CN114802200A - Method for tracking and controlling stability of tracks of intelligent automobile under extreme working conditions - Google Patents

Method for tracking and controlling stability of tracks of intelligent automobile under extreme working conditions Download PDF

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CN114802200A
CN114802200A CN202210366511.XA CN202210366511A CN114802200A CN 114802200 A CN114802200 A CN 114802200A CN 202210366511 A CN202210366511 A CN 202210366511A CN 114802200 A CN114802200 A CN 114802200A
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vehicle
control
stability
model
follows
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吴迪
郭鸣明
李维汉
黄鹤
张栋
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Hefei University of Technology
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Hefei University of Technology
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    • 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
    • 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
    • B60W30/04—Control of vehicle driving stability related to roll-over prevention
    • 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
    • B60W30/18—Propelling the vehicle
    • B60W30/18009—Propelling the vehicle related to particular drive situations
    • 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
    • B60W40/00—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models
    • B60W40/10—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models related to vehicle motion
    • 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
    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • 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
    • B60W60/00—Drive control systems specially adapted for autonomous road vehicles
    • B60W60/001—Planning or execution of driving tasks
    • 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
    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B60W2050/0001—Details of the control system
    • B60W2050/0002—Automatic control, details of type of controller or control system architecture
    • B60W2050/0018—Method for the design of a control system
    • 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
    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B60W2050/0001—Details of the control system
    • B60W2050/0019—Control system elements or transfer functions
    • B60W2050/0028—Mathematical models, e.g. for simulation
    • 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
    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B60W2050/0001—Details of the control system
    • B60W2050/0019—Control system elements or transfer functions
    • B60W2050/0028—Mathematical models, e.g. for simulation
    • B60W2050/0037—Mathematical models of vehicle sub-units

Abstract

The invention discloses an intelligent automobile track stable tracking control method under a limit working condition, which comprises transverse control and stability control, and comprises the following steps: the optimal steering angle of the vehicle tracking control is solved by adopting a model prediction control method, meanwhile, a three-degree-of-freedom vehicle model is simplified into a two-degree-of-freedom model, the optimal additional yaw moment of the vehicle stability control is solved by adopting a model prediction control method, finally, a Pareto optimal balance principle is adopted to carry out game on the vehicle track tracking control and the transverse stability control, the additional yaw moment and the balance solution of the front wheel turning angle are solved, and the tracking precision of the vehicle is improved on the premise of ensuring the vehicle stability.

Description

Method for tracking and controlling stability of tracks of intelligent automobile under extreme working conditions
Technical Field
The invention relates to the technical field of intelligent automobiles, in particular to a method for tracking and controlling stability of a track of an intelligent automobile under a limit working condition.
Background
With the improvement of the requirements of people on the comfort and the safety of automobiles, the intelligent driving technology becomes one of the research hotspots in recent years. The intelligent driving technology comprises four modules of perception, decision, planning and control, and the control module plays a very important role as the last ring of the intelligent driving system. The track tracking control is one of the core contents of the control module, and directly influences the performance of the intelligent automobile. Currently, the trajectory tracking Control method mainly includes Model Predictive Control (MPC), Linear Quadratic Regulator (LQR), proportional-integral-derivative Control (PID), fuzzy Control, sliding mode Control, and the like. Compared with other control methods, the model prediction controller can consider various constraints among space state variables, can be applied to linear and nonlinear systems, has better robustness, and is widely applied to vehicle trajectory tracking control.
In the current design of the trajectory tracking controller, a control target usually adopts fixed weight and is difficult to adapt to different working conditions. At present, a related algorithm in the motion control field can obtain a better control effect under a low-speed working condition, but the vehicle track tracking control capability and the stability control capability of the related algorithm under a limit working condition are to be improved.
Disclosure of Invention
The invention aims to provide a method for tracking and controlling stability of a track of an intelligent automobile under a limit working condition, so that the track tracking control capability and the stability control capability of the automobile under the limit working condition are taken into consideration, and the situations of instability, rollover and the like of the automobile under the limit working condition are prevented.
