WO2023240760A1 - 面向电动汽车横向稳定控制的经济型优化策略构建方法 - Google Patents
面向电动汽车横向稳定控制的经济型优化策略构建方法 Download PDFInfo
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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
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
- B60L15/00—Methods, circuits, or devices for controlling the traction-motor speed of electrically-propelled vehicles
- B60L15/20—Methods, circuits, or devices for controlling the traction-motor speed of electrically-propelled vehicles for control of the vehicle or its driving motor to achieve a desired performance, e.g. speed, torque, programmed variation of speed
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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
- 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
- B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
- B60L2240/00—Control parameters of input or output; Target parameters
- B60L2240/40—Drive Train control parameters
- B60L2240/42—Drive Train control parameters related to electric machines
- B60L2240/423—Torque
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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
- 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
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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
- 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
- B60W2050/0031—Mathematical model of the vehicle
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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
- B60W2710/00—Output or target parameters relating to a particular sub-units
- B60W2710/08—Electric propulsion units
- B60W2710/083—Torque
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- 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
Definitions
- the invention relates to the technical field of electric vehicle control, and in particular to an economical optimization strategy construction method, system and computer-readable storage medium for lateral stability control of electric vehicles.
- LSC Lateral stability control
- AFS and DYC integrated control (AFS and DYC integrated control, AFS/DYC).
- 4WID-EV Four-wheel independent drive electric vehicle
- 4WID-EV Four-wheel independent drive electric vehicle
- 4WID-EV adopts a new drive structure, and its wheel hub motor can be independently controlled by a controller.
- cascade control structures based on AFS/DYC integrated control have emerged, but the effective working ranges of the AFS and DYC parts are difficult to coordinate.
- Electrification provides a new direction to solve the environmental pollution problems caused by traditional vehicles, but the development of electric vehicles is seriously restricted by problems such as short cruising range.
- the torque distribution of in-wheel motors has great potential in improving the overall efficiency of the motor, an economical optimization strategy that can achieve reasonable distribution of in-wheel motor torque is urgently needed.
- the purpose of the present invention is to provide an economical optimization strategy construction method and system for lateral stability control of electric vehicles.
- the present invention provides the following solutions:
- An economical optimization strategy construction method for electric vehicle lateral stability control including:
- the lateral stability control system model and reference model of the four-wheel independent drive electric vehicle with active distribution optimization are determined according to the vehicle system dynamics model; the lateral stability control system model includes coordination variables;
- the objective function of the economic saturation optimal planning and the constraints of the objective function are established with the goal of optimizing the overall efficiency of the motor;
- the coordination variables in the objective function are adjusted according to the workflow to optimize the working efficiency of the motor.
- the vehicle system dynamics model is:
- the state vector control vector system matrix control matrix constant matrix is the first - order differential of the state vector
- the moment of inertia of f is the active front wheel steering angle, and ⁇ is the center of mass sideslip angle of the vehicle.
- the lateral stability control system model is:
- the deviation of the system state quantity from the reference model is the side slip angle deviation of the center of mass, is the yaw angular velocity deviation, for The first-order differential of , coefficient matrix L is the coordination variable, coefficient matrix
- the reference model is:
- ⁇ is the front wheel steering angle
- ⁇ ref and r ref are the desired center of mass side slip angle and yaw angular velocity respectively.
- the lateral stability controller is:
- J is the cost function of the lateral stability control system
- the matrices Q and R are both constant positive definite matrices
- ⁇ is the weight coefficient
- T is the unit step time interval
- N p is the prediction step size
- X ref (t) are the reference value at time t and the state quantity of the kth prediction step respectively
- I is the unit matrix
- ⁇ U is the change value of the control quantity
- ⁇ U are the upper and lower limits of ⁇ U respectively
- ⁇ ⁇ and ⁇ U are both relaxation coefficients.
- the objective function is:
- J e is the cost function of hub motor torque distribution
- coefficient matrix ⁇ [1 1 -1 -1]b/(2R)
- R is the wheel radius
- b is the left and right wheel track
- U T [T lf T lr T rf T rr ] T
- the subscripts lf, lr, rr, rf represent the left front wheel, left rear wheel, right rear wheel, respectively.
- v ei and p T are both weight coefficients
- Q T and R T are weight matrices
- sat() is a saturation function.
- constraints of the objective function are:
- ⁇ U T are the maximum and minimum values of the increment ⁇ U T respectively
- T r is the total driving torque
- U Tmax is the maximum control input
- sign() is the sign function.
- the workflow of determining the regulator of the coordination variable based on the three-dimensional space surface includes:
- a two-dimensional plane is determined according to the three-dimensional space curved surface; the two-dimensional plane is the plane when the vertical axis of the three-dimensional space curved surface is zero; the coordinate axis X T and the coordinate axis Y T of the three-dimensional space curved surface are both hubs Motor torque, the coordinate axis Z E of the three-dimensional space surface is the motor efficiency;
- the torque constraints are: Among them, the hub motor torques T lf , T lr , T rr , and T rf are x 1 , y 1 , x 2 , and y 2 respectively, T r /2 is recorded as z * , and R ⁇ M/b is recorded as ⁇ z;
- the geometric relationship of the torque constraint determines the first line and the second line; the projections of the points on the first line and the second line in the two-dimensional plane on the X and Y coordinate axes are respectively the hub motor torque x 1 and y 1 , x 2 , y 2 ;
- the workflow is determined according to the first line, the second line, the three-dimensional space surface and the two-dimensional plane.
- An economical optimization strategy construction system for electric vehicle lateral stability control including:
- the dynamic model building module is used to build a vehicle system dynamics model based on the physical parameters of the vehicle traveling at a constant speed;
- a control system model building module for determining a lateral stability control system model and a reference model of a four-wheel independent drive electric vehicle with active distribution optimization based on the vehicle system dynamics model; the lateral stability control system model includes coordination variables;
- a controller determination module configured to construct a lateral stability controller with optimized allocation based on the lateral stability control system model and the reference model;
- a constraint determination module configured to establish an objective function of the economic saturation optimal planning and the constraint conditions of the objective function based on the lateral stability controller and with the optimization of the overall efficiency of the motor as the goal;
- a curved surface construction module for constructing a three-dimensional space curved surface based on the additional yaw moment output by the lateral stability controller and the coordination variable;
- a process determination module for determining the workflow of the regulator of the coordination variable based on the three-dimensional space surface
- An adjustment module is used to adjust the coordination variables in the objective function according to the work process to optimize the working efficiency of the motor.
- a computer-readable storage medium with a computer program stored thereon When the computer program is executed by a processor, the economical optimization strategy construction method for electric vehicle lateral stability control as described in any one of claims 1 to 8 is realized. steps in.
- the present invention discloses the following technical effects:
- the present invention provides an economical optimization strategy construction method, system and computer-readable storage medium for electric vehicle lateral stability control.
- a lateral stability control system model containing active distribution optimization is constructed, and the coordination variable L is used to achieve effective control of each part. Coordinated allocation of work areas.
