CN114572191A - Independently-driven electric automobile trajectory tracking and stability integrated control method - Google Patents

Independently-driven electric automobile trajectory tracking and stability integrated control method Download PDF

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CN114572191A
CN114572191A CN202111587808.0A CN202111587808A CN114572191A CN 114572191 A CN114572191 A CN 114572191A CN 202111587808 A CN202111587808 A CN 202111587808A CN 114572191 A CN114572191 A CN 114572191A
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vehicle
controller
stability
equation
state
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李聪
景晖
谢云峰
王刚
安伟彪
常君宇
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Guilin University of Electronic Technology
Guilin University of Aerospace Technology
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Guilin University of Electronic Technology
Guilin University of Aerospace 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
    • B60W30/02—Control of vehicle driving stability
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/60—Other road transportation technologies with climate change mitigation effect
    • Y02T10/72—Electric energy management in electromobility

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  • Automation & Control Theory (AREA)
  • Transportation (AREA)
  • Mechanical Engineering (AREA)
  • Control Of Driving Devices And Active Controlling Of Vehicle (AREA)
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Abstract

The invention discloses an integrated control method for tracking and stability of an independently driven electric automobile track. A trajectory tracking controller is designed, and a stability integrated controller is designed based on a layered integrated control structure for improving the control effect of a control system under different working conditions. The selection of the determination conditions of the rolling and lateral stability state of the vehicle and the formulation of a coordination strategy are discussed, and a control strategy of a stability integrated controller based on a hierarchical integrated control system is designed. A roll stability controller and a transverse stability controller based on an MPC algorithm are designed to improve the stability and the accuracy of high-speed trajectory tracking of the vehicle, reduce the instability risk of the four-wheel independent drive vehicle under certain working conditions and improve the driving safety of the vehicle.

Description

Independently-driven electric automobile trajectory tracking and stability integrated control method
Technical Field
The invention relates to the technical field of automobiles, in particular to a trajectory tracking and stability integrated control method for an independently driven electric automobile.
Background
Many achievements have been made in the research of track tracking and stability control of vehicles at home and abroad, but some problems still exist. For example, in the track tracking process, the control model is inaccurate and the track tracking fails due to the influence of tire nonlinearity, side inclination and other factors under the extreme working condition of the vehicle, and how to establish the high-assurance dynamic model needs to be deeply researched. In the prior art, the vehicle roll control technology of the new energy electric vehicle is mainly realized through active steering control, active suspension control, an active transverse stabilizer bar and differential braking control. In order to improve the lateral stability of the vehicle, researchers have combined control technologies such as ABS and DYC to design an electronic stability control system (ESC). However, a single controller is only designed for a fixed working condition, so that the single controller does not have good adaptability generally, the control effect is poorer when the complex and variable working condition is faced, some coordination control algorithms are more complex, the solving burden of the controller is increased, the real-time performance of the controller is reduced, the problems of coupling phenomenon between controllers, poor switching smoothness effect and the like exist in the stability integrated control.
Disclosure of Invention
The invention aims to provide a method for tracking a track and controlling stability of an independently driven electric automobile, and aims to solve the technical problems that a vehicle track tracking and stability integrated controller in the prior art is poor in effect and easy to destabilize.
In order to achieve the purpose, the invention adopts an integrated control method for tracking and stability of an independently driven electric automobile, which comprises the following steps:
constructing a vehicle state dynamic model, establishing a state equation of a controller, and obtaining a state quantity and a control quantity;
building a vehicle state observer, and estimating the state quantity of the vehicle in real time;
a track tracking and stability integrated control architecture;
establishing a vehicle track tracking controller;
establishing a vehicle roll stability controller;
establishing a vehicle lateral stability controller;
and carrying out corresponding stability control operation by using the stability integrated controller.
The vehicle state dynamics model is established based on a full vehicle plane four-wheel dynamics model and a vehicle roll dynamics model, and the state equation of the controller is a nonlinear state equation established by a transverse dynamics differential equation, a yaw rate dynamics differential equation and a vehicle roll dynamics differential equation and used for designing the controller.
The method comprises the steps that a vehicle state observer is built on the basis of unscented Kalman filtering, in the process of building the vehicle state observer and estimating the state quantity of a vehicle in real time, after discretization processing is carried out on a state equation of a controller, the observed quantity corresponding to the vehicle state observer is obtained through unscented transformation, the vehicle state observer is initialized, the corresponding sigma point is calculated, and the observed quantity is updated.
The method comprises the steps of estimating state quantities of a vehicle in real time, calculating the cornering stiffness of tires in real time based on transverse motion and yaw motion dynamic equations of the vehicle, firstly obtaining differential equations of cornering angles and lateral acceleration equations of the vehicle corresponding to front wheels and rear wheels of the vehicle in the process of calculating the cornering stiffness of the tires in real time based on the transverse motion and yaw motion dynamic equations of the vehicle, and combining the differential equations of the transverse motion and the yaw velocity dynamic differential equations after simplification to obtain estimated equations of the cornering stiffness corresponding to the front wheels and the rear wheels of the vehicle.
