden of a system can be reduced; according to the method, the prediction model of the system is adjusted in a self-adaptive mode in the prediction time domain according to the change trend of the lateral force of the tire, the control effect of the nonlinear MPC can be achieved, and the control effect of the AFS under the limit working condition is improved.
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 view of the cornering performance of a tyre.
FIG. 4 is a three-dimensional view of a tire lateral force gradient.
FIG. 5 is a tire model linearization diagram.
FIG. 6 is a schematic diagram of tire model linearization during rolling prediction.
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 for adaptive adjustment of active front wheel steering of an automobile based on model predictive control, the system mainly comprises a reference model 1, a tire data processor 2, an MPC controller 3 and a Carsim automobile model 4; the reference model 1 is used to determine a desired yaw rate of the vehicle; the tire data processor 2 is used for determining the slip angle, the lateral force and the lateral force gradient of the tire; the CarSim automobile model 4 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; and the MPC controller 3 optimizes and solves the additional turning angle of the front wheels of the automobile according to the expected yaw angular velocity of the automobile and the actual motion state information of the automobile, outputs the additional turning angle to the CarSim automobile model 4, and controls the automobile to realize yaw 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 Main parameters of CarSim automobile
Figure BDA0001721802410000071
The establishment of the reference model 1 comprises two parts: 1.1, establishing a linear two-degree-of-freedom automobile model; 1.2 determining a desired yaw rate of the vehicle;
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 BDA0001721802410000081
wherein β is the mass center slip angle of the automobile, gamma is the yaw rate of the automobile, IzIs the horizontal swinging moment inertia around the vertical axis of the mass center of the automobile; u shapexIs the vehicle longitudinal speed; lfAnd lrThe distances from the mass center of the automobile to the front axle and the front axle respectively; cfAnd CrThe cornering stiffness of the front and rear tires of the automobile respectively;f,driis the front wheel steering angle generated by the driver's steering input.
In section 1.2, the differential equation of motion of the linear two-degree-of-freedom automobile model is converted into a transfer function, which is in the form of:
Figure BDA0001721802410000082
to achieve the desired closed loop effect, the desired yaw rate of the vehicle is obtained based on equation (2):
Figure BDA0001721802410000083
wherein: gamma rayrefIs the desired yaw rate; w is anIs the natural frequency of the system, ξ is the system damping, Gω(s) is the transfer function gain; w is ad＝k1wn,ξd＝k2ξ,Gkω(s)＝k3Gω(s)；k1、k2、k3Is a parameter for improving the phase delay and the response speed of the system; w is an、ξ、Gω(s)、KωThe calculation process of (2) is as follows:
Figure BDA0001721802410000084
Figure BDA0001721802410000085
Figure BDA0001721802410000086
the design of the tire data processor 2 includes two parts: 2.1 designing a tire slip angle calculation module; 2.2 designing a tire lateral force and tire lateral force gradient calculation module;
in part 2.1, the front and rear tire sidewall angles are calculated by:
Figure BDA0001721802410000091
wherein αfAnd αrRespectively are the slip angles of the front and rear tires of the automobile;fis the front wheel corner of the car;
in section 2.2, in order to obtain the nonlinear characteristic of the tire, based on a Pacejka tire model, obtaining the relationship curve of the tire lateral force and the tire cornering angle under different road adhesion coefficients to obtain a three-dimensional graph of the tire cornering characteristic, such as a graph shown in FIG. 3; and obtaining a relation curve of the tire lateral force to the tire side deflection angle derivative under different road adhesion coefficients to obtain a tire lateral force gradient three-dimensional graph, such as the graph shown in FIG. 4. The tire data processor 2 inputs the actual tire cornering angle and road surface adhesion coefficient at the current moment into the tire cornering power three-dimensional map and the tire lateral force gradient three-dimensional map respectively, obtains the tire lateral force and the tire lateral force gradient at the current moment respectively through a linear interpolation method, and outputs the tire lateral force and the tire lateral force gradient to the MPC controller 3. The tire data processor updates the tire lateral force and tire lateral force gradient values once per control cycle.