- a lateral stability controller is designed under the model predictive control framework. Among them, the designed objective function J makes the vehicle's motion state track the expected value at steady state, and the objective function J e is used for torque distribution.
- a three-dimensional space surface is constructed; and in a specific embodiment, the Gauss surface theory is used to analyze the impact of the coordination variable L on the overall efficiency of the hub motor, and determine the coordination Variable L regulator workflow to improve overall hub motor efficiency.
- Figure 1 is a flow chart of an economical optimization strategy construction method in an embodiment provided by the present invention
- Figure 2 is a schematic diagram of the economical optimization strategy of the in-wheel motor in the embodiment provided by the present invention.
- Figure 3 is a schematic diagram of a monorail vehicle model in an embodiment provided by the present invention.
- Figure 4 is a schematic diagram of the active allocation optimization scheme in the embodiment provided by the present invention.
- Figure 5 is a schematic diagram of wheel rotation balance analysis in an embodiment provided by the present invention.
- Figure 6 is a schematic diagram of the X T Y T Z Z three-dimensional space curved surface S in the embodiment provided by the present invention.
- Figure 7 is the overall working flow of the coordinated variable L regulator in the embodiment provided by the present invention.
- Figure 8 is a sub-workflow of the coordination variable L regulator in the embodiment provided by the present invention.
- an embodiment means that a particular feature, structure or characteristic described in connection with the embodiment can be included in at least one embodiment of the present application.
- the appearances of this phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. Those skilled in the art understand, both explicitly and implicitly, that the embodiments described herein may be combined with other embodiments.
- the purpose of the present invention is to provide an economical optimization strategy construction method, system and computer-readable storage medium for lateral stability control of electric vehicles, which can improve the overall efficiency of the wheel hub motor.
- Figure 1 is a flow chart of an economical optimization strategy construction method in an embodiment provided by the present invention. As shown in Figure 1, the present invention provides an economical optimization strategy construction method for electric vehicle lateral stability control, which includes:
- Step 100 Construct a vehicle system dynamics model based on the physical parameters of the vehicle traveling at a constant speed
- Step 200 Determine the lateral stability control system model and reference model of the four-wheel independent drive electric vehicle with active distribution optimization according to the vehicle system dynamics model; the lateral stability control system model includes coordination variables;
- Step 300 Construct a lateral stability controller with optimized allocation according to the lateral stability control system model and the reference model;
- Step 400 According to the lateral stability controller, establish the objective function of the economic saturation optimal planning and the constraints of the objective function with the optimization of the overall efficiency of the motor as the goal;
- Step 500 Construct a three-dimensional space curved surface according to the additional yaw moment output by the lateral stability controller and the coordination variable;
- Step 600 The workflow of determining the regulator of the coordination variable based on the three-dimensional space surface
- Step 700 Adjust the coordination variables in the objective function according to the workflow to optimize the working efficiency of the motor.
- Figure 2 is a schematic diagram of an economical optimization strategy for an in-wheel motor in an embodiment provided by the present invention. As shown in Figure 2, this embodiment includes five steps, which are establishing a vehicle system dynamics model and determining an active distribution optimization strategy. 4WID-EV lateral stability control system model, determining the reference model of the lateral stability control system, constructing the lateral stability controller according to the MPC algorithm and designing the coordination variable L regulator.
- the vehicle system dynamics model is:
- the state vector control vector system matrix control matrix constant matrix is the first - order differential of the state vector
- the moment of inertia of f is the active front wheel steering angle, and ⁇ is the center of mass sideslip angle of the vehicle.
- step (1) in this embodiment establishes the vehicle system dynamics model as follows:
- the vehicle monorail model is shown in Figure 3. Assuming that the vehicle is traveling at a constant speed and does not consider the effects of vehicle suspension, steering system, air resistance, etc., the dynamics of the vehicle at this time can be expressed as:
- the state vector control vector system matrix control matrix constant matrix is the first - order differential of the state vector
- the moment of inertia of f is the active front wheel steering angle, and ⁇ is the center of mass sideslip angle of the vehicle.
- step (2) in this embodiment is to determine the 4WID-EV lateral stability control system model including active distribution optimization, as follows:
- the control quantity input to the system can be expressed as As shown in Figure 4, assuming that the controller working range at any time is jointly determined by AFS and DYC, when the control variable Under the action, the deviation of the system state quantity will pass through the intermediate state vector reaches its reference value.
- the active allocation optimization plan containing coordination variable L can be expressed as:
- the deviation of the system state quantity from the reference model is the side slip angle deviation of the center of mass, is the yaw angular velocity deviation, for The first-order differential of , coefficient matrix L is the coordination variable, coefficient matrix
- the reference model is:
- ⁇ is the front wheel steering angle
- ⁇ ref and r ref are the desired center of mass side slip angle and yaw angular velocity respectively.
- step (3) in this embodiment is to determine the reference model of the lateral stability control system, and the expression is as follows:
- ⁇ is the front wheel steering angle.
- ⁇ ref is small
- ⁇ ref ⁇ 0 is often taken in the study of LSC.
- lateral acceleration is often limited by the tire-road adhesion coefficient ⁇ .
- the lateral stability controller is:
- J is the cost function of the lateral stability control system
- the matrices Q and R are both constant positive definite matrices
- ⁇ is the weight coefficient
- T is the unit step time interval
- N p is the prediction step size
- X ref (t) are the reference value at time t and the state quantity of the kth prediction step respectively
- I is the unit matrix
- ⁇ U is the change value of the control quantity
- ⁇ U are the upper and lower limits of ⁇ U respectively
- ⁇ ⁇ and ⁇ U are both relaxation coefficients.
- the objective function is:
- J e is the cost function of hub motor torque distribution
- coefficient matrix ⁇ [1 1 -1 -1]b/(2R)
- R is the wheel radius
- b is the left and right wheel track
- U T [T lf T lr T rf T rr ] T
- the subscripts lf, lr, rr, rf represent the left front wheel, left rear wheel, right rear wheel, respectively.
- v ei and p T are both weight coefficients
- Q T and R T are weight matrices
- sat() is a saturation function.
- constraints of the objective function are:
- ⁇ U T are the maximum and minimum values of the increment ⁇ U T respectively
- T r is the total driving torque
- U Tmax is the maximum control input
- sign() is the sign function.
- step (4) in this embodiment is to construct a lateral stability controller based on the MPC algorithm, as follows:
- the optimal control problem of MPC can be expressed as making the vehicle's motion state track the expected value of the reference model while satisfying the I/O constraints.
- the corresponding objective function J can be expressed as:
- J is the cost function of LSC
- matrices Q and R are constant positive definite matrices
- ⁇ is the weight coefficient
- T is the unit step time interval
- N p is the prediction step size
- X ref (t) are the reference value at time t and the state quantity of the kth prediction step respectively
- I is the unit matrix
- ⁇ U is the change value of the control quantity
- ⁇ U are the upper and lower limits of ⁇ U respectively
- slack variable ⁇ ⁇ and ⁇ U are the relaxation coefficients.