In order to achieve the purpose, the invention provides the following technical scheme: an intelligent automobile track stable tracking control method under extreme conditions comprises transverse control and stability control; the transverse control and the stability control both adopt a model prediction control method, the transverse control adopts a three-degree-of-freedom vehicle model to calculate and track and control an optimal corner solution through a quadratic index, and the stability control obtains an optimal additional yaw moment through the model prediction control method; and (4) performing game on the front wheel corner and the additional yaw moment of the vehicle through a game theory, solving the Pareto optimal solution of the front wheel corner and the additional yaw moment, and considering the tracking performance and the stability of the vehicle.
The method comprises the following steps:
step 1: establishing a three-degree-of-freedom vehicle dynamic model:
Figure BDA0003587345490000021
wherein m is the overall vehicle servicing mass, y is the longitudinal displacement under the vehicle coordinate system, l f ，l r Respectively the distance of the center of mass to the front-rear axis,
Figure BDA0003587345490000022
is the yaw angle of the vehicle,
Figure BDA0003587345490000023
is the yaw rate of the vehicle,
Figure BDA0003587345490000024
is yaw angular acceleration, upsilon x ，υ y Respectively the longitudinal speed and the lateral speed of the vehicle,
Figure BDA0003587345490000025
longitudinal and transverse accelerations, respectively, F xf ，F yf Force of the front tire resolved into the vehicle coordinate system, F xr ，F yr Is the force of the rear wheel resolved into the vehicle coordinate system, I z Is the moment of inertia of the vehicle about the z-axis;
step 2: building a tire model, and defining the tire model as follows:
F i ＝-C i α i (2)；
wherein, F i For longitudinal or lateral forces of the tyre, C i Cornering stiffness, alpha, of the front and rear wheels of a tyre i For the front and rear tire slip angles, the front and rear wheel slip angles are defined as follows:
Figure BDA0003587345490000026
the lateral force of the simplified available rear wheel is expressed as follows:
Figure BDA0003587345490000031
and step 3: designing a locus tracking MPC controller, wherein the process comprises the following sub-steps:
step 3.1, establishing a prediction model, substituting the tire model in the step 2 into the automobile dynamic model in the step 1, and obtaining the prediction model of the MPC controller:
Figure BDA0003587345490000032
wherein the content of the first and second substances,
Figure BDA0003587345490000033
step 3.2: the output equation of the system prediction model obtained by discretizing and linearizing the system state space by adopting Taylor expansion and a first-order difference quotient method is as follows:
Figure BDA0003587345490000034
step 3.3: and respectively constraining the centroid slip angle, the lateral acceleration, the control quantity and the control increment by taking the difference between the expected lateral displacement and the actual lateral displacement of the automobile and the change rate of the front wheel angle of the automobile as track tracking performance indexes, and describing the track tracking optimization problem as follows:
Figure BDA0003587345490000035
and 4, step 4: designing a vehicle stability MPC controller, wherein the process comprises the following sub-processes:
step 4.1: simplifying according to the vehicle dynamics model in the step 1, and designing a two-degree-of-freedom system state space equation as follows:
Figure BDA0003587345490000041
wherein the content of the first and second substances,
Figure BDA0003587345490000042
step 4.2: the vehicle taking in a steady state
Figure BDA0003587345490000043
Combining the lateral motion equation and the yaw motion equation in the vehicle dynamic model, the ideal yaw velocity and centroid yaw angle expression can be obtained as follows:
Figure BDA0003587345490000044
Figure BDA0003587345490000045
wherein, L is the wheelbase, and K is the stability factor;
when the vehicle reaches a steady state under the current steering wheel angle input condition, the conditions are satisfied:
Figure BDA0003587345490000046
the two-degree-of-freedom model of the vehicle with the additional yaw moment is as follows:
Figure BDA0003587345490000047