The integrated control architecture of the trajectory tracking and the stability comprises a stability integrated controller and a trajectory tracking controller, wherein the stability integrated controller comprises an MPC stability controller, an MPC lateral stability controller and a coordination control module.
In the process of establishing the vehicle trajectory tracking controller, after the state equation of the controller is subjected to linearization and discretization in sequence, the course angle r and the transverse position Y are used as output quantities of a state space, matrix conversion is carried out on a predicted output quantity equation, a target function is established, and after input and output of the vehicle trajectory tracking controller are restrained according to constraint regulation, the target function is converted into a standard quadratic programming equation.
The method comprises the steps of obtaining a state equation of the vehicle roll stability controller according to the state equation of the controller in the process of building the vehicle roll stability controller, carrying out linearization and discretization treatment on the state equation of the controller in sequence, carrying out matrix conversion on a prediction output equation calculated according to a transverse load transfer coefficient equation, building a target function, and converting the target function into a standard quadratic programming equation after constraint adjustment is carried out on input and output of the vehicle roll stability controller.
Wherein, at the in-process of establishing vehicle lateral stability controller, according to the equation of state of controller obtains vehicle lateral stability controller equation of state, carries out linearization and discretization in proper order to controller equation of state and handles the back, will carry out the matrix conversion according to the prediction output quantity equation that sideslip coefficient equation calculated, establishes the objective function, and it is right according to the restraint regulation after vehicle lateral stability controller's input and output carry out the restraint, convert the objective function into standard quadratic programming equation.
The invention discloses an integrated control method for tracking and stability of an independently driven electric automobile track. A trajectory tracking controller is designed, and a stability integrated controller is designed based on a layered integrated control structure for improving the control effect of a control system under different working conditions. The selection of the determination conditions of the rolling and lateral stability state of the vehicle and the formulation of a coordination strategy are discussed, and a control strategy of a stability integrated controller based on a hierarchical integrated control system is designed. A roll stability controller and a transverse stability controller based on an MPC algorithm are designed to improve the stability and the accuracy of high-speed trajectory tracking of the vehicle, reduce the instability risk of the four-wheel independent drive vehicle under certain working conditions and improve the driving safety of the vehicle.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a plane four-wheel dynamic model of a whole vehicle provided by the invention.
FIG. 2 is a vehicle roll dynamics model provided by the present invention.
FIG. 3 is a logic diagram of MPC based stability control provided by the present invention.
FIG. 4 is a flow chart of a coordination strategy of the stability integrated controller provided by the present invention.
FIG. 5 is a logic diagram for trajectory tracking stability control provided by the present invention.
FIG. 6 is a comparison of an actual trajectory to a reference trajectory for an embodiment of the present invention.
FIG. 7 is a chart of course angle comparison and nose wheel steering angle comparison for an embodiment of the present invention.
Fig. 8 is a graph of longitudinal velocity comparison and yaw-rate comparison for an embodiment of the present invention.
FIG. 9 is a graph comparing lateral load transfer coefficients and centroid slip angles for an embodiment of the present invention.
FIG. 10 is a trajectory tracking stability controller additional torque chart of an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The invention provides an integrated control method for tracking and stability of an independently driven electric automobile, which comprises the following steps:
s1: constructing a vehicle state dynamic model, establishing a state equation of a controller, and obtaining a state quantity and a control quantity;
s2: building a vehicle state observer, and estimating the state quantity of the vehicle in real time;
s3: a track tracking and stability integrated control architecture;
s4: establishing a track tracking controller;
s5: establishing a vehicle roll stability controller;
s6: establishing a vehicle lateral stability controller;
s7: and carrying out corresponding stability control operation by using the stability integrated controller.
The following is further described according to the flow steps of the method for tracking the trajectory and controlling the stability of the independently driven electric vehicle:
s1, constructing a vehicle state dynamic model, establishing a state equation of the controller, and obtaining a state quantity and a control quantity;
the vehicle state dynamics model is established based on a full vehicle plane four-wheel dynamics model and a vehicle roll dynamics model, and the state equation of the controller is a nonlinear state equation established by a transverse dynamics differential equation, a yaw rate dynamics differential equation and a vehicle roll dynamics differential equation and used for state estimation.
Specifically, please refer to the full-plane four-wheel dynamics model provided in fig. 1 and the vehicle roll dynamics model provided in fig. 2, which includes lateral and yaw dynamics characteristics of the vehicle, specifically:
the longitudinal dynamic equation of the plane four-wheel dynamic vehicle of the whole vehicle along the x-axis direction is as follows:
Figure BDA0003428617990000041
the transverse dynamic equation of the whole plane four-wheel dynamic vehicle along the y-axis direction is as follows:
Figure BDA0003428617990000042
the dynamic equation of the yaw moment of the plane four-wheel dynamic vehicle of the whole vehicle around the z-axis direction is as follows:
Figure BDA0003428617990000051
in the formula, m is the mass of the whole vehicle; r, vx, vy are respectively the yaw velocity, the longitudinal velocity and the lateral velocity under the vehicle coordinate system; delta is the front wheel rotation angle, beta is the centroid slip angle of the vehicle; iz is the moment of inertia of the vehicle about the z-axis; l is the distance from the vehicle center of mass C.G to the front and rear axles (═ f (front), r (rear)), respectively; t represents the track of the front and rear wheels (═ f, r); fyij and Fxij are lateral and longitudinal forces of the four wheels, respectively (ij ═ fl (left front wheel), fr (right front wheel), rl (left rear wheel), rr (right rear wheel)).
