A path tracking control method for a distributed drive electric vehicle

Abstract

The application discloses a path tracking control method, system and device for a distributed drive electric vehicle, and relates to the technical field of vehicle chassis control. The application comprises receiving vehicle parameter information, constructing a vehicle dynamics model and a magic formula tire model according to the vehicle parameter information, and constructing a vehicle-road system model for trajectory tracking control based on the vehicle dynamics model and the magic formula tire model. The application comprehensively considers various uncertain disturbances in the vehicle driving process, designs a minimum-maximum robust model predictive control architecture, and enhances the robustness of the path tracking control system; meanwhile, an online observer based on a minimum robust positive invariance set is designed, real-time and accurate acquisition of key vehicle parameters is realized without increasing hardware cost, and a cooperative control method for active front wheel steering and torque vectoring is designed, so that coordinated operation between a steering system and a four-wheel drive system is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vehicle chassis control, in particular to a path tracking control method for a distributed drive electric vehicle. BACKGROUND

[0002] Thanks to the high integration design of the hub motor, the distributed drive electric vehicle can control the single wheel independently, thereby significantly improving the dynamic control performance of the vehicle. However, due to the existence of many uncertainties of the vehicle driving road environment, the vehicle internal state parameters, and the changeable driving tasks, the vehicle path tracking control system has many disturbances, which seriously affects the safety and stability of the vehicle driving. Therefore, it is of great significance to establish a robust path tracking control architecture for the distributed drive electric vehicle to improve the safety of the vehicle driving. Especially considering that there may be functional overlap and control interference between the active steering system and the four-wheel torque control system of the distributed drive electric vehicle, the uncertainties and disturbances in the system may further amplify the problem. SUMMARY

[0003] The present application aims to provide a path tracking control method, system and device for a distributed drive electric vehicle, effectively solving various uncertainties and disturbances in the vehicle driving process, coordinating the operation between the steering system and the four-wheel drive system, and enhancing the stability and tracking accuracy of the distributed drive electric vehicle under different driving conditions.

[0004] To achieve the above-mentioned purpose, the present application provides the following technical scheme: a path tracking control method for a distributed drive electric vehicle, comprising the following steps:

[0005] Receiving vehicle parameter information, constructing a vehicle dynamics model and a magic formula tire model according to the vehicle parameter information, and constructing a vehicle-road system model for trajectory tracking control based on the vehicle dynamics model and the magic formula tire model, thereby constructing an LPV system equation;

[0006] According to the obtained LPV system equation, an online observer is designed based on the robust positive invariant set, which is used to obtain the vehicle mass center side slip angle data in real time, and the conservatism is reduced by online updating the minimum robust positive invariant set;

[0007] According to the designed online observer, a minimum-maximum robust predictive control model based on the online observer is constructed by using linear matrix inequality;

[0008] The compound differential equation is constituted based on the vehicle dynamics equation and the magic formula tire model, the β-γ phase trajectory is drawn according to the compound differential equation, the predetermined longitudinal velocity, the front wheel steering angle and the road surface friction coefficient, the stable point and the saddle point are calculated by searching the balance solution, and the vehicle parameters in different working conditions are obtained by changing the vehicle longitudinal velocity, the front wheel steering angle and the road surface friction coefficient, and the vehicle stability domain boundary is obtained through parameter fitting;

[0009] The design optimization objective function is designed, the optimal moment distribution strategy objective function is solved according to the obtained expected additional yaw moment and the longitudinal expected vehicle speed, so as to optimize the four-wheel torque distribution of the four-wheel independent drive electric vehicle.

[0010] Further, the vehicle parameter information includes the front wheel steering angle, the longitudinal velocity, the mass center side slip angle, the yaw angular velocity, the additional yaw moment and the tire lateral force, and the vehicle parameter information is collected by the steering angle sensor, the gyroscope and the tire six-component force tester respectively.

[0011] Further, the vehicle dynamics model and the magic formula tire model are respectively constructed according to the vehicle parameter information, and specifically as follows: (31) focusing on the trajectory tracking control of the distributed drive electric vehicle, the vehicle dynamics equation is described as follows:

[0012]

[0013] In the formula, m is the vehicle mass, I z is the yaw moment of inertia, l f and l r are the lengths from the vehicle mass center to the front and rear axles respectively, v x is the vehicle longitudinal velocity, β and γ are the mass center side slip angle and the yaw angular velocity respectively, δ f is the front wheel steering angle, ΔM z is the additional yaw moment, F yf and F yr are the front and rear wheel lateral forces respectively.