where Δ M is the additional yaw moment, B ═ 01/I z ]；
The error state space between the actual values of the centroid yaw angle and the yaw rate and the reference value is:
Figure BDA0003587345490000048
taking state variables
Figure BDA0003587345490000049
U＝ΔM；；
Step 4.3: selecting a centroid slip angle as a measure index of vehicle yaw stability, and designing a stability quadratic index by taking a front wheel steering angle as a control variable as follows:
Figure BDA00035873454900000410
vehicle stability control requires adding constraints to the vehicle's center of mass yaw angle and yaw rate, then vehicle stability optimization can be described as:
Figure BDA0003587345490000051
and 5: a collaborative optimal framework based on a Pareto equilibrium theory is designed, and the trajectory tracking control and the stability control are played to obtain the collaborative optimal trajectory tracking control and the stability control, and the method specifically comprises the following steps:
step 5.1: the quadratic index of track tracking control and stability control is changed into:
Figure BDA0003587345490000052
wherein R is 1 Weighting matrix for Pareto optimal global performance index, where rho 1 ，ρ 2 For the weighting coefficient, in order to facilitate the design of the Pareto cooperative optimal controller, the trajectory tracking and stability model is rewritten as follows:
Figure BDA0003587345490000053
wherein the content of the first and second substances,
Figure BDA0003587345490000054
step 5.2: the essential conditions of the solution of the discrete-time linear quadratic Pareto game are as follows:
Figure BDA0003587345490000055
in the formula
Figure BDA0003587345490000056
And
Figure BDA0003587345490000057
is a co-modal vector, and satisfies the following relationship:
Figure BDA0003587345490000058
the linear relationship between the co-modal vector and the state variable can be obtained according to the above equation:
Figure BDA0003587345490000061
the above equation can be found in a coupled ricacies equation set forth as follows:
Figure BDA0003587345490000062
in the formula
Figure BDA0003587345490000063
And
Figure BDA0003587345490000064
for the initial conditions of the iteration, will be in
Figure BDA0003587345490000065
And
Figure BDA0003587345490000066
the iteration result is substituted into an equation, and the optimal control input meeting Pareto at the current moment is obtained by combining the rolling time domain idea.
Compared with the prior art, the invention has the beneficial effects that:
the method comprises the steps of firstly establishing a three-degree-of-freedom vehicle model and a tire model, solving the optimal steering angle of vehicle tracking control by adopting a model prediction control method, simultaneously simplifying the three-degree-of-freedom vehicle model into a two-degree-of-freedom model, solving the optimal additional yaw moment of vehicle stability control by adopting the model prediction control method, finally carrying out game on vehicle track tracking control and transverse stability control by adopting a Pareto optimal balance principle, solving the balance solutions of the additional yaw moment and the front wheel corner, and improving the tracking precision of the vehicle on the premise of ensuring the vehicle stability.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, the present invention provides a technical solution: a method for controlling track tracking and stability of an intelligent automobile under limit working conditions comprises the following steps:
firstly, a vehicle track tracking controller:
in the research of the vehicle control system, a vehicle kinematic model or a dynamic model is generally selected for analysis, and in the research in the field, the vehicle kinematic model or the simple dynamic model is mostly adopted in the research in the field. The former can only reflect the motion characteristics of the vehicle, and cannot consider the influence of the stress of the vehicle. When a vehicle prediction model is designed, the more accurate model is more complex, the too simple dynamic model cannot accurately reflect the characteristics of the vehicle, the too complex model is low in operation speed and poor in real-time performance, and the requirement on equipment is also too high. The vehicle dynamics model adopts a three-degree-of-freedom bicycle model.