Wherein: the Pacejka tire model is as follows:
Figure BDA0001721802410000092
Figure BDA0001721802410000093
wherein: j ═ f, r, representing the front and rear wheels; fy,jIs the tire lateral force, αjIs the tire slip angle; b, C, D and E depend on the wheel vertical load Fz；a0＝1.75；a1＝0；a2＝1000；a3＝1289；a4＝7.11；a5＝0.0053；a6＝0.1925。
The design of the MPC controller 3 comprises three parts: 3.1 establishing a prediction model and a prediction equation; 3.2 designing 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 three parts: 3.1.1 linearizing the tire model; 3.1.2 establishing a prediction model; 3.1.3 establishing a prediction equation;
in section 3.1.1, at the current slip angle
Figure BDA0001721802410000094
Here, as shown in fig. 5, the tire model is linearized, which is expressed as follows:
Figure BDA0001721802410000095
wherein:
Figure BDA0001721802410000096
is at the current slip angle
Figure BDA0001721802410000097
A tire lateral force gradient value of (a);
Figure BDA0001721802410000098
is the residual lateral force of the tire, as shown in fig. 5, calculated by the following formula:
Figure BDA0001721802410000099
wherein:
Figure BDA0001721802410000101
is the tire lateral force obtained by a linear interpolation method based on a tire lateral deviation characteristic three-dimensional graph (figure 3);
Figure BDA0001721802410000102
the gradient of the lateral force of the tire is obtained by a linear interpolation method based on a tire cornering stiffness characteristic three-dimensional graph (figure 4);
Figure BDA0001721802410000103
is the actual tire slip angle at the present time.
Based on equation (5), in the rolling prediction process, as shown in fig. 6, the tire lateral force expression is designed as follows:
Figure BDA0001721802410000104
wherein:
Figure BDA0001721802410000105
wherein: p is the prediction time domain; the superscript "k + i | k" indicates the predicted future i-th time at the current time k; rhok+i|kAnd ξk+i|kIs to adjust
Figure BDA0001721802410000106
And
Figure BDA0001721802410000107
a varying weighting factor.
In section 3.1.2, the prediction model adopts a linear two-degree-of-freedom automobile model shown in fig. 2, and the motion differential equation expression is as follows:
Figure BDA0001721802410000108
substituting equation (7) into equation (9) yields a prediction model in the rolling prediction process as:
Figure BDA0001721802410000109
in section 3.1.3, equation (10) is written as a state space equation for designing the prediction equation as follows:
Figure BDA00017218024100001010
wherein:
x＝γ；u＝f；
Figure BDA0001721802410000111
Figure BDA0001721802410000112
Figure BDA0001721802410000113
Figure BDA0001721802410000114
in order to realize the tracking control of the yaw rate of the automobile, a prediction model of a continuous time system is converted into an incremental model of a discrete time system:
Figure BDA0001721802410000115
wherein: sample time k int (T/T)s) T is simulation time, TsIs the simulation step length;
Figure BDA0001721802410000116
Figure BDA0001721802410000117
C＝1。
the design of optimization objectives and constraints in section 3.2 includes three parts: 3.2.1 designing a yaw rate tracking performance index; 3.2.2 designing a steering smoothing index; 3.2.3 setting actuator physical constraints;
in section 3.2.1, the two norms of the expected yaw rate of the automobile and the actual yaw rate error of the automobile are used as the yaw rate tracking performance index, the track tracking characteristic of the automobile is embodied, and the expression is as follows:
Figure BDA0001721802410000118
wherein: gamma rayrefIs the desired yaw rate of the vehicle; gamma is the actual vehicle yaw rate; p is the prediction time domain; k represents the current time; q is a weighting factor.
In the 3.2.2 part, the two-norm of the control quantity change rate is used as a steering smooth index to reflect the steering smooth characteristic in the yaw rate tracking process, the control quantity u is the automobile front wheel rotation angle, and the discrete quadratic steering smooth index is established as follows:
Figure BDA0001721802410000119
wherein: m is a control time domain; Δ u is the amount of change in the control amount; k represents the current time; s is a weighting factor.
In the section 3.2.3, the physical constraints of the steering actuator are obtained by limiting the front wheel steering angle and the upper and lower limits of the variation thereof by using a linear inequality, and the mathematical expression of the physical constraints is as follows:
Figure BDA0001721802410000121
wherein:fminis the lower limit of the front wheel steering angle,fmaxis the upper limit of the front wheel steering angle △fminIs the lower limit of the amount of change in the steering angle of the front wheel △fmaxIs front wheel angle changeThe upper limit of the chemical amount.