[0014] (32) the magic formula tire model is constructed to represent the longitudinal force and the lateral force of the tire, and the lateral force of the tire can be calculated by the following formula:

[0015]

[0016] In the formula, α n , (n = f, r) is the tire side slip angle, a0-a 13 are fitting parameters,

[0017]

[0018] BCD y = a3sin[2arctan(F z / a4)], E y = a6F z + a7

[0019] S hy = a8F z + a9+ a 10 χ, S vy = a 11 F z χ + a 12 F z + a 13 .

[0020] Offline linearization is performed for each side slip angle:

[0021] F yf = K f α f , F yr = K r α r (3)

[0022] In the formula, K n , n = f, r is the equivalent tire side slip stiffness;

[0023] Adjustment factors ε f and ε r are introduced, so that K n is expressed as:

[0024] K f = ε f C f , K r = ε r C r (4)

[0025] In the formula, C f and C r are the side slip stiffness values of the front and rear wheels in the approximate linear region, respectively;

[0026] (33) A deviation tracking model is constructed according to the kinematic relationship between the vehicle and the road, specifically:

[0027]

[0028] In the formula, ρ r is the road curvature, e y and are the lateral tracking deviation and the heading angle deviation, respectively, and l p is the preview distance;

[0029] Combined with formulas (1) to (5), the vehicle-road system model for trajectory tracking control is as follows:

[0030]

[0031] In the formula is the state vector, u=[δ f ΔM z ] T is the control input, ω=ρ r is the system disturbance, H 2×1 It is a constant matrix introduced to describe the unknown disturbance in the measurement output process.

[0032] Furthermore, the LPV system equation is constructed as follows:

[0033] (41) All time-varying terms in formula (6) are linearly stripped off to define the variable parameters σ1~σ7 of the LPV system:

[0034]

[0035] The maximum and minimum values ​​of σ1, σ3 and σ5 are all reached synchronously, which is exactly opposite to the maximum and minimum values ​​of σ7. Similarly, the maximum and minimum values ​​of σ2, σ4 and σ6 are also reached synchronously.

[0036] (42) Redefine the following four LPV system variable parameters λ1~λ4 as follows:

[0037] λ1=[σ 1min ,σ 2min ,σ 3min ,σ 4min ,σ 5min ,σ 6min ,σ 7max ],

[0038] λ2=[σ 1max ,σ 2min ,σ 3max ,σ 4min ,σ 5max ,σ 6min ,σ 7min ],

[0039] λ3=[σ 1min ,σ 2max ,σ 3min ,σ 4max ,σ 5min ,σ 6max ,σ 7max ],

[0040] λ4=[σ 1max ,σ 2max ,σ 3max ,σ 4max ,σ 5max ,σ 6max, σ 7min ], (7)

[0041] The linear and nonlinear terms of the coefficient matrix of formula (6) are stripped using variable parameters λ1-λ4, and the following coefficient matrix is obtained:

[0042]

[0043] Wherein:

[0044]

[0045] Combined with formula (6) and formula (8), the model is discretized by using zero-order holding method, and the discrete LPV system model is obtained:

[0046] x(k+1)=E(η(k))x(k)+F(η(k))u(k)+G(η(k))ω(k)

[0047] y(k)=Cx(k)+Hw(k) (9)

[0048] Wherein, T s is the sampling period,

[0049]

[0050] The weight coefficient η j (k)≥0, (j=1, 2, 3, 4) satisfies And can be defined as:

[0051]

[0052] In the formula, x(k), u(k), ω(k) and y(k) are the discrete forms of state vector, control input, system disturbance, and output vector, is the discrete coefficient matrix of the vehicle-road system model in formula (6), E(η(k)), F(η(k)), G(η(k)) are the coefficient matrices of the LPV model, η j (k) is the weight coefficient.