The motion balance equation of the whole plane four-wheel dynamic vehicle relative to the global coordinate system can be expressed as follows:
Figure BDA0003428617990000052
in order to meet the requirements of real-time performance and the like, the model is simplified into a single-track dynamic model capable of reflecting the dynamic characteristics of the vehicle, and the model comprises the transverse and transverse dynamic characteristics of the vehicle. Simplified lateral acceleration differential equation for vehicle:
differential equation of lateral acceleration of vehicle:
Figure BDA0003428617990000053
yaw rate differential equation of vehicle:
Figure BDA0003428617990000054
wherein, in the formula, Cαf，CαrIs divided into front and rear wheel cornering stiffness; alpha is alphafIs the front wheel side slip angle, αrIs the rear wheel side slip angle; i isZIs the moment of inertia of the vehicle about the z-axis; mZIs an additional yaw moment in order to maintain a stable driving of the vehicle.
The vehicle roll dynamics differential equation is expressed as follows:
Figure BDA0003428617990000055
wherein, IxMoment of inertia about the x-axis, hrHeight of the vehicle roll center to the center of mass, msIs the sprung mass of the vehicle,
Figure BDA0003428617990000056
in order to provide the roll stiffness of the suspension,
Figure BDA0003428617990000057
is the roll damping coefficient of the suspension, phi is the roll angle,
Figure BDA0003428617990000058
in order to determine the roll angle velocity,
Figure BDA0003428617990000059
is the roll angular acceleration.
And based on the vehicle state dynamic model, giving a system state equation, a state quantity and a control quantity of the designed vehicle roll stability controller and the vehicle lateral stability controller.
For the vehicle track tracking controller, firstly, a state equation is established, according to a model prediction control theory, a nonlinear state equation is established by combining the established longitudinal dynamic equation of the whole vehicle plane four-wheel dynamic vehicle along the x-axis direction, the established transverse dynamic equation of the vehicle along the y-axis direction, the established yaw moment dynamic equation of the vehicle around the z-axis direction, a motion balance equation of the vehicle relative to a global coordinate system and the like, and the nonlinear state equation is specifically expressed as follows:
Figure BDA0003428617990000061
in the formula, state quantity
Figure BDA0003428617990000062
Control quantity u (t) δf。
For the vehicle roll stability controller, firstly, a state equation is established, and according to a model prediction control theory, a nonlinear state equation is established by combining the transverse acceleration differential equation, the yaw rate differential equation, the tire slip angle differential equation, the vehicle roll motion dynamics equation and the like which are established after the vehicle is simplified:
Figure BDA0003428617990000063
quantity of state
Figure BDA0003428617990000064
Control quantity
Figure BDA0003428617990000065
Wherein epsilonLRepresenting a relaxation factor, and ensuring that the controller has an optimal solution within a specified calculation time;
Figure BDA0003428617990000066
the control variable generated for the roll stability controller is the additional torque for the four wheels (ij ═ fl, fr, rl, rr).
For the vehicle lateral stability controller, a nonlinear state equation is established in combination with the vehicle simplified lateral acceleration differential equation, the yaw rate differential equation, and the tire slip angle differential equation established above:
Figure BDA0003428617990000067
quantity of state xs＝[r vy αf αr]TControl amount of
Figure BDA0003428617990000068
S2, building a vehicle state observer, and estimating the state quantity of the vehicle in real time;
the vehicle state observer is built on the basis of unscented Kalman filtering, in the process of building the vehicle state observer and estimating the state quantity of the vehicle in real time, after discretizing the state equation of the controller, the observed quantity corresponding to the vehicle state observer is obtained by unscented transformation, the vehicle state observer is initialized, the corresponding sigma point is calculated, and the observed quantity is updated.
Estimating the state quantity of the vehicle in real time, and calculating the cornering stiffness of the tire in real time based on the lateral motion and the yaw motion dynamic equation of the vehicle. In the process of calculating the cornering stiffness of the tire in real time based on the transverse motion and yaw motion dynamic equations of the vehicle, firstly, acquiring a cornering angle differential equation and a vehicle lateral acceleration equation corresponding to front wheels and rear wheels of the vehicle, and combining the cornering angle differential equation and the vehicle lateral acceleration equation with the transverse dynamic differential equation and the yaw velocity dynamic differential equation after simplification to obtain an cornering stiffness estimation equation corresponding to the front wheels and the rear wheels of the vehicle.