- J e is the cost function of hub motor torque distribution
- coefficient matrix ⁇ [1 1 -1 -1]b/(2R)
- R is the wheel radius
- b is the left and right wheel track
- U T [T lf T lr T rf T rr ] T
- the subscripts lf, lr, rr, rf represent the left front wheel, left rear wheel, right rear wheel, respectively.
- p T is the weight coefficient
- Q T and R T are the weight matrices
- ⁇ U T is the maximum and minimum values of increment ⁇ U T
- T r is the total driving torque
- U Tmax is the maximum control input
- v ei is the weight coefficient
- Equation (6) is the discrete form of the distribution optimization scheme (2), in which the coefficient matrix changes with the change of the coordination variable L. That is, the ⁇ M(L) output by the upper-layer controller makes the motor torque distribution in the lower-layer control have multiple possibilities. , reasonable adjustment of the coordination variable L is expected to improve the overall working efficiency of the motor.
- the workflow of determining the regulator of the coordination variable based on the three-dimensional space surface includes:
- a two-dimensional plane is determined according to the three-dimensional space curved surface; the two-dimensional plane is the plane when the vertical axis of the three-dimensional space curved surface is zero; the coordinate axis X T and the coordinate axis Y T of the three-dimensional space curved surface are both hubs Motor torque, the coordinate axis Z E of the three-dimensional space surface is the motor efficiency;
- the torque constraints are: Among them, the hub motor torques T lf , T lr , T rr , and T rf are x 1 , y 1 , x 2 , and y 2 respectively, T r /2 is recorded as z * , and R ⁇ M/b is recorded as ⁇ z;
- the geometric relationship of the torque constraint determines the first line and the second line; the projections of the points on the first line and the second line in the two-dimensional plane on the X and Y coordinate axes are respectively the hub motor torque x 1 and y 1 , x 2 , y 2 ;
- the workflow is determined according to the first line, the second line, the three-dimensional space surface and the two-dimensional plane.
- the in-wheel motor generates additional yaw moment ⁇ M through torque distribution, and it is necessary to ensure that the generated total driving torque T r can overcome air resistance, rolling resistance, slope resistance, etc.
- the corresponding constraints are expressed as:
- R is the wheel radius
- T fi is the rolling resistance couple moment of each wheel
- ⁇ i is the rotation speed of each wheel.
- T r ′ T r +[T flf +T flr -(T frr +T frf )], If load transfer is not considered, T r ′ ⁇ T r .
- 4WID-EV uses the motor control unit to adjust the output torque of the wheel hub motor, thereby changing the longitudinal tire force to control the yaw movement of the car. Discussing the optimal planning problem shown in equation (10), the complexity of the optimal analysis of the overall efficiency of the motor increases significantly with the increase in the number of motors. In order to facilitate the discussion of the impact of coordination variable L on motor efficiency, equation (14) is abbreviated as
- the hub motor torques T lf , T lr , T rr , and T rf are recorded as x 1 , y 1 , x 2 , and y 2 respectively, T r /2 is recorded as z * , and R ⁇ M/b is recorded as ⁇ z.
- the X T Y T Z E three-dimensional surface S shown in Figure 6 is constructed in the three-dimensional Euclidean space to visually represent the overall changing trend of the torque and efficiency of the four wheel hub motors.
- the coordinate axes X T and Y T are the hub motor torque
- the longitudinal coordinate axis Z E is the motor efficiency.
- Equation (15) When the motor efficiency is zero (that is, on the XOY plane), the geometric relationship of Equation (15) is shown as the dotted line in Figure 6.
- the projections of the points on the dotted lines l 1 and l 2 in the XOY plane (black marked points M 1 and M 2 ) on the X and Y coordinate axes are the hub motor torques x 1 , y 1 , x 2 , and y 2 respectively.
- the functional relationship between the symmetrical center lines of the two dotted lines is
- the slope intercept z * is only related to the desired torque T r . It is not difficult to find that the slopes of the three dotted lines are k ⁇ -1, and the position of the dotted lines is determined by and only the intercepts z * - ⁇ z, z * , z * + ⁇ z. L actively adjusts ⁇ z, and the intercept of the dotted line corresponding to equation (15) will change accordingly (when the L value decreases, the
- the parametric surface S can be regarded as the distortion of the plane area D.
- the point coordinates (u, v) on the area D are recorded as the curve coordinates of the surface S.
- the parametric equation of the surface S can be expressed as
- (u, v) are the point coordinates in the plane D
- (x, y, z) are the point coordinates in the surface S.
- the vector equation form of surface S is
- the curvature of the constructed regular parametric surface S geometrically reflects the changing trend of the efficiency of the four wheel hub motors. Based on the Euler formula related to normal curvature, it can be seen that calculating the main direction and main curvature is the main means to understand the curvature of the surface at the current coordinate point. Solving the eigendirections and eigenvalues k 1 and k 2 of the Weinbaum map of the surface S can obtain the main direction and main curvature of the surface. Among them, the expressions of the average curvature H and Gauss curvature K of the surface generated based on k 1 and k 2 are respectively:
- the second-order differential of the functional relationship g(x) between efficiency and torque can partially reflect the basic shape of the surface at the coordinate point.
- the vector angle cos ⁇ e Z ,n> between the unit vector e Z and the unit normal vector n can reflect the opening orientation of the curved surface.
- e Z is the Z-axis unit vector
- n is the unit normal vector of the tangent plane ⁇ at the coordinate point
- H of the surface is:
- Corollary 2 The projection of coordinate points M 1 and M 2 on the surface S onto the XOY plane is basically distributed in the area near the 45° diagonal (see the gray shaded area in Figure 6).
- the workflow of the coordinated variable L regulator that improves the overall efficiency of the in-wheel motor is determined, as shown in Figures 7 and 8.
- is the slope threshold is the slope of the curve L
- this embodiment also provides an economical optimization strategy construction system for lateral stability control of electric vehicles, including:
- the dynamic model building module is used to build a vehicle system dynamics model based on the physical parameters of the vehicle traveling at a constant speed;
- a control system model building module for determining a lateral stability control system model and a reference model of a four-wheel independent drive electric vehicle with active distribution optimization based on the vehicle system dynamics model; the lateral stability control system model includes coordination variables;
- a controller determination module configured to construct a lateral stability controller with optimized allocation based on the lateral stability control system model and the reference model;
- a constraint determination module configured to establish an objective function of the economic saturation optimal planning and the constraint conditions of the objective function based on the lateral stability controller and with the optimization of the overall efficiency of the motor as the goal;
- a curved surface construction module for constructing a three-dimensional space curved surface based on the additional yaw moment output by the lateral stability controller and the coordination variable;
- a process determination module for determining the workflow of the regulator of the coordination variable based on the three-dimensional space surface
- An adjustment module is used to adjust the coordination variables in the objective function according to the work process to optimize the working efficiency of the motor.
- This embodiment also provides a computer-readable storage medium on which a computer program is stored.
- the computer program is executed by a processor, the lateral stability control for electric vehicles as described in any one of claims 1 to 8 is implemented. Steps in a method for building economical optimization strategies.