[0053] Further, according to the obtained LPV system equation, an online observer is designed based on robust positive invariant set, which is used to obtain vehicle mass center side slip angle data in real time, and the conservatism is reduced by online updating the minimum robust positive invariant set, as follows:

[0054] (51) The online observer performs real-time state estimation:

[0055] x h (k+1)=E(η(k))x h(k) + F(η(k))u(k) + L(η(k))(y(k) - Cx h (k) + F(η(k))u(k) + L(η(k))(y(k) - Cx

[0056] where x h is the estimated state, is the observer gain, where L q , q e [1, 2,..., q m ] are the observer gains of the q subsystems to be solved;

[0057] Therefore, the state observation error is defined as x e (k) = x(k) - x h (k); combining equation 9 and equation 10, the observation error system dynamics equation can be obtained as follows:

[0058] x e (k + 1) = (E(η(k)) - L(η(k))C)x e (k) + (G(η(k)) - L(η(k))H)w(k) (11)

[0059] Define the quadratic performance function of state observation where P e is a symmetric positive definite matrix; according to the quadratic boundedness theory, if the following inequality holds, the observation error will always be in the robust positive invariance

[0060] set:

[0061]

[0062] For the observation system equation (11), assume that the system disturbance is bounded, i.e. Assume that there exists a matrix P e , R q , q e [1, 2,..., q m ], and a positive definite scalar θ e (0, 1) such that the following optimization problem has a solution:

[0063]

[0064] Then equation (12) always holds, and the gain of the online observer is calculated by , thereby further calculating the minimum robust positive invariance set of equation (11) where θ, Q w are given positive definite scalars, and q e [1, 2,..., q m ] are the labels of each fuzzy subsystem;

[0065] (52) Robust positive invariance set online update:

[0066] (52.1) Introduce known scalar such that holds, where is obtained by solving the optimization problem of formula (13); according to can be obtained:

[0067]

[0068] Definition as an upper bound, since θ ∈ (0, 1), when , get that is, it can force the observation error to gradually decrease; when , get then the observation error will converge to the robust positive invariant set

[0069] Therefore, the set is when , the robust positive invariant set of the system observation error;

[0070] (52.2) Correspondingly, can be used to limit the observation error allowed boundary at time k+1;

[0071] Find the minimum robust positive invariant set at time k+1

[0072] The observation error boundary at time k is where is a known scalar, and the optimal observation error boundary at time k+1 is obtained by solving the following optimization problem:

[0073]

[0074] In the formula, κ1≥0 and κ2≥0 are two scalars to be solved, Λ 22 , Λ 32 , Λ 33 are matrix elements.

[0075] Further, according to the designed online observer, a robust Min-Max predictive control model based on the online observer is constructed by using linear matrix inequality, as follows:

[0076] (61) For the LPV system formula (9), after introducing the observer formula (10), the predictive control input u(i|k) at time k is given by the following equation, where i≥0 is the prediction length:

[0077]

[0078] In the formula, N q(k), q = 1,..., q m is the control gain to be solved at time k;

[0079] (62) Constructing the augmented system Combined with formula (9), formula (11) and formula (14), the closed-loop prediction model of the augmented system is obtained as follows:

[0080] ξ(i+1|k) = ∏(i, k)ξ(i|k) + Ξ(i, k)w(k+i), i ≥ 0 (17)

[0081] Wherein:

[0082]

[0083] For the augmented system formula (17), a robust prediction control model based on the minimum-maximum at each time k is constructed, wherein

[0084]

[0085] In the formula, γ is a performance index, matrix S = diag{S1, S2}, wherein S1>0, S2>0, T>0 and U>0 are weight matrices, Ω represents a set of uncertain systems, is the maximum control input according to the actual physical constraints or for safety considerations, represents the maximum system state allowed, and Φ is a general constant matrix.

[0086] Further, the β-γ phase trajectory is drawn, the stable point and saddle point are calculated by searching for the equilibrium solution, and the vehicle stability domain boundary is obtained by parameter fitting according to the vehicle parameters under different working conditions, as follows:

[0087] (71) According to the compound differential equation composed of formula (1) and formula (2), the β-γ phase trajectory is drawn according to the predetermined longitudinal velocity, front wheel steering angle and road friction coefficient, and then based on the bifurcation stability theory, the stable point and saddle point are calculated by searching for the equilibrium solution;

[0088] (72) By changing the vehicle driving conditions, the vehicle stability state and data under different conditions are obtained, and the following vehicle dynamic stability domain boundary is calculated by parameter fitting method:

[0089] -Ψ1≤φ1β+ζ1γ≤Ψ1

[0090] -Ψ2≤φ2β+ζ2γ≤Ψ2 (23)

[0091] In the formula, φ1, ζ1, Ψ1, φ2, ζ2, Ψ2 are fitting parameters;

[0092] Considering the physical constraints of the actual steering system and the four-wheel independent drive system, the limits of the control inputs are set as follows:

[0093]

[0094] where, and are the maximum front wheel steering angle and the maximum additional yaw moment, respectively.