Specifically, a nonlinear state equation is established based on the lateral dynamics differential equation, the yaw rate dynamics differential equation, and the vehicle roll dynamics differential equation, and is expressed as:
Figure BDA0003428617990000071
where v (t) is measurement noise, w (t) is process noise, x (t) is a state variable, y (t) is an observation variable, and u (t) is system input.
Setting the sampling time of the UKF estimation algorithm as delta t, carrying out discretization processing on the nonlinear state equation, then initializing, setting the initial value and the variance of the state quantity, calculating the corresponding sigma point, and then updating the observed quantity, including state prediction updating and measurement prediction updating.
The resulting state estimation expression is as follows:
Figure BDA0003428617990000072
Pk＝P(k∣k-1)-K(k)PyyK(k)T
the cornering stiffness of the tire is an important parameter for the linearization of a vehicle dynamic equation, and the parameter can be dynamically changed along with the running condition of the vehicle, so that the stability of the vehicle can be indirectly reflected. In order to improve the adaptability and robustness of the stability controller, the tire side deflection rigidity is estimated on line according to the state quantity fed back by the vehicle in real time. The specific estimation equation is as follows:
Figure BDA0003428617990000073
the cornering stiffness estimation equation is derived from a lateral dynamics differential equation and a yaw rate differential equation, wherein
Figure BDA0003428617990000074
And
Figure BDA0003428617990000075
respectively representing the front wheel side deflection rigidity and the rear wheel side deflection rigidity at the current sampling moment; alpha is alphaf0And alphar0Front wheel side deflection angle and rear wheel side deflection angle of current sampling momentDeflection angle;
Figure BDA0003428617990000076
the yaw rate of the vehicle at the current sampling moment; mFx0An additional yaw moment at the current sampling moment; delta0The front wheel rotation angle at the current sampling moment.
S3: a track tracking and stability integrated control architecture;
the track following and stability control architecture comprises a stability integrated controller and a track following controller, wherein the stability integrated controller comprises an MPC roll stability controller, an MPC lateral roll stability controller and a coordination control module.
Specifically, in order to improve the accuracy of track tracking of the vehicle on high and low adhesion coefficient roads at a high speed and ensure the stability of the vehicle, the transverse load transfer coefficient and the centroid slip angle are maintained within a safe threshold range. The MPC trajectory tracking controller and the designed MPC stability integrated controller are integrated, and the trajectory tracking stability controller is designed based on a layered integrated control structure. Wherein the specific composition of the trajectory tracking stability control logic is shown in fig. 3.
The two dotted line boxes in the middle of the diagram are respectively an MPC track tracking controller and an MPC stability integrated controller, wherein the MPC track tracking controller tracks an expected track by generating a front wheel corner, the stability integrated controller monitors a lateral load transfer coefficient and a sideslip coefficient in real time by a coordination control module, the MPC roll stability controller and the MPC lateral stability controller are enabled according to an internal coordination strategy, and the stability control of the vehicle in the track tracking process is realized by generating an additional torque. The dotted line frame at the upper left corner is a state parameter input and output module which respectively inputs the state parameters fed back by the vehicle in real time and the state parameters estimated by UKF into the MPC controller, so as to realize the closed-loop control of the whole control system.
The stability integrated controller is divided into an upper layer and a lower layer, the upper layer supervision decision module comprises a coordination controller, and the lower layer execution control module comprises each sub MPC controller.
Referring to the MPC based stability control logic provided in FIG. 4, the driver drives the vehicle, sending drive torque and steering wheel angle to the full vehicle model. The UKF state estimator receives partial measurable state quantity and tire force to the lateral speed v of the vehicleyAnd estimating the state quantities such as the roll angle phi in real time, and then sending the estimated state quantities and the measurable state quantities fed back by the vehicle to the vehicle stability integrated controller. The vehicle stability integrated controller can monitor the real-time running state of the vehicle, and when the vehicle is monitored to have a side-rolling or side-slipping trend, the stability controller can enable the corresponding stability controller to generate additional torque to ensure the stable running of the vehicle.
Aiming at the problem that the single controller cannot achieve the expected control effect due to poor adaptability of different adhesion coefficient pavements, in order to exert the performance of each MPC controller to the maximum extent, a stable integrated controller is designed by adopting a layered integrated control structure. The designed stability integrated controller is divided into an upper layer and a lower layer, the upper layer supervision decision module comprises a coordination controller, and the lower layer execution control module comprises each sub MPC controller. The upper layer supervision decision module is used as the key of the design of the stability integrated controller, and the reasonability and the control accuracy of the control system are directly influenced. The design of the module also comprises the selection of the judgment condition of the vehicle stability state and the formulation of a coordination strategy.