- the L regulator designed in the present invention can optimize the torque distribution of the 4WID-EV in-wheel motor in real time, ensuring the lateral stability of the vehicle while improving the overall efficiency of the in-wheel motor. Ultimately, the energy consumption and economy of electric vehicles will be improved, allowing electric vehicles to achieve a higher cruising range while driving safely.
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- Electric Propulsion And Braking For Vehicles (AREA)
Abstract
一种面向电动汽车横向稳定控制的经济型优化策略构建方法、系统及计算机可读存储介质，首先构建含主动分配优化的横向稳定控制系统模型，借助协调变量L实现对各部分有效工作区间的协调分配。其次，基于含主动分配优化的系统模型，在模型预测控制框架下设计横向稳定性控制器。其中，所设计的目标函数J使车辆的运动状态跟踪稳态时的期望值，目标函数J e用于扭矩分配。最后，考虑控制器输出的附加横摆力矩与协调变量L之间的映射关系，构建三维空间曲面；并分析协调变量L对轮毂电机整体效率的影响，确定协调变量L调节器的工作流程，以提高轮毂电机的整体效率。
Description
本申请要求于2022年06月16日提交中国专利局、申请号为202210682844.3、发明名称为“面向电动汽车横向稳定控制的经济型优化策略构建方法”的中国专利申请的优先权，其部分内容通过引用结合在本申请中。
本发明涉及电动汽车控制技术领域，特别是涉及一种面向电动汽车横向稳定控制的经济型优化策略构建方法、系统及计算机可读存储介质。
智能辅助驾驶技术有助于降低车辆的能耗、改善驾驶体验，已成为车辆控制技术领域中的研究热点。横向稳定性控制(Lateral stability control，LSC)系统是智能辅助驾驶的关键组成部分，其控制策略可归结为三类：
(1)直接横摆力矩控制(Direct yaw moment control，DYC)。
(2)主动前轮转向控制(Active front steering control，AFS)。
(3)AFS和DYC集成控制(AFS and DYC integrated control，AFS/DYC)。
目前，对LSC系统的研究大多都集中在上层控制器的设计和优化，较少涉及下层的转矩分配规律。
四轮独立驱动电动汽车(Four-wheel independent drive electric vehicle，4WID-EV)采用新的驱动结构，其轮毂电机可通过控制器进行独立控制。近年来，出现了多种基于AFS/DYC集成控制的级联控制结构，但AFS和DYC部分的有效工作区间难以协调。电动化为解决传统车辆带来的环境污染问题提供了新的方向，但电动汽车的发展严重受续航里程较短等问题制约。考虑到轮毂电机的扭矩分配在改善电机整体效率方面具有较大的潜能，一种能够实现对轮毂电机扭矩的合理分配的经济型的优化策略亟待出现。
发明内容
为了克服现有技术的不足，本发明的目的是提供一种面向电动汽车横向稳定控制的经济型优化策略构建方法及系统。
为实现上述目的，本发明提供了如下方案：
一种面向电动汽车横向稳定控制的经济型优化策略构建方法，包括：
根据车辆在匀速行驶下的物理参数构建车辆系统动力学模型；
根据所述车辆系统动力学模型确定含主动分配优化的四轮独立驱动电动汽车的横向稳定控制系统模型和参考模型；所述横向稳定控制系统模型包括协调变量；
根据所述横向稳定控制系统模型和所述参考模型构建带优化分配的横向稳定性控制器；
根据所述横向稳定性控制器，以电机整体效率最优为目标建立经济饱和最优规划的目标函数及所述目标函数的约束条件；
根据所述横向稳定性控制器输出的附加横摆力矩和所述协调变量构建三维空间曲面；
基于所述三维空间曲面确定所述协调变量的调节器的工作流程；
根据所述工作流程对所述目标函数中的协调变量进行调整，以使电机的工作效率达到最优。
优选地，所述车辆系统动力学模型为：
其中，状态向量
控制向量
系统矩阵
控制矩阵
常数矩阵
为状态向量X的一阶微分，m为整车质量，v
y为侧向速度，v
x为纵向速度，r为横摆角速度，ΔM为附加横摆力矩，I
z为车辆质心处绕z轴的转动惯量，l
f、l
r分别为质心到前、后轮中心的距离，C
f、C
r分别为前、后轮的 侧偏刚度，δ
f为驾驶员输入的前轮转向角，Δδ
f为主动前轮转向角，β为车辆的质心侧偏角。
优选地，所述横向稳定控制系统模型为：
其中，系统状态量与参考模型的偏差
为质心侧偏角偏差，
为横摆角速度偏差，
为
的一阶微分，系数矩阵
L为所述协调变量，系数矩阵
优选地，所述参考模型为：
其中，δ为前轮转向角，β
ref和r
ref分别为期望的质心侧偏角及横摆角速度。
优选地，所述横向稳定性控制器为：
其中，J为横向稳定性控制系统的代价函数，矩阵Q、R均为常值正定矩阵，ρ为权重系数，T为单位步长时间间隔，N
p为预测步长，X
ref(t)、
分别为t时刻的参考值和第k个预测步长的状态量，I为单位矩阵，ΔU为控制量的变化值，
Δ
U分别为ΔU的上下限，
为松弛变量，σ
δ、σ
U均为松弛系数。
优选地，所述目标函数为：
其中，J
e为轮毂电机扭矩分配的代价函数，系数矩阵Λ＝[1 1 -1 -1]b/(2R)，R为车轮半径，b为左右车轮轮距，控制量U
T＝[T
lf T
lr T
rf T
rr]
T，T
i(i＝lf、lr、rr、rf)为电机扭矩，下标lf、lr、rr、rf分别代表左前轮、左后轮、右后轮、右前轮，v
ei和p
T均为权重系数，Q
T、R
T均为权重矩阵，sat()为饱和函数。
优选地，所述目标函数的约束条件为：
[1 1 1 1]U
T＝T
r；
其中，
Δ
U
T分别为增量ΔU
T的最大值和最小值，T
r为总驱动扭矩，U
Tmax为最大的控制输入，sign()为符号函数。
优选地，所述基于所述三维空间曲面确定所述协调变量的调节器的工作流程，包括：