Wherein, the formula (1) includes a longitudinal motion equation of the vehicle:
Figure BDA0003587345490000071
vehicle lateral motion equation:
Figure BDA0003587345490000072
vehicle yaw equation of motion:
Figure BDA0003587345490000073
wherein m is the overall vehicle servicing mass, y is the longitudinal displacement under the vehicle coordinate system, l f ，l r Respectively the distance of the center of mass to the front-rear axis,
Figure BDA0003587345490000074
is the yaw angle of the vehicle,
Figure BDA0003587345490000075
is the yaw rate of the vehicle,
Figure BDA0003587345490000076
is yaw angular acceleration, v x ，v y Respectively the longitudinal speed and the lateral speed of the vehicle,
Figure BDA0003587345490000077
longitudinal and transverse accelerations, respectively, F xf ，F yf Force of the front tire resolved into the vehicle coordinate system, F xr ，F yr Is the force of the rear wheel resolved into the vehicle coordinate system, I z Is the moment of inertia of the vehicle about the z-axis.
When designing a vehicle dynamics model, generally, the more complex the model is, the better the effect is, but the model is often not the most appropriate, and the computational complexity cannot meet the requirements of real vehicle operation, so that the model needs to be properly simplified.
Now assume the following:
1. ignoring tire vertical behavior, the effect of suspension is not considered, and only the motion of the vehicle in a plane is discussed.
2. The longitudinal speed is constant, taking into account only the influence of the lateral speed on the stability of the vehicle.
3. The vehicle is assumed to meet the small angle assumption under certain conditions.
The tire slip angle represents the angle between the actual direction of motion of the wheel and the rolling direction of advance, and is expressed as follows:
Figure BDA0003587345490000081
wherein upsilon is l And v c Representing the speed of the wheel centre in the longitudinal and lateral directions respectively, is generally not directly available, so analysis can give its expression:
Figure BDA0003587345490000082
wherein v is x And v y Representing the speed of the tire in the x-axis and y-axis directions, respectively.
The component of the tire velocity in the x-axis direction and the component in the y-axis can be derived from the longitudinal velocity and the lateral velocity at the centroid:
Figure BDA0003587345490000083
to further simplify the amount of computation, it can be assumed that the vehicle is traveling at a small angle, so the trigonometric function is simplified as follows:
cosθ≈1，sinθ≈θ，tanθ≈θ (30)
the tire slip angle and the slip ratio are suitable for the proportional relationship between the lateral force and the longitudinal force in a small range, and the expression of the slip angle and the slip ratio is as follows:
F i ＝-C i α i (2)
wherein, F i For longitudinal or lateral forces of the tyre, C i The cornering stiffness of the front and rear wheels of the tire.
Through the simplification, the relation expression of the tire slip angle can be obtained as follows:
Figure BDA0003587345490000091
thus, the lateral force of the rear tire is:
Figure BDA0003587345490000092
the above formula is introduced into the kinetic model to simplify and obtain:
Figure BDA0003587345490000093
selecting the lateral position, the lateral speed, the course angle and the yaw angular speed of the vehicle as system state quantities, wherein the expression is as follows:
Figure BDA0003587345490000094
selecting a front wheel steering angle as a system control quantity, wherein the expression is as follows:
u＝[δ f ] (33)
selecting a vehicle course angle and a transverse position as system output quantities, wherein the expression is as follows:
Figure BDA0003587345490000095
the system space expression is then:
Figure BDA0003587345490000096
η＝Cξ+Du (5)
wherein the content of the first and second substances,
Figure BDA0003587345490000101
in this case, the prediction model is a nonlinear model, and thus discretization and linearization are required.
Taking a certain working point of the system as ([ xi ] 0 ，u 0 ) The system state quantity is obtained by applying a constant control quantity:
ξ 0 (k+1)＝f(ξ 0 (k)，u 0 )，ξ 0 (0)＝ξ 0 (35)
at point (xi) 0 ，u 0 ) The taylor expansion is performed, only the first order term is retained, and the following formula can be obtained by neglecting the high order term: finishing to obtain:
ξ(k+1)＝A k，0 ξ(k)+B k，0 u(k)+D k，0 (36)
in the above formula, the first and second carbon atoms are,
Figure BDA0003587345490000102
D k，0 ＝ξ 0 (k+1)-A k，0 ξ 0 (k)-B k，0 u 0 (33)
from this, the expression at any time t can be:
ξ(k+1)＝A k，t ξ(k)+B k，t u(k)+D k，t (37)
at the moment, the coefficient matrixes are all linearly time-varying, and then the model is discretized by using first-order difference quotient.