The lateral load transfer coefficient (LTR) is used as a determination condition for describing the rollover stability state of the vehicle, and the magnitude of the lateral load transfer coefficient directly reflects the degree of risk of rolling of the vehicle. The sideslip coefficient (ρ) can be used to evaluate the lateral stability of a vehicle during driving, where ρ depends on the lateral force F of the tireyAnd a vertical force FzThe smaller the value of p, the more likely the vehicle is to slip-destabilize. Since both of the above coefficients can quickly reflect the stability state of the vehicle, the present invention is based on the object of study, and uses the sideslip coefficient (ρ) and the lateral load transfer coefficient (LTR) as the vehicle stability state determination conditions.
Figure BDA0003428617990000091
The lateral load transfer coefficient is expressed as follows:
Figure BDA0003428617990000092
wherein, Fzl,FzrThe vertical loads of the left wheel and the right wheel respectively, the transverse load transfer coefficient is calculated according to the equation to be 0-1, and when the coefficient reaches 1, the vehicle is proved to have turned over.
The lateral load transfer coefficient approximation equation is expressed as follows:
Figure BDA0003428617990000093
wherein h isrHeight from the roll center to the center of mass of the vehicle,/sG is the gravitational acceleration.
Referring to the coordination strategy flow chart of the stability integrated controller provided in fig. 5, multiple sets of simulation tests are performed by setting different vehicle speeds and different steering wheel angles, threshold intervals of the determination condition LTR and the sideslip coefficient ρ are determined, and the following coordination strategy is formulated:
when the speed and the steering wheel angle of the vehicle are lower than the set threshold values, the vehicle is in a safe driving state, and the MPC lateral stability controller and the MPC roll stability controller are not started;
when the vehicle speed and the steering wheel angle exceed set thresholds, the upper layer supervision decision module monitors the transverse load transfer coefficient LTR and the sideslip coefficient rho in real time. When the sideslip coefficient rho is less than 0.5 and LTR is less than 0.6, the fact that the vehicle runs on a road surface with a low adhesion coefficient and transverse sideslip instability is easy to occur is shown, and only an MPC transverse stability controller needs to be started;
when the sideslip coefficient rho is more than or equal to 0.5 and the LTR is more than or equal to 0.6, the vehicle is indicated to run on a road surface with a higher adhesion coefficient, rollover instability is easy to occur under working conditions such as high-speed sharp turn and the like, and an MPC sideslip stability controller needs to be started;
the MPC lateral stability controller is set to be turned on taking into account that the determination conditions may be within other threshold ranges, such as the sideslip coefficient ρ being greater than 0.5 and LTR being less than 0.6.
S4, establishing a vehicle track tracking controller;
according to the longitudinal dynamic equation of the vehicle along the x-axis direction, the transverse dynamic equation of the vehicle along the y-axis direction, the dynamic equation of the yaw moment of the vehicle around the z-axis direction, the motion balance equation of the vehicle relative to the global coordinate system and the like, a nonlinear state equation can be constructed, and the specific expression is as follows:
Figure BDA0003428617990000101
in the formula, state quantity
Figure BDA0003428617990000102
Control quantity u (t ═ δ)f。
And (4) carrying out linearization processing on the nonlinear state equation, and designing the trajectory tracking controller by adopting a linearization control method.
Selecting the above nonlinear equation of state with Taylor expansion0(t),u0(t-1)) carrying out linearization treatment, wherein the expression after linearization is as follows:
Figure BDA0003428617990000103
Figure BDA0003428617990000104
Figure BDA0003428617990000105
wherein the content of the first and second substances,
Figure BDA0003428617990000106
discretizing the linear state equation to obtain a discrete state space expression, which is as follows:
Figure BDA0003428617990000107
make it
Figure BDA0003428617990000108
It can be arranged as follows:
x(k+1)＝Ax(k)+Bu(k)+d(k)
in the formula
Figure BDA0003428617990000109
I is the identity matrix of the same order as matrix a and T is the sampling period.
Considering that the control quantity may generate a sudden change phenomenon, the control increment in each sampling period needs to be limited. Correspondingly converting the sorted discrete state space expression to obtain a new state equation containing the control increment delta u (k), which is specifically as follows:
Figure BDA00034286179900001010
the concrete parameters are as follows:
Figure BDA0003428617990000111
Figure BDA0003428617990000112
Δu(k)＝u(k)-u(k-1)
where m represents the controlled quantity dimension and n represents the state quantity dimension.
The prediction output equation is specifically expressed as follows:
Figure BDA0003428617990000113
wherein the output quantity y (k ═ r Y)]T，
Figure BDA0003428617990000114
Combining the new state equation and the prediction output equation, a state space expression of the MPC trajectory tracking controller can be obtained, specifically:
Figure BDA0003428617990000115
the predicted output expression for the discrete state is shown below:
Figure BDA0003428617990000116
according to the expression, the yaw rate in the prediction time domain can be calculated
Figure BDA0003428617990000118
And the value of the transverse position Y, and is applied to the subsequent operation of the control algorithm.