根据所述三维空间曲面确定二维平面；所述二维平面是在所述三维空间曲面的纵轴为零时的平面；所述三维空间曲面的坐标轴X
T、坐标轴Y
T均为轮毂电机扭矩，所述三维空间曲面的坐标轴Z
E为电机效率；
构建轮毂电机的扭矩约束；所述扭矩约束为：
其中，轮毂电机扭矩T
lf、T
lr、T
rr、T
rf分别为x
1、y
1、x
2、y
2，T
r/2记为z
*，RΔM/b记为Δz；
将所述扭矩约束的几何关系确定第一线条和第二线条；所述二维平面内第一线条和第二线条上的点在X和Y坐标轴的投影分别为轮毂电机扭矩x
1、y
1、x
2、y
2；
基于Gauss曲面理论分析，根据所述第一线条、所述第二线条、所述三维空间曲面和所述二维平面确定所述工作流程。
一种面向电动汽车横向稳定控制的经济型优化策略构建系统，包括：
动力学模型构建模块，用于根据车辆在匀速行驶下的物理参数构建车辆系统动力学模型；
控制系统模型构建模块，用于根据所述车辆系统动力学模型确定含主动分配优化的四轮独立驱动电动汽车的横向稳定控制系统模型和参考模型；所述横向稳定控制系统模型包括协调变量；
控制器确定模块，用于根据所述横向稳定控制系统模型和所述参考模型构建带优化分配的横向稳定性控制器；
约束条件确定模块，用于根据所述横向稳定性控制器，以电机整体效率最优为目标建立经济饱和最优规划的目标函数及所述目标函数的约束条件；
曲面构建模块，用于根据所述横向稳定性控制器输出的附加横摆力矩和所述协调变量构建三维空间曲面；
流程确定模块，用于基于所述三维空间曲面确定所述协调变量的调节器的工作流程；
调节模块，用于根据所述工作流程对所述目标函数中的协调变量进行调整，以使电机的工作效率达到最优。
一种计算机可读存储介质，其上存储有计算机程序，所述计算机程序被处理器执行时实现如权利要求1到8中任一项记载的面向电动汽车横向稳定控制的经济型优化策略构建方法中的步骤。
根据本发明提供的具体实施例，本发明公开了以下技术效果：
本发明提供了一种面向电动汽车横向稳定控制的经济型优化策略构建方法、系统及计算机可读存储介质，首先构建含主动分配优化的横向稳定控制系 统模型，借助协调变量L实现对各部分有效工作区间的协调分配。其次，基于含主动分配优化的系统模型，在模型预测控制框架下设计横向稳定性控制器。其中，所设计的目标函数J使车辆的运动状态跟踪稳态时的期望值，目标函数J
e用于扭矩分配。最后，考虑控制器输出的附加横摆力矩与协调变量L之间的映射关系，构建三维空间曲面；并在具体实施例中利用Gauss曲面理论分析协调变量L对轮毂电机整体效率的影响，确定协调变量L调节器的工作流程，以提高轮毂电机的整体效率。
说明书附图
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动性的前提下，还可以根据这些附图获得其他的附图。
图1为本发明提供的实施例中的经济型优化策略构建方法流程图；
图2为本发明提供的实施例中的轮毂电机经济型优化策略示意图；
图3为本发明提供的实施例中的单轨车辆模型示意图；
图4为本发明提供的实施例中的主动分配优化方案示意图；
图5为本发明提供的实施例中的车轮转动平衡分析示意图；
图6为本发明提供的实施例中的X
TY
TZ
Z三维空间曲面S示意图；
图7为本发明提供的实施例中的协调变量L调节器的总工作流程；
图8为本发明提供的实施例中的协调变量L调节器的子工作流程。
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
在本文中提及“实施例”意味着，结合实施例描述的特定特征、结构或特性 可以包含在本申请的至少一个实施例中。在说明书中的各个位置出现该短语并不一定均是指相同的实施例，也不是与其它实施例互斥的独立的或备选的实施例。本领域技术人员显式地和隐式地理解的是，本文所描述的实施例可以与其它实施例相结合。
本申请的说明书和权利要求书及所述附图中的术语“第一”、“第二”、“第三”和“第四”等是用于区别不同对象，而不是用于描述特定顺序。此外，术语“包括”和“具有”以及它们任何变形，意图在于覆盖不排他的包含。例如包含了一系列步骤、过程、方法等没有限定于已列出的步骤，而是可选地还包括没有列出的步骤，或可选地还包括对于这些过程、方法、产品或设备固有的其它步骤元。
本发明的目的是提供一种面向电动汽车横向稳定控制的经济型优化策略构建方法、系统及计算机可读存储介质，能够提高轮毂电机的整体效率。
为使本发明的上述目的、特征和优点能够更加明显易懂，下面结合附图和具体实施方式对本发明作进一步详细的说明。
图1为本发明提供的实施例中的经济型优化策略构建方法流程图，如图1所示，本发明提供了一种面向电动汽车横向稳定控制的经济型优化策略构建方法，包括：
步骤100：根据车辆在匀速行驶下的物理参数构建车辆系统动力学模型；
步骤200：根据所述车辆系统动力学模型确定含主动分配优化的四轮独立驱动电动汽车的横向稳定控制系统模型和参考模型；所述横向稳定控制系统模型包括协调变量；
步骤300：根据所述横向稳定控制系统模型和所述参考模型构建带优化分配的横向稳定性控制器；
步骤400：根据所述横向稳定性控制器，以电机整体效率最优为目标建立经济饱和最优规划的目标函数及所述目标函数的约束条件；
步骤500：根据所述横向稳定性控制器输出的附加横摆力矩和所述协调变量构建三维空间曲面；
步骤600：基于所述三维空间曲面确定所述协调变量的调节器的工作流程；
步骤700：根据所述工作流程对所述目标函数中的协调变量进行调整，以使电机的工作效率达到最优。
图2为本发明提供的实施例中的轮毂电机经济型优化策略示意图，如图2所示，本实施例中包括了五个步骤，分别为建立车辆系统动力学模型、确定含主动分配优化的4WID-EV横向稳定控制系统模型、确定横向稳定控制系统的参考模型、根据MPC算法构建横向稳定性控制器和设计协调变量L调节器。
优选地，所述车辆系统动力学模型为：
其中，状态向量
控制向量
系统矩阵
控制矩阵
常数矩阵
为状态向量X的一阶微分，m为整车质量，v
y为侧向速度，v
x为纵向速度，r为横摆角速度，ΔM为附加横摆力矩，I
z为车辆质心处绕z轴的转动惯量，l
f、l
r分别为质心到前、后轮中心的距离，C
f、C
r分别为前、后轮的侧偏刚度，δ
f为驾驶员输入的前轮转向角，Δδ
f为主动前轮转向角，β为车辆的质心侧偏角。
具体的，本实施例中的步骤(1)建立车辆系统动力学模型如下：
车辆单轨模型如图3所示，假设车辆匀速行驶且不考虑车辆悬架、转向系统及空气阻力等的影响，此时车辆的动态可表示为：