[0095] Further, the design optimization objective function is designed, according to the obtained expected additional yaw moment, combined with the longitudinal expected vehicle speed, using the optimal moment distribution strategy objective function to solve, thereby optimizing the four-wheel torque distribution of the four-wheel independent drive electric vehicle, as follows:

[0096] (81) The optimization problem objective function is designed as:

[0097]

[0098] where J is the performance index, represents the utilization rate of the single wheel adhesion, τ = fl, fr, rl, rr is the label of each wheel; is a given scalar to adjust the weight distribution;

[0099] (82) The optimization problem of formula (25) is converted into a standard quadratic programming problem, and the built-in QP function of Matlab is used to solve it. The equality and inequality constraints of the QP problem are as follows:

[0100]

[0101] where ΔM z is the additional yaw moment, F x , F y , F z are the longitudinal, lateral and vertical forces of the tire, τ = fl, fr, rl, rr represents different wheels, μ is the road adhesion coefficient, l f is the front track, T max is the maximum output torque of a single wheel, r ω is the equivalent wheel rolling radius, t ω is the left and right wheel width of the vehicle.

[0102] According to the second aspect of the present application, the present application provides a distributed drive electric vehicle path tracking control system based on a vehicle stability domain, which is used to realize the distributed drive electric vehicle path tracking control method described above, comprising:

[0103] The model construction module is configured to receive vehicle parameter information, construct a vehicle dynamics model and a magic formula tire model respectively according to the vehicle parameter information, and construct a vehicle-road system model for trajectory tracking control based on the vehicle dynamics model and the magic formula tire model, so as to obtain an LPV system equation.

[0104] The observer design module is configured to design an online observer based on a robust positive invariant set according to the obtained LPV system equation, so as to obtain vehicle mass center side slip angle data in real time and reduce the conservativeness by online updating a minimum robust positive invariant set.

[0105] The prediction control module is configured to construct a minimum-maximum robust prediction control model based on the online observer by using a linear matrix inequality according to the designed online observer.

[0106] The stability domain boundary derivation module is configured to construct a compound differential equation based on the vehicle dynamics equation and the magic formula tire model, draw a b-g phase trajectory according to the compound differential equation, a predetermined longitudinal velocity, a front wheel steering angle and a road surface friction coefficient, calculate a stable point and a saddle point by searching for a balance solution, and obtain vehicle parameters in different working conditions by changing the longitudinal velocity, the front wheel steering angle and the road surface friction coefficient, so as to obtain a vehicle stability domain boundary by parameter fitting.

[0107] The optimization module is configured to design an optimization objective function, solve the optimization objective function by using an optimal torque distribution strategy objective function according to the obtained expected additional yaw moment and a longitudinal expected vehicle speed, so as to optimize four-wheel torque distribution of the four-wheel independent drive electric vehicle.

[0108] According to a third aspect of the present application, the present application provides a terminal device comprising a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the memory stores a computer program capable of running on the processor, and the processor loads and executes the computer program, and the distributed drive electric vehicle path tracking control method is adopted.

[0109] The present application has at least the following advantages:

[0110] 1. The present application comprehensively considers various uncertain disturbances in the vehicle driving process, designs a minimum-maximum robust model prediction control architecture, and enhances the robustness of the path tracking control system.

[0111] 2.The application designs an active front wheel steering and torque vectoring collaborative control method, realizes the coordinated operation between the steering system and the four-wheel drive system, enhances the operation stability and path tracking accuracy of the distributed drive electric vehicle under different driving conditions, and improves the safety of the vehicle on the road.

[0112] Of course, implementing any product of the application does not necessarily require achieving all the advantages described above at the same time. BRIEF DESCRIPTION OF DRAWINGS

[0113] Fig. 1 A flowchart of the method of the application is shown.

[0114] Fig. 2 A path tracking control architecture of the distributed drive electric vehicle of the application. DETAILED DESCRIPTION

[0115] The technical solutions in the embodiments of the present disclosure will be described clearly and completely below with reference to the drawings in the embodiments of the present disclosure. Obviously, the described embodiments are only part of the embodiments of the present disclosure, rather than all the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present disclosure.