In order to obtain the desired control effect, an objective function of the form:
Figure BDA0003428617990000117
in the formula, NpAnd NcThe time domain is a control time domain and a prediction time domain respectively, Q is an output weighting matrix, R is a control weighting matrix, rho is a weight coefficient, and epsilon is a relaxation factor. The first item of the objective function reflects the fast tracking capability of the control system to the expected track, and the second item reflects the requirement of the control system to the stable change of the control quantity. Meanwhile, the real-time change of the control system is considered, and the generation of the target function in each control period cannot be guaranteedAnd (5) optimal solution. Therefore, the relaxation factor is added into the objective function, and the control system can replace the optimal solution with the obtained suboptimal solution under the condition of no optimal solution, so that the situation of no solution is avoided.
Considering that the steering actuator of an actual vehicle has a certain operating range, in order to avoid the controller from generating a front wheel steering angle that exceeds the operating range, it is necessary to restrict the amount of control, the amount of control increase, and the like generated by the controller.
Umin(k)≤U(k)≤Umax(k)
ΔUmin(k)≤ΔU(k)≤ΔUmax(k)
Meanwhile, the prediction output is also constrained, and the constraint is set as follows:
Figure BDA0003428617990000121
solving the constrained optimization problem in each sampling period to obtain NpA sequence of control increments within a range.
U*(k)＝[Δu*(k|k)Δu*(k+1|k)...Δu*(k+Nc-1|k)]
The model predictive control algorithm selects the first control increment delta u from the control increment sequence*(k | k), the optimal control amount for the trajectory tracking of the vehicle at the present time is thus expressed as follows:
u(k|k)＝u(k-1|k)+Δu*(k|k)
the above equation is an optimization problem that the control system completes at the current time k, and the control system will still repeat the above steps at the time k + 1. The optimal front wheel rotating angle is calculated in a reciprocating mode and acts on the vehicle, and the expected track is tracked.
S5, establishing a vehicle roll stability controller;
in the process of establishing the vehicle roll stability controller, a vehicle roll stability controller state equation is obtained according to the state equation of the controller, after the controller state equation is subjected to linearization and discretization in sequence, matrix conversion is carried out on a prediction output quantity equation calculated according to a transverse load transfer coefficient equation, an objective function is established, and after input and output of the vehicle roll stability controller are restrained according to restraint regulation, the objective function is converted into a standard quadratic programming equation.
Specifically, according to the established vehicle roll stability controller equation of state, expressed as:
Figure BDA0003428617990000122
wherein, the specific variables are as follows:
Figure BDA0003428617990000123
wherein x represents the state quantity of the model,
Figure BDA0003428617990000124
respectively, the additional torque of 4 wheels, and epsilon is a relaxation variable;
carrying out linearization processing on the nonlinear state equation to obtain the following equation:
Figure BDA0003428617990000125
in the formula:
Figure BDA0003428617990000131
Figure BDA0003428617990000132
Figure BDA0003428617990000133
since the model predictive control is a discrete time-varying control method, discretization processing is required, and the discretization state equation is as follows:
Figure BDA0003428617990000134
wherein the content of the first and second substances,
Figure BDA0003428617990000135
i is the identity matrix, TsIs the sampling period.
Wherein the state matrix
Figure BDA0003428617990000136
Updating is carried out in each sampling period, so that the accuracy of the model is ensured; t is a matrix transposition symbol.
Then, establishing a prediction output equation, and in order to ensure the driving stability of the vehicle on the road surface with the low adhesion coefficient, selecting an approximate transverse load transfer coefficient LTR' as an output quantity, wherein the prediction output equation is as follows:
yk＝Cxk
C＝[0,0,2hrCαrcosδ/(mlsg),2hrCαr/(mlsg),2hr/ls,0]
wherein C is an output matrix; y iskIs the output of the predictive model.
Converting a specific constrained output equation in a matrix form in a prediction time domain, specifically as follows:
Figure BDA0003428617990000137
then, an objective function in the MPC controller is designed, and the objective function is designed to obtain an optimal control sequence. The specific objective function is designed as follows:
Figure BDA0003428617990000141
wherein the specific variables are:
Figure BDA0003428617990000142
T＝diag(tT tT tT tT tε)，R＝diag(rT rT rT rT r2ε)
wherein N ispIs the prediction time domain;
Figure BDA0003428617990000143
is the desired additional torque for the four wheels generated by the controller
Figure BDA0003428617990000144
wLIn (1)
Figure BDA0003428617990000145
The four-wheel driving torque is input by a driver and is used for maintaining the vehicle speed;
Figure BDA0003428617990000146
the control quantity is solved at the last moment of the controller;
Figure BDA0003428617990000147
is a weight for the roll stability controller control increments,
Figure BDA0003428617990000148
is a weight of the roll stability controller control amount,
Figure BDA0003428617990000149
and
Figure BDA00034286179900001410
respectively, the weights of the associated relaxation factors. The target function is divided into three terms, the first term is used for controlling the target value to be greater than a set threshold value when the controller detects that the target value is greater than the set threshold valueAt value, the controller will generate additional torque; the second term ensures the stable change of the control quantity and avoids generating larger oscillation to influence the normal running of the vehicle; the third term is to avoid the controller from having a no-solution condition.