其中，状态向量
控制向量
系统矩阵
控制矩阵
常数矩阵
为状态向量X的一阶微分，m为整车质量，v
y为侧向速度，v
x为纵向速度，r为横摆角速度，ΔM为附加横摆力矩，I
z为车辆质心处绕z轴的转动惯量，l
f、l
r分别为质心到前、后轮中心的距离，C
f、C
r分别为前、后轮的侧偏刚度，δ
f为驾驶员输入的前轮转向角，Δδ
f为主动前轮转向角，β为车辆的质心侧偏角。
进一步地，本实施例中步骤(2)为确定含主动分配优化的4WID-EV横向稳定控制系统模型，具体如下：
若将4WID-EV横向稳定控制系统的工作区间划分为AFS和DYC两部分并考虑中间状态向量
(其中L为协调变量)，则系统输入的控制量可表示为
如图4所示，假设任意时刻的控制器工作区间均由AFS和DYC共同确定，在控制量
作用下，系统状态量的偏差
将通过中间状态向量
达到其参考值。此时，含协调变量L的主动分配优化方案可表示为：
其中，系统状态量与参考模型的偏差
为质心侧偏角偏差，
为横摆角速度偏差，
为
的一阶微分，系数矩阵
L为所 述协调变量，系数矩阵
优选地，所述参考模型为：
其中，δ为前轮转向角，β
ref和r
ref分别为期望的质心侧偏角及横摆角速度。
具体的，本实施例中步骤(3)为确定横向稳定控制系统的参考模型，表达式如下：
其中，δ为前轮转向角。考虑到β
ref较小，对LSC的研究中常取β
ref≈0。此外，侧向加速度常受限于轮胎-路面附着系数μ。当侧向加速度a
y≤μg时(g为重力加速度)，r
ref需满足条件：
优选地，所述横向稳定性控制器为：
其中，J为横向稳定性控制系统的代价函数，矩阵Q、R均为常值正定矩 阵，ρ为权重系数，T为单位步长时间间隔，N
p为预测步长，X
ref(t)、
分别为t时刻的参考值和第k个预测步长的状态量，I为单位矩阵，ΔU为控制量的变化值，
Δ
U分别为ΔU的上下限，
为松弛变量，σ
δ、σ
U均为松弛系数。
优选地，所述目标函数为：
其中，J
e为轮毂电机扭矩分配的代价函数，系数矩阵Λ＝[1 1 -1 -1]b/(2R)，R为车轮半径，b为左右车轮轮距，控制量U
T＝[T
lf T
lr T
rf T
rr]
T，T
i(i＝lf、lr、rr、rf)为电机扭矩，下标lf、lr、rr、rf分别代表左前轮、左后轮、右后轮、右前轮，v
ei和p
T均为权重系数，Q
T、R
T均为权重矩阵，sat()为饱和函数。
优选地，所述目标函数的约束条件为：
[1 1 1 1]U
T＝T
r；
其中，
Δ
U
T分别为增量ΔU
T的最大值和最小值，T
r为总驱动扭矩，U
Tmax为最大的控制输入，sign()为符号函数。
具体的，本实施例中步骤(4)为根据MPC算法构建横向稳定性控制器，具体如下：
MPC的最优控制问题可表述为在满足I/O约束的条件下，使车辆的运动状态跟踪参考模型的期望值，相应的目标函数J可表示为：
约束条件：
其中，J为LSC的代价函数，矩阵Q、R为常值正定矩阵，ρ为权重系数，T为单位步长时间间隔，N
p为预测步长，X
ref(t)、
分别为t时刻的参考值和第k个预测步长的状态量，I为单位矩阵，ΔU为控制量的变化值，
Δ
U分别为ΔU的上下限，
为松弛变量，σ
δ、σ
U为松弛系数。由于轮毂电机的效率e
i与电机扭矩T
i以及转速s相关，即e
i＝g(s,T
i)，电机的整体效率会随控制器配置的各独立驱动轮毂电机输出扭矩的变化而变化。为使轮毂电机的整体效率∑e
i达到最大，设计以电机整体效率最优为目标的经济型饱和最优规划问题：
约束条件：
[1 1 1 1]U
T＝T
r (11)
其中，J
e为轮毂电机扭矩分配的代价函数，系数矩阵Λ＝[1 1 -1 -1]b/(2R)，R为车轮半径，b为左右车轮轮距，控制量U
T＝[T
lf T
lr T
rf T
rr]
T，T
i(i＝lf、lr、rr、rf)为电机扭矩，下标lf、lr、rr、rf分别代表左前轮、左后轮、右后轮、右前轮，p
T为权重系数，Q
T、R
T为权重矩阵，
Δ
U
T为增量ΔU
T的最大值和最小值，T
r为总驱动扭矩，U
Tmax为最大的控制输入，v
ei为权重系数。若将各轮毂电机视为同等重要，可取Q
T＝q
TI、R
T＝r
TI，q
T和r
T皆为正实数。
式(6)为分配优化方案(2)的离散形式，其中的系数矩阵随协调变量L的变化而变化，即上层控制器输出的ΔM(L)使得下层控制中的电机扭矩分配具有多种可能，合理调整协调变量L有望提升电机整体的工作效率。
优选地，所述基于所述三维空间曲面确定所述协调变量的调节器的工作流程，包括：
根据所述三维空间曲面确定二维平面；所述二维平面是在所述三维空间曲面的纵轴为零时的平面；所述三维空间曲面的坐标轴X
T、坐标轴Y
T均为轮毂电机扭矩，所述三维空间曲面的坐标轴Z
E为电机效率；
构建轮毂电机的扭矩约束；所述扭矩约束为：
其中，轮毂电机扭矩T
lf、T
lr、T
rr、T
rf分别为x
1、y
1、x
2、y
2，T
r/2记为z
*，RΔM/b记为Δz；
将所述扭矩约束的几何关系确定第一线条和第二线条；所述二维平面内第一线条和第二线条上的点在X和Y坐标轴的投影分别为轮毂电机扭矩x
1、y
1、x
2、y
2；
基于Gauss曲面理论分析，根据所述第一线条、所述第二线条、所述三维空间曲面和所述二维平面确定所述工作流程。
具体的，本实施例中最后一个步骤为设计协调变量L调节器，假设车辆处于匀速行驶状态，即加速度a＝0，制动扭矩T
bi＝0，其中i＝lf、lr、rr和rf分别表示左前、左后、右后和右前车轮。轮毂电机通过扭矩分配生成附加横摆力矩ΔM，且需保证生成的总驱动扭矩T
r能够克服空气阻力、滚动阻力和坡度阻力等，相应的约束条件表示为：
其中，b为左右车轮轮距，F
i为各个车轮的纵向力。车轮的转动平衡(忽略车轮打滑)如图5所示，其动态平衡方程为：
其中，R为车轮半径，T
fi为各个车轮滚动阻力偶矩，ω
i为各个车轮转速。若
将式(13)代入(12)，得：
其中，T
r′＝T
r+[T
flf+T
flr-(T
frr+T
frf)]，
若不考虑载荷转移，T
r′≈T
r。4WID-EV利用电机控制单元调整轮毂电机的输出扭矩，进而改变纵向轮胎力以控制汽车的横摆运动。讨论式(10)所示的最优规划问 题，电机整体效率最优分析的复杂程度随电机数目的增加显著上升。为便于讨论协调变量L对电机效率的影响，将式(14)简记为
其中，轮毂电机扭矩T
lf、T
lr、T
rr、T
rf分别记为x
1、y
1、x
2、y
2，T
r/2记为z