Figure BDA0003587345490000103
Finishing to obtain:
Figure BDA0003587345490000104
finally, the state equation of the discrete system prediction model is obtained as follows:
Figure BDA0003587345490000105
design optimization goals and constraints
The trajectory tracking quadratic index is as in formula (17):
Figure BDA0003587345490000106
wherein B is P ，S P Is a weighting matrix.
And (4) considering the vehicle state and road surface condition optimization problem constraint conditions, and respectively constraining the centroid slip angle, the lateral acceleration, the control quantity and the control increment. The optimization problem can be described as:
Figure BDA0003587345490000111
secondly, designing a vehicle stability controller:
a two-degree-of-freedom vehicle dynamic model (under small angle assumption) is formed by a vehicle transverse motion equation and a yaw motion equation:
Figure BDA0003587345490000112
the state space of the two-degree-of-freedom model of the vehicle is then:
Figure BDA0003587345490000113
wherein the content of the first and second substances,
Figure BDA0003587345490000114
the vehicle taking in a steady state
Figure BDA0003587345490000115
Combining the lateral motion equation and the yaw motion equation in the vehicle dynamic model, the ideal yaw velocity and centroid yaw angle expression can be obtained as follows:
Figure BDA0003587345490000116
Figure BDA0003587345490000117
wherein, L is the wheel base, and K is the stability factor.
When the vehicle reaches a steady state under the current steering wheel angle input condition, the conditions are satisfied:
Figure BDA0003587345490000121
the two-degree-of-freedom model of the vehicle with the additional yaw moment is as follows:
Figure BDA0003587345490000122
wherein Δ M is the additional horizontalMoment of oscillation, B ═ 01/I z ]。
The error state space between the actual values of the centroid yaw angle and the yaw rate and the reference value is:
Figure BDA0003587345490000123
taking state variables
Figure BDA0003587345490000124
U＝ΔM
The same linear discretization as the track tracking part procedure above establishes a prediction model,
in stability control, a mass center slip angle is selected as a measurement index of vehicle yaw stability, and a front wheel steering angle is used as a control variable to design a stability quadratic index as follows:
Figure BDA0003587345490000125
wherein B is A ，S A Is a weighting matrix.
Vehicle stability control requires adding constraints to the vehicle's center of mass yaw angle and yaw rate, then vehicle stability optimization can be described as:
Figure BDA0003587345490000126
s.t.β min ＜β＜β max
Figure BDA0003587345490000127
the motion state of the vehicle is affected by both the front wheel turning angle and the additional yaw moment, and the optimal front wheel turning angle calculated by the trajectory tracking controller may adversely affect the control of the stability of the vehicle, so that it is necessary to find a balance point between optimal tracking and optimal stability.
Thirdly, a cooperative control strategy based on Pareto optimal balance:
in the game theory of Pareto equilibrium, one cooperation is a game strategy, and in the dynamic evolution of the system, each control participant considers not only the own interest function but also the interest functions of other participants. In order to keep the optimal track tracking capability of the vehicle under the condition of stability under the limit working condition, a collaborative optimal framework based on a Pareto equilibrium theory is designed.