Aiming at the output constraint of the controller, the soft constraint of the vehicle rollover index is designed. The specific approximate vertical load factor constraint equation is as follows:
|yk|≤LTR′max+εk
s6, establishing a vehicle lateral stability controller;
in the process of establishing vehicle lateral stability controller, according to the equation of state of controller obtains vehicle lateral stability controller equation of state, carries out linearization and discretization to controller equation of state in proper order and handles the back, will carry out the matrix conversion according to the prediction output quantity equation that sideslip coefficient equation calculated, establishes the objective function, and it is right according to the restraint regulation after vehicle lateral stability controller's input and output carry out the restraint, convert the objective function into standard quadratic programming equation.
Specifically, according to the establishment of a vehicle lateral stability controller state equation, the following is expressed:
Figure BDA00034286179900001411
quantity of state xs＝[r vy αf αr]TControl quantity of
Figure BDA00034286179900001412
Carrying out linearization processing on the nonlinear state equation to obtain a linearized state equation:
Figure BDA00034286179900001413
in the formula:
Figure BDA00034286179900001414
Figure BDA0003428617990000151
discretizing the linearized state equation, wherein the expression of the discretized state equation is as follows:
Figure BDA0003428617990000152
in the formula
Figure BDA0003428617990000153
Vehicle lateral stability controller selects lateral velocity v of vehicleyFor the output quantity, the predicted output equation is:
Figure BDA0003428617990000154
wherein Cs ═ 0100.
Will [ k, k + Np]Recombining the prediction output equations at the moment to obtain a prediction output expression in a discrete state:
Figure BDA0003428617990000155
in the formula
Figure BDA0003428617990000156
And
Figure BDA0003428617990000157
the specific variables constitute a prediction output expression that can be referenced to a discrete state in the roll stability controller.
The objective function of the lateral stability controller is designed as follows:
Figure BDA0003428617990000158
in order to realize the driving stability of the vehicle on a low-attachment road surface, the centroid slip angle of the vehicle is constrained, and the constraint equation is as follows:
Figure BDA0003428617990000159
in the formula betamaxIs a set centroid slip angle threshold, which is set at 3 degrees.
The roll and lateral stability controller of the invention is designed for the same type of vehicle, so the constrained design of the control quantity of the stability controller is consistent with the roll stability controller, and the design steps can refer to the expression for constraining the control quantity and controlling quantity constraint in the roll stability controller.
And S7, performing corresponding track tracking and stability control operation by using the controller.
Further, please refer to fig. 6 to fig. 10, the present invention further provides a specific embodiment for verifying the performance of the MPC stability integrated controller, and a joint simulation system is built, and the superiority of the model predictive control algorithm is explained by analyzing the simulation result.
The initial speed of the simulated vehicle is 80km/h, the adhesion coefficient of the road surface at the longitudinal position of 0-200 meters is set as 0.85, and the adhesion coefficient of the road surface at the position of 200-500 meters is set as 0.35. The specific simulation results are shown in fig. 6 to 10:
analyzing fig. 6, the control effects of the MPC trajectory tracking controller (MPC _ AFS) and the trajectory tracking stability controller (MPC _ Integrated) were compared. When the vehicle runs on a road surface with a high adhesion coefficient at the speed of 80km/h, the real-time accurate tracking of the expected track is realized under the action of the MPC-AFS controller and the MPC-Integrated controller. When the vehicle enters the low-adhesion-coefficient road surface, the actual track and the expected track are greatly deviated under the action of the MPC-AFS controller, and the track tracking fails. Under the action of the MPC _ Integrated controller, the actual trajectory then converges to the desired trajectory very quickly, although at large changes in road curvature the actual trajectory deviates to some extent from the desired trajectory.
Analyzing the fig. 7 and fig. 8, when the vehicle adopting the MPC _ AFS controller tracks on a road surface with a high adhesion coefficient, the heading angle, the front wheel turning angle and the yaw rate all have oscillation with a larger amplitude at a longitudinal position of about 90 meters, and the vehicle has a potential instability hazard. When the vehicle tracks on a road surface with an adhesion coefficient of 0.35, the three state quantities all have monotonous change, and meanwhile, the longitudinal vehicle speed begins to rapidly decrease, which indicates that the vehicle has severe sideslip. When the vehicle adopts an MPC-Integrated controller to track the road surface at a medium and high speed, the course angle and the front wheel steering angle do not have oscillation with a larger amplitude, the longitudinal vehicle speed is stably changed, and the yaw rate is also controlled in a safe range.
Analyzing fig. 9, compared to the MPC _ AFS controller, the MPC _ Integrated controller ensures the driving safety and stability of the vehicle when performing the double-traverse trajectory tracking on the road surface, and effectively limits the lateral load transfer coefficient and the centroid slip angle within a reasonable range, wherein the maximum value of the centroid slip angle is about 4 °.
FIG. 10 shows the additional torque generated by the MPC _ Integrated controller, which can quickly generate the additional torque to adjust the steady state of the vehicle with the input of the front wheel steering angle, and the action time is short, so that the trace tracking effect is not influenced too much by the excessive application of the additional torque.