*，RΔM/b记为Δz。为便于分析，在三维欧氏空间中构建如图6所示的X
TY
TZ
E三维曲面S，以直观表征四个轮毂电机的扭矩和效率整体变化趋势。其中，坐标轴X
T、Y
T为轮毂电机扭矩，纵向坐标轴Z
E为电机效率。当电机效率为零时(即在XOY平面上)，式(15)的几何关系如图6中虚线所示。XOY平面内虚线l
1、l
2上的点(黑色标记点M
1、M
2)在X和Y坐标轴的投影分别为轮毂电机扭矩x
1、y
1、x
2、y
2。此外，两条虚线的对称中心线的函数关系为
y＝-x+z
* (16)
其中，斜截距z
*仅与期望扭矩T
r相关。不难发现，三条虚线的斜率k≡-1，虚线的位置由且仅由截距z
*-Δz、z
*、z
*+Δz决定。L对Δz进行主动调整，式(15)对应的虚线截距会出现相应的改变(L值减小时，|Δz|值增大，远离对称中心线；L值增大时，|Δz|值减小，靠近对称中心线)。需要注意的是，相较于传统的AFS/DYC集成控制策略，调整L可以使图6中点M
1和M
2的移动情况由一条直线(见图6中虚线)拓展到二维的XOY平面。利用Gauss曲面理论，进行如下分析：
参数曲面S可以视作平面区域D的扭曲变形，区域D上的点坐标(u,v)记为曲面S的曲纹坐标，曲面S的参数方程可以表示为
其中，(u,v)为平面D中的点坐标，(x,y,z)为曲面S中的点坐标。曲面S的向量方程形式为
r＝(u,v,-g(0)+g(u)+g(v)) (18)
其中，向量r对变量u，v的偏导分别为
由于
曲面S为正则参数曲面。
所构造的正则参数曲面S的弯曲程度从几何上反映了四个轮毂电机效率的变化趋势。基于法曲率相关的Euler公式可知，计算主方向和主曲率是了解曲面在当前坐标点处弯曲情况的主要手段。求解曲面S的Weingarten映射的特征方向和特征值k
1、k
2能够获得曲面的主方向和主曲率。其中，基于k
1、k
2生成的曲面的平均曲率H和Gauss曲率K表达式分别为：
其中，
显然，Gauss曲率K的正负性由
决定。当
时，K>0，曲面S在点(x(u,v),y(u,v),z(u,v))的Dupin标形为椭圆抛物线，近似曲面为椭圆抛物面(见图6中的区域I和区域IV)；当
时，K<0，曲面S在点(x(u,v),y(u,v),z(u,v))的Dupin标形为两对共轭双曲线，近似曲面为双曲抛物面(见图6中的区域II和区域III)；当
时，K＝0，该点为平点。
由上可知，效率和扭矩的函数关系g(x)的二阶微分能够部分反映坐标点处曲面的基本形状。此外，单位向量e
Z和单位法向量n的向量夹角cos<e
Z,n>能够反映曲面开口朝向。当M
1、M
2都符合
及cos<e
Z,n>∈[0,π/2)时，M
1、M
2位于的区域I内，增大协调变量L值会使Δz值变小，进而点M
1、M
2靠近中心线l，电机的整体效率增大。同理，当点M
1、M
2都符合
且cos<e
Z,n>∈[π/2,π]时，减小协调变量L会使效率增大。当M
1、M
2都符合
且仅有M
1或者M
2符合cos<e
Z,n>∈[0,π/2)时，坐标点分别位于区域I和区域IV。平均曲率H能够表征点坐标处曲面的弯曲程度。H
1>H
2，则M
1点处曲面的弯曲程度更大，M
1的移动对整体效率的变化起决定性作用。若
时令协调变量L值增大，
时令协调变量L值减小，则M
1点向上移动，电机总体效率增大。H
1<H
2时，可进行同理分析。进而有以下推论：
推论1：假设轮毂电机转速不变，电机效率-扭矩的函数关系近似为e＝g(x)， 且连续函数g(x)二次可微，那么构造的曲面S为正则参数曲面。相应地，L值的调整能够使得轮毂电机的平均效率增大的充分条件为：
(1)点M
1、M
2都符合
且cos<e
Z,n>∈[0,π/2)时，协调变量L需要增大；
(2)点M
1、M
2都符合
且cos<e
Z,n>∈[π/2,π]时，协调变量L需要减小；
(3)M
1、M
2都符合
且仅有M
1符合cos<e
Z,n>∈[0,π/2)时，判断H值：(a)H
1>H
2，当
时，协调变量L需要增大；当
时，协调变量L需要减小；(b)H
1<H
2，当
时，协调变量L需要增大；当
时，协调变量L需要减小。
其中，e
Z为Z轴单位向量，n为坐标点处切平面Π的单位法向量，曲面平均曲率H的具体表达式为
备注1：(3)中若仅有M
2符合cos<e
Z,n>∈[0,π/2)，可进行类似分析。
曲面S上，式(10)所示的最优规划问题中轮毂电机的扭矩分配由点M
1、M
2坐标表征。其中，
和式(14)很大程度上限制了点M
1、M
2的分布，具体而言：
其中，
将式(14)代入式(22)，可得：
其中，当且仅当Δm
1＝Δm
2＝0时，等号成立。若使式(10)中的J
e达到最小，
应尽可能地小，即存在一个较小的常数M≥0，使Δm
1≤M、Δm
2≤M。进一步，有以下推论：
推论2：曲面S上坐标点M
1、M
2在XOY平面上的投影基本上分布于45°对角线附近区域(见图6中的灰色阴影区域)。
进一步，基于前述的推论1和推论2，确定改善轮毂电机整体效率的协调变量L调节器的工作流程，见图7和图8所示。其中，
为斜率阈值，
为曲线L的斜率，K＝-1、K＝0和K＝1分别表征L的三种变化趋势(包括减小、不变和增大)。当满足如下条件时：
近似认为曲面S在坐标点M
1、M
2处变化极小。
对应上述方法，本实施例还提供了一种面向电动汽车横向稳定控制的经济型优化策略构建系统，包括：
动力学模型构建模块，用于根据车辆在匀速行驶下的物理参数构建车辆系统动力学模型；
控制系统模型构建模块，用于根据所述车辆系统动力学模型确定含主动分配优化的四轮独立驱动电动汽车的横向稳定控制系统模型和参考模型；所述横向稳定控制系统模型包括协调变量；
控制器确定模块，用于根据所述横向稳定控制系统模型和所述参考模型构建带优化分配的横向稳定性控制器；
约束条件确定模块，用于根据所述横向稳定性控制器，以电机整体效率最优为目标建立经济饱和最优规划的目标函数及所述目标函数的约束条件；
曲面构建模块，用于根据所述横向稳定性控制器输出的附加横摆力矩和所述协调变量构建三维空间曲面；
流程确定模块，用于基于所述三维空间曲面确定所述协调变量的调节器的工作流程；
调节模块，用于根据所述工作流程对所述目标函数中的协调变量进行调整，以使电机的工作效率达到最优。
本实施例还提供了一种计算机可读存储介质，其上存储有计算机程序，所述计算机程序被处理器执行时实现如权利要求1到8中任一项记载的面向电动汽车横向稳定控制的经济型优化策略构建方法中的步骤。
本发明的有益效果如下：