According to the Pareto optimal balance theory, the quadratic objective function shown by the trajectory tracking control and the stability control is as follows:
Figure BDA0003587345490000131
wherein R is 1 Weighting matrix for Pareto optimal global performance index, where rho 1 ，ρ 2 For the weighting coefficient, in order to facilitate the design of the Pareto cooperative optimal controller, the trajectory tracking and stability model is rewritten as follows:
Figure BDA0003587345490000132
wherein
Figure BDA0003587345490000133
The essential conditions of the solution of the discrete-time linear quadratic Pareto game are as follows:
Figure BDA0003587345490000134
in the formula (I), the compound is shown in the specification,
Figure BDA0003587345490000135
and
Figure BDA0003587345490000136
as a co-modal vector, the following relationship is satisfied:
Figure BDA0003587345490000137
the linear relationship between the co-modal vector and the state variable can be obtained according to the above equation:
Figure BDA0003587345490000138
the above equation can be found in a coupled ricacies equation set forth as follows:
Figure BDA0003587345490000141
in the formula
Figure BDA0003587345490000142
And
Figure BDA0003587345490000143
is the initial condition for the iteration. In the formula
Figure BDA0003587345490000144
And
Figure BDA0003587345490000145
the iteration result is substituted into an equation, and the optimal control input meeting Pareto at the current moment is obtained by combining the rolling time domain idea.
In summary, the following steps: the method comprises the steps of firstly establishing a three-degree-of-freedom vehicle model and a tire model, solving the optimal steering angle of vehicle tracking control by adopting a model prediction control method, simultaneously simplifying the three-degree-of-freedom vehicle model into a two-degree-of-freedom model, solving the optimal additional yaw moment of vehicle stability control by adopting the model prediction control method, finally carrying out game on vehicle track tracking control and transverse stability control by adopting a Pareto optimal balance principle, solving the balance solutions of the additional yaw moment and the front wheel corner, and improving the tracking precision of the vehicle on the premise of ensuring the vehicle stability.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (2)

1. An intelligent automobile track stable tracking control method under limit working conditions is characterized in that: including lateral control and stability control, the method comprising the steps of:
step 1: establishing a three-degree-of-freedom vehicle dynamic model:
Figure FDA0003587345480000011
wherein m is the overall vehicle servicing mass, y is the longitudinal displacement under the vehicle coordinate system, l f ，l r Respectively the distance of the center of mass to the front-rear axis,
Figure FDA0003587345480000012
is the yaw angle of the vehicle,
Figure FDA0003587345480000013
is the yaw rate of the vehicle,
Figure FDA0003587345480000014
is yaw angular acceleration, v x ，v y Respectively the longitudinal speed and the lateral speed of the vehicle,
Figure FDA0003587345480000015
longitudinal and transverse accelerations, respectively, F xf ，F yf Force of the front tire resolved into the vehicle coordinate system, F xr ，F yr Is the force of the rear wheel resolved into the vehicle coordinate system, I z Is the moment of inertia of the vehicle about the z-axis;
step 2: building a tire model, and defining the tire model as follows:
F i ＝-C i α i (2)；
where Fi is the tire longitudinal force or lateral force, Ci is the cornering stiffness of the front and rear wheels of the tire, α i is the front and rear tire cornering angle, and the front and rear wheel cornering angles are defined as follows:
Figure FDA0003587345480000016
the lateral force of the simplified available rear wheel is expressed as follows:
Figure FDA0003587345480000017
and step 3: designing a locus tracking MPC controller, wherein the process comprises the following sub-steps:
step 3.1, establishing a prediction model, substituting the tire model in the step 2 into the automobile dynamic model in the step 1, and obtaining the prediction model of the MPC controller:
Figure FDA0003587345480000021
wherein the content of the first and second substances,
Figure FDA0003587345480000022
step 3.2: the output equation of the system prediction model obtained by discretizing and linearizing the system state space by adopting Taylor expansion and a first-order difference quotient method is as follows:
Figure FDA0003587345480000023
step 3.3: and respectively constraining the centroid slip angle, the lateral acceleration, the control quantity and the control increment by taking the difference between the expected lateral displacement and the actual lateral displacement of the automobile and the change rate of the front wheel angle of the automobile as track tracking performance indexes, and describing the track tracking optimization problem as follows:
Figure FDA0003587345480000024
and 4, step 4: designing a vehicle stability MPC controller, wherein the process comprises the following sub-processes:
step 4.1: simplifying according to the vehicle dynamics model in the step 1, and designing a two-degree-of-freedom system state space equation as follows:
Figure FDA0003587345480000025
wherein the content of the first and second substances,
Figure FDA0003587345480000026
step 4.2: the vehicle taking in a steady state
Figure FDA0003587345480000031
Combining the lateral motion equation and the yaw motion equation in the vehicle dynamic model, the ideal yaw velocity and centroid yaw angle expression can be obtained as follows:
Figure FDA0003587345480000032
Figure FDA0003587345480000033
wherein, L is the wheelbase, and K is the stability factor;
when the vehicle reaches a steady state under the current steering wheel angle input condition, the conditions are satisfied:
Figure FDA0003587345480000034
the two-degree-of-freedom model of the vehicle with the additional yaw moment is as follows:
Figure FDA0003587345480000035
where Δ M is the additional yaw moment, B ═ 01/I z ]；
The error state space between the actual values of the centroid yaw angle and the yaw rate and the reference value is:
Figure FDA0003587345480000036
taking state variables
Figure FDA0003587345480000037
U＝ΔM
Step 4.3: selecting a mass center slip angle as a measurement index of the yaw stability of the vehicle, and designing a stability quadratic index by taking a front wheel steering angle as a control variable as follows:
Figure FDA0003587345480000038
vehicle stability control requires adding constraints to the vehicle's center of mass yaw angle and yaw rate, then vehicle stability optimization can be described as:
Figure FDA0003587345480000039
and 5: a collaborative optimal framework based on a Pareto equilibrium theory is designed, and the trajectory tracking control and the stability control are played to obtain the collaborative optimal trajectory tracking control and the stability control, and the method specifically comprises the following steps:
step 5.1: the quadratic index of track tracking control and stability control is changed into:
Figure FDA0003587345480000041
wherein R is 1 Weighting matrix for Pareto optimal global performance index, where rho 1 ，ρ 2 For the weighting coefficient, in order to facilitate the design of the Pareto cooperative optimal controller, the trajectory tracking and stability model is rewritten as follows:
Figure FDA0003587345480000042
wherein the content of the first and second substances,
Figure FDA0003587345480000043
step 5.2: the essential conditions of the solution of the discrete-time linear quadratic Pareto game are as follows:
Figure FDA0003587345480000044
in the formula
Figure FDA0003587345480000045
And
Figure FDA0003587345480000046
is a co-modal vector, and satisfies the following relationship:
Figure FDA0003587345480000047
the linear relationship between the co-modal vector and the state variable can be obtained according to the above equation:
Figure FDA0003587345480000048
the above equation can be found in a coupled ricacies equation set forth as follows:
Figure FDA0003587345480000051
in the formula
Figure FDA0003587345480000052
And
Figure FDA0003587345480000053
for the initial conditions of the iteration, will be in
Figure FDA0003587345480000054
And
Figure FDA0003587345480000055
the iteration result of the method is substituted into an equation, and the optimal control input meeting the Pareto at the current moment is obtained by combining the rolling time domain idea.
2. The method for controlling the track tracking and the stability of the intelligent automobile under the limit working condition according to claim 1, is characterized in that: the transverse control and the stability control both adopt a model prediction control method, the transverse control adopts a three-degree-of-freedom vehicle dynamics model, the optimal turning angle solution is calculated, tracked and controlled through quadratic indexes, and the stability control obtains the optimal additional yaw moment through the model prediction control method; and finally, based on a game theory, carrying out a game on the front wheel corner and the additional yaw moment of the vehicle, solving the Pareto optimal solution of the front wheel corner and the additional yaw moment, and considering the tracking performance and the stability of the vehicle.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115805939A (en) * 2022-11-29 2023-03-17 长安大学 Intelligent electric vehicle path tracking control method and device

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115805939A (en) * 2022-11-29 2023-03-17 长安大学 Intelligent electric vehicle path tracking control method and device

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