The invention discloses an integrated control method for tracking and stability of an independently driven electric automobile track. A trajectory tracking controller is designed, and a stability integrated controller is designed based on a layered integrated control structure for improving the control effect of a control system under different working conditions. The selection of the determination conditions of the rolling and lateral stability state of the vehicle and the formulation of a coordination strategy are discussed, and a control strategy of a stability integrated controller based on a hierarchical integrated control system is designed. A roll stability controller and a transverse stability controller based on an MPC algorithm are designed to improve the stability and the accuracy of high-speed trajectory tracking of the vehicle, reduce the instability risk of the four-wheel independent drive vehicle under certain working conditions and improve the driving safety of the vehicle.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.

Claims (8)

1. An integrated control method for tracking and stability of an independently driven electric automobile is characterized by comprising the following steps:
constructing a vehicle state dynamic model, establishing a state equation of a controller, and obtaining a state quantity and a control quantity;
constructing a vehicle state observer, and estimating the state quantity of the vehicle in real time;
a track tracking and stability integrated control architecture;
establishing a vehicle track tracking controller;
establishing a vehicle roll stability controller;
establishing a vehicle lateral stability controller;
and carrying out corresponding track tracking and stability control operation by using the controller.
2. The method for integrated trajectory tracking and stability control of an independently driven electric vehicle of claim 1, wherein the vehicle state dynamics model is built based on a full vehicle planar four-wheel dynamics model and a vehicle roll dynamics model, and the state equation of the controller is a nonlinear state equation built from a lateral dynamics differential equation, a yaw rate dynamics differential equation and a vehicle roll dynamics differential equation, and is used for the design of the controller.
3. The integrated control method for tracking and stabilizing the trajectory of the independently driven electric vehicle according to claim 1, wherein the vehicle state observer is built based on unscented kalman filtering, in the process of building the vehicle state observer and estimating the state quantity of the vehicle in real time, after discretizing the state equation of the controller, the observed quantity corresponding to the vehicle state observer is obtained by unscented transformation, the vehicle state observer is initialized, and the corresponding sigma point is calculated to update the observed quantity.
4. The integrated trajectory tracking and stability control method for an independently driven electric vehicle according to claim 1, wherein the state quantity of the vehicle is estimated in real time, and further comprising calculating the cornering stiffness of the tire in real time based on the lateral motion and yaw motion kinetic equations of the vehicle, and in calculating the cornering stiffness of the tire in real time based on the lateral motion and yaw motion kinetic equations of the vehicle, the cornering stiffness estimation equations corresponding to the front and rear wheels of the vehicle are obtained by first obtaining the cornering differential equations corresponding to the front and rear wheels of the vehicle and the lateral acceleration equation of the vehicle, and combining the transverse dynamic differential equations and the yaw rate kinetic differential equations after simplification.
5. The method as claimed in claim 1, wherein the trajectory tracking and stability control architecture comprises a stability integrated controller and a trajectory tracking controller, wherein the stability integrated controller comprises an MPC stability controller, an MPC lateral stability controller and a coordination control module.
6. The method as claimed in claim 1, wherein in the process of establishing the vehicle trajectory tracking controller, after the controller state equation is linearized and discretized in sequence, the heading angle r and the transverse position Y are used as output quantities of the state space, matrix conversion is performed on the predicted output quantity equation, the objective function is established, and after the input and output of the vehicle trajectory tracking controller are constrained according to constraint adjustment, the objective function is converted into a standard quadratic programming equation.
7. The method according to claim 1, wherein during the process of establishing the vehicle roll stability controller, the state equation of the vehicle roll stability controller is obtained according to the state equation of the controller, after the state equation of the controller is linearized and discretized in sequence, the predicted output equation calculated according to the transverse load transfer coefficient equation is subjected to matrix transformation to establish the objective function, and after constraint adjustment is performed on the input and output of the vehicle roll stability controller, the objective function is converted into a standard quadratic programming equation.
8. The method according to claim 1, wherein in the process of establishing the vehicle lateral stability controller, the vehicle lateral stability controller state equation is obtained according to the state equation of the controller, after linearization and discretization are sequentially performed on the controller state equation, the predicted output equation calculated according to the sideslip coefficient equation is subjected to matrix transformation to establish the objective function, and after constraint adjustment is performed on the input and output of the vehicle lateral stability controller, the objective function is converted into a standard quadratic programming equation.
CN202111587808.0A 2021-12-23 2021-12-23 Independently-driven electric automobile trajectory tracking and stability integrated control method Pending CN114572191A (en)

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Cited By (2)

* 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
WO2023240760A1 (en) * 2022-06-16 2023-12-21 常州工学院 Economical optimization policy construction method for lateral stability control over electric vehicle

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2023240760A1 (en) * 2022-06-16 2023-12-21 常州工学院 Economical optimization policy construction method for lateral stability control over electric vehicle
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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