(1)本发明设计的L调节器能够实时优化4WID-EV轮毂电机的扭矩分配，在保证车辆横向稳定的同时提升轮毂电机的整体效率。最终实现电动汽车能耗经济性的改善，使电动汽车在安全行驶的前提下获得更高的续航里程。
(2)利用本发明构建的X
TY
TZ
Z三维空间曲面S，更易于分析4WID-EV轮毂电机群组的整体效率；考虑到电机输出扭矩的饱和特性，基于MPC框架设计的横向稳定性控制器更适用于采用电机驱动的车辆系统。
本说明书中各个实施例采用递进的方式描述，每个实施例重点说明的都是与其他实施例的不同之处，各个实施例之间相同相似部分互相参见即可。对于实施例公开的方法而言，由于其与实施例公开的装置相对应，所以描述的比较简单，相关之处参见装置部分说明即可。
本文中应用了具体个例对本发明的原理及实施方式进行了阐述，以上实施例的说明只是用于帮助理解本发明的方法及其核心思想；同时，对于本领域的一般技术人员，依据本发明的思想，在具体实施方式及应用范围上均会有改变之处。综上所述，本说明书内容不应理解为对本发明的限制。
Claims (10)
- 一种面向电动汽车横向稳定控制的经济型优化策略构建方法，其特征在于，包括：根据车辆在匀速行驶下的物理参数构建车辆系统动力学模型；根据所述车辆系统动力学模型确定含主动分配优化的四轮独立驱动电动汽车的横向稳定控制系统模型和参考模型；所述横向稳定控制系统模型包括协调变量；根据所述横向稳定控制系统模型和所述参考模型构建带优化分配的横向稳定性控制器；根据所述横向稳定性控制器，以电机整体效率最优为目标建立经济饱和最优规划的目标函数及所述目标函数的约束条件；根据所述横向稳定性控制器输出的附加横摆力矩和所述协调变量构建三维空间曲面；基于所述三维空间曲面确定所述协调变量的调节器的工作流程；根据所述工作流程对所述目标函数中的协调变量进行调整，以使电机的工作效率达到最优。
- 根据权利要求1所述的面向电动汽车横向稳定控制的经济型优化策略构建方法，其特征在于，所述车辆系统动力学模型为：
其中，状态向量控制向量
系统矩阵
控制矩阵
常数矩阵
为状态向量X的一阶微分，m为整车质量，v y为侧向速度，v x 为纵向速度，r为横摆角速度，ΔM为附加横摆力矩，I z为车辆质心处绕z轴的转动惯量，l f、l r分别为质心到前、后轮中心的距离，C f、C r分别为前、后轮的侧偏刚度，δ f为驾驶员输入的前轮转向角，Δδ f为主动前轮转向角，β为车辆的质心侧偏角。
- 根据权利要求2所述的面向电动汽车横向稳定控制的经济型优化策略构建方法，其特征在于，所述横向稳定控制系统模型为：
其中，系统状态量与参考模型的偏差
为质心侧偏角偏差，
为横摆角速度偏差，
为
的一阶微分，系数矩阵
L为所述协调变量，系数矩阵
- 根据权利要求2所述的面向电动汽车横向稳定控制的经济型优化策略构建方法，其特征在于，所述参考模型为：
其中，δ为前轮转向角，β ref和r ref分别为期望的质心侧偏角及横摆角速度。 - 根据权利要求2所述的面向电动汽车横向稳定控制的经济型优化策略构建方法，其特征在于，所述横向稳定性控制器为：
其中，J为横向稳定性控制系统的代价函数，矩阵Q、R均为常值正定矩阵，ρ为权重系数，T为单位步长时间间隔，N p为预测步长，X ref(t)、分别为t时刻的参考值和第k个预测步长的状态量，I为单位矩阵，ΔU为控制量的变化值，
Δ U分别为ΔU的上下限，
为松弛变量，σ δ、σ U均为松弛系数。
- 根据权利要求2所述的面向电动汽车横向稳定控制的经济型优化策略构建方法，其特征在于，所述目标函数为：
其中，J e为轮毂电机扭矩分配的代价函数，系数矩阵Λ＝[1 1 -1 -1]b/(2R)，R为车轮半径，b为左右车轮轮距，控制量U T＝[T lf T lr T rf T rr] T，T i(i＝lf、lr、rr、rf)为电机扭矩，下标lf、lr、rr、rf分别代表左前轮、左后轮、右后轮、右前轮，v ei和p T均为权重系数，Q T、R T均为权重矩阵，sat()为饱和函数。 - 根据权利要求6所述的面向电动汽车横向稳定控制的经济型优化策略构建方法，其特征在于，所述目标函数的约束条件为：
[1 1 1 1]U T＝T r；
其中，Δ U T分别为增量ΔU T的最大值和最小值，T r为总驱动扭矩，U Tmax为最大的控制输入，sign()为符号函数。
- 根据权利要求2所述的面向电动汽车横向稳定控制的经济型优化策略构建方法，其特征在于，所述基于所述三维空间曲面确定所述协调变量的调节 器的工作流程，包括：根据所述三维空间曲面确定二维平面；所述二维平面是在所述三维空间曲面的纵轴为零时的平面；所述三维空间曲面的坐标轴X T、坐标轴Y T均为轮毂电机扭矩，所述三维空间曲面的坐标轴Z E为电机效率；构建轮毂电机的扭矩约束；所述扭矩约束为：其中，轮毂电机扭矩T lf、T lr、T rr、T rf分别为x 1、y 1、x 2、y 2，T r/2记为z *，RΔM/b记为Δz；
将所述扭矩约束的几何关系确定第一线条和第二线条；所述二维平面内第一线条和第二线条上的点在X和Y坐标轴的投影分别为轮毂电机扭矩x 1、y 1、x 2、y 2；基于Gauss曲面理论分析，根据所述第一线条、所述第二线条、所述三维空间曲面和所述二维平面确定所述工作流程。 - 一种面向电动汽车横向稳定控制的经济型优化策略构建系统，其特征在于，包括：动力学模型构建模块，用于根据车辆在匀速行驶下的物理参数构建车辆系统动力学模型；控制系统模型构建模块，用于根据所述车辆系统动力学模型确定含主动分配优化的四轮独立驱动电动汽车的横向稳定控制系统模型和参考模型；所述横向稳定控制系统模型包括协调变量；控制器确定模块，用于根据所述横向稳定控制系统模型和所述参考模型构建带优化分配的横向稳定性控制器；约束条件确定模块，用于根据所述横向稳定性控制器，以电机整体效率最优为目标建立经济饱和最优规划的目标函数及所述目标函数的约束条件；曲面构建模块，用于根据所述横向稳定性控制器输出的附加横摆力矩和所述协调变量构建三维空间曲面；流程确定模块，用于基于所述三维空间曲面确定所述协调变量的调节器的 工作流程；调节模块，用于根据所述工作流程对所述目标函数中的协调变量进行调整，以使电机的工作效率达到最优。
- 一种计算机可读存储介质，其上存储有计算机程序，其特征在于，所述计算机程序被处理器执行时实现如权利要求1到8中任一项记载的面向电动汽车横向稳定控制的经济型优化策略构建方法中的步骤。
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