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 section 3.3.1, the yaw rate tracking performance index of the formula (13) and the steering smooth index of the formula (14) are converted into a single index by using a linear weighting method, and a multi-target optimization control problem of the yaw stability of the automobile is constructed, wherein the problem is to meet the physical constraint of a steering actuator, and the input and the output of the problem accord with a prediction model:
Figure BDA0001721802410000122
subject to
i) Prediction model
ii) the constraint is formula (15)
In section 3.3.2, in the controller, a quadratic programming algorithm is used to solve the multi-objective optimization control problem (16) to obtain an optimal open-loop control sequence △fComprises the following steps:
Figure BDA0001721802410000123
selecting △ the first element in the optimal open-loop control sequence at the current timef(0) Feedback is carried out, and the front wheel rotation angle is obtained after linear superposition with the previous momentfAnd the yaw stability control is output to the CarSim automobile model 4 to realize the yaw stability control of the automobile.

Claims (1)

1. The model predictive control-based automobile active front wheel steering self-adaptive adjustment method is characterized by comprising a reference model, a tire data processor, an MPC controller and a CarSim automobile model; the reference model is used to determine a desired yaw rate of the vehicle; the tire data processor is used for determining a slip angle, a lateral force and a lateral force gradient 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 optimally solves the additional turning angle of the front wheel of the automobile according to the expected yaw velocity of the automobile and the actual motion state information of the automobile, outputs the additional turning angle to the CarSim automobile model and controls the automobile to realize yaw stability control;
the method comprises the following steps:
step 1, establishing a reference model, and determining an expected automobile yaw angular velocity, 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 FDA0002576180700000011
wherein β is the mass center slip angle of the automobile, gamma is the yaw rate of the automobile, IzIs the horizontal swinging moment inertia around the vertical axis of the mass center of the automobile; u shapexIs the vehicle longitudinal speed; lfAnd lrThe distances from the center of mass of the automobile to the front axle and the rear axle respectively; cfAnd CrThe cornering stiffness of the front and rear tires of the automobile respectively;f,driis the front wheel steering angle generated by the driver steering input;
step 1.2, converting a motion differential equation of the linear two-degree-of-freedom automobile model into a transfer function in the following form:
Figure FDA0002576180700000012
to achieve the desired closed loop effect, the desired yaw rate of the vehicle is obtained based on equation (2):
Figure FDA0002576180700000013
wherein: gamma rayrefIs the desired yaw rate of the vehicle; w is anIs the natural frequency of the system, ξ is the system damping, Gω(s) is the transfer function gain; w is ad＝k1wn,ξd＝k2ξ,Gkω(s)＝k3Gω(s)；k1、k2、k3Is a parameter for improving the phase delay and the response speed of the system;
step 2, designing a tire data processor, wherein the process comprises the following substeps:
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 FDA0002576180700000014
wherein αfAnd αrRespectively are the slip angles of the front and rear tires of the automobile;fis the front wheel corner of the car;
2.2, designing a tire lateral force and tire lateral force gradient calculation module, and acquiring a relation curve of the tire lateral force and the tire lateral deflection angle under different road surface adhesion coefficients based on a Pacejka tire model in order to acquire the nonlinear characteristic of the tire to obtain a tire lateral deflection characteristic three-dimensional graph; obtaining a relation curve of tire lateral force to tire sidewall deflection angle derivatives under different road adhesion coefficients to obtain a tire lateral force gradient three-dimensional graph; the tire data processor respectively inputs the actual tire cornering angle and the road surface adhesion coefficient at the current moment into a tire cornering characteristic three-dimensional graph and a tire lateral force gradient three-dimensional graph, respectively obtains the tire lateral force and the tire lateral force gradient at the current moment through a linear interpolation method, and outputs the tire lateral force and the tire lateral force gradient to the MPC controller; updating the tire lateral force and the tire lateral force gradient value once by the tire data processor in each control cycle;
wherein: the Pacejka tire model is as follows:
Fy,j＝μD sin(Ca tan(Bαj-E(Bαj-αjtan(Bαj))))
Figure FDA0002576180700000021
wherein: μ is the road adhesion coefficient; j ═ f, r, and denotes front and rear wheels；Fy,jIs the tire lateral force, αjIs the tire slip angle; b, C, D and E depend on the wheel vertical load Fz；a0＝1.75；a1＝0；a2＝1000；a3＝1289；a4＝7.11；a5＝0.0053；a6＝0.1925；
Step 3, designing an MPC controller, wherein the process comprises the following substeps:
step 3.1, establishing a prediction model, wherein the process comprises the following substeps:
step 3.1.1, linearizing the tire model, wherein the expression is as follows:
Figure FDA0002576180700000022
wherein:
Figure FDA0002576180700000023
is at the current slip angle
Figure FDA0002576180700000024
A tire lateral force gradient value of (a);
Figure FDA0002576180700000025
is the residual lateral force of the tire, calculated by the following equation:
Figure FDA0002576180700000026
wherein:
Figure FDA0002576180700000027
the method is based on a tire lateral force three-dimensional graph obtained by a linear interpolation method;
Figure FDA0002576180700000028
the method is based on a tire cornering stiffness characteristic three-dimensional graph, and a tire lateral force gradient is obtained through a linear interpolation method;
Figure FDA0002576180700000029
is the actual tire slip angle at the current time;
based on equation (5), during rolling prediction, the tire lateral force expression is designed as follows:
Figure FDA0002576180700000031
wherein:
Figure FDA0002576180700000032
wherein: p is the prediction time domain; the superscript "k + i | k" indicates the predicted future i-th time at the current time k; rhok+i|kAnd ξk+i|kIs to adjust
Figure FDA0002576180700000033
And
Figure FDA0002576180700000034
a varying weight factor;
step 3.1.2, establishing a prediction model, wherein the motion differential equation expression of the prediction model is as follows:
Figure FDA0002576180700000035
substituting equation (7) into equation (9) yields a prediction model in the rolling prediction process as:
Figure FDA0002576180700000036
3.1.3, establishing a prediction equation for predicting the future output of the system, writing the equation (10) into a state space equation for designing the prediction equation, wherein the specific steps are as follows:
Figure FDA0002576180700000037
wherein:
x＝γ；u＝f；
Figure FDA0002576180700000038
Figure FDA0002576180700000041
Figure FDA0002576180700000042
Figure FDA0002576180700000043
in order to realize the tracking control of the yaw rate of the automobile, a prediction model of a continuous time system is converted into an incremental model of a discrete time system:
Figure FDA0002576180700000044
wherein: sample time k int (T/T)s) T is simulation time, TsIs the simulation step length;
Figure FDA0002576180700000045
Figure FDA0002576180700000046
C＝1；
step 3.2, designing an optimization target and constraint conditions, wherein the process comprises the following substeps:
step 3.2.1, using a two-norm of the error between the expected automobile yaw rate and the actual automobile yaw rate as a yaw rate tracking performance index to reflect the track tracking characteristic of the automobile, wherein the expression is as follows:
Figure FDA0002576180700000047
wherein: gamma rayrefIs the desired yaw rate of the vehicle; gamma is the actual vehicle yaw rate; p is the prediction time domain; k represents the current time; q is a weighting factor;
step 3.2.2, using the two-norm of the control quantity change rate as a steering smooth index to reflect the steering smooth characteristic in the yaw rate tracking process, wherein the control quantity u is the automobile front wheel corner, and the discrete quadratic steering smooth index is established as follows:
Figure FDA0002576180700000048
wherein: m is a control time domain; Δ u is the amount of change in the control amount; k represents the current time; s is a weighting factor;
step 3.2.3, setting physical constraints of the actuator to meet the requirements of the actuator:
the method comprises the following steps of utilizing a linear inequality to limit a front wheel steering angle and upper and lower limits of variable quantity of the front wheel steering angle to obtain physical constraints of a steering actuator, wherein the mathematical expression is as follows:
Figure FDA0002576180700000049
wherein:fminis the lower limit of the front wheel steering angle,fmaxis the front wheel steering angle upper limit; deltafminIs the lower limit of the front wheel steering angle variation; deltafmaxIs the upper limit of the front wheel steering angle variation;
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 smooth index in the step 3.2.2 into a single index by using a linear weighting method, and constructing a multi-target optimization control problem of the yaw stability of the automobile, wherein the problem is to meet the physical constraint of a steering actuator, and the input and output of the problem accord with a prediction model:
Figure FDA0002576180700000051
subject to
i) Prediction model
ii) the constraint is formula (15)
3.3.2, solving the multi-objective optimization control problem (16) in the controller by adopting a quadratic programming algorithm to obtain an optimal open-loop control sequence deltafComprises the following steps:
Figure FDA0002576180700000052
selecting a first element delta in the optimal open loop control sequence at the current momentf(0) Feedback is carried out, and the front wheel rotation angle is obtained after linear superposition with the previous momentfAnd the yaw stability control is output to a CarSim automobile model to realize the yaw stability control of the automobile.
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