[0116] Embodiment one:

[0117] Please refer to Figs. 1-2 The application provides a technical solution: a path tracking control method for a distributed drive electric vehicle, comprising the following steps:

[0118] Step S1: chassis collaborative control system modeling: receiving vehicle parameter information, constructing a vehicle dynamics model and a magic formula tire model according to the vehicle parameter information, and constructing a vehicle-road system model for trajectory tracking control based on the vehicle dynamics model and the magic formula tire model, so as to construct an LPV system equation:

[0119] Step S11: vehicle-road system modeling

[0120] Focusing on the trajectory tracking control of the distributed drive electric vehicle, the vehicle dynamics equation is described as follows:

[0121]

[0122] In the formula, m is the vehicle mass, I z is the yaw moment of inertia, l f and l r are the lengths from the vehicle mass center to the front and rear axles, v x is the vehicle longitudinal speed, β and γ are the mass center side slip angle and yaw angular velocity respectively, δ fis the front wheel steering angle, AM z is the additional yaw moment, F yf and F yr are the front and rear wheel side forces, respectively;

[0123] A magic formula tire model is constructed for representing the longitudinal and lateral forces of the tire. The lateral force of the tire can be calculated by the following equation:

[0124]

[0125] where a n (n = f, r) is the tire slip angle, a0~ a 13 are the fitting parameters,

[0126]

[0127] BCD y = a3sin[2arctan(F z / a4)], E y = a6F z +a7

[0128] S hy = a8F z +a9+a 10 χ, S vy = a 11 F z χ+a 12 F z +a 13 .

[0129] Each slip angle is linearized offline:

[0130] F yf = K f a f , F yr = K r a r (3)

[0131] where K n , n = f, r is the equivalent tire cornering stiffness;

[0132] Adjustment factors e f and e r are introduced, so that K n is expressed as:

[0133] K f = e f C f , K r = e r C r (4)

[0134] C f and C r are the cornering stiffness values of the front and rear wheels in the linear region, respectively;

[0135] To achieve trajectory tracking control, a deviation tracking model can be constructed according to the kinematic relationship between the vehicle and the road, specifically:

[0136]

[0137] where ρ r is the road curvature, e y and are the lateral tracking deviation and the heading angle deviation, respectively, and l p is the preview distance;

[0138] In combination with formulas (1) to (5), the vehicle-road system model for trajectory tracking control is as follows:

[0139]

[0140] where is the state vector, u = [δ f ΔM z ] T is the control input, w = ρ r is the system disturbance, and H 2×1 is a constant matrix introduced to describe the unknown disturbance existing in the measurement output process;

[0141] Step S12: LPV system construction. The LPV method can convert a nonlinear system into a linear system, thereby simplifying the calculation process, improving the solving efficiency, and ensuring real-time performance:

[0142] All time-varying terms in formula (6) are linearly stripped to define the variable parameters σ1 to σ7 of the LPV system:

[0143]

[0144] The maximum and minimum values of σ1, σ3, and σ5 are reached simultaneously, and are just opposite to the maximum and minimum values of σ7. Similarly, the maximum and minimum values of σ2, σ4, and σ6 are also reached simultaneously.

[0145] Therefore, to reduce the number of polytope vertices, the following four LPV system variable parameters λ1 to λ4 can be redefined as:

[0146] λ1 = [σ 1min , σ 2min , σ 3min , σ 4min , σ 5min , σ6min , σ 7max ],

[0147] λ2= [σ 1max , σ 2min , σ 3max , σ 4min , σ 5max , σ 6min , σ 7min ],

[0148] λ3= [σ 1min , σ 2max , σ 3min , σ 4max , σ 5min , σ 6max , σ 7max ],

[0149] λ4= [σ 1max , σ 2max , σ 3max , σ 4max , σ 5max , σ 6max , σ 7min ], (7)

[0150] The coefficient matrix of formula (6) is linear and nonlinear term stripped using variable parameters λ1-λ4, and the following coefficient matrix is obtained:

[0151]

[0152] wherein,

[0153]

[0154] Combined with formula (6) and formula (8), the model is discretized by using zero-order holding method, and the discrete LPV system model is obtained:

[0155] x(k+1)=e(η(k))x(k)+F(η(k))u(k)+G(η(k))w(k)

[0156] y(k)=Cx(k)+Hw(k) (9)

[0157] wherein, T s is a sampling period,

[0158]

[0159] The weight coefficient η j (k)≥0, (j=1, 2, 3, 4) satisfies and can be defined as:

[0160]

[0161] where x(k), u(k), w(k) and y(k) are the discrete forms of state vector, control input, system disturbance, and output vector, respectively, is the coefficient matrix of the discrete vehicle-road system model in formula (6), E(η(k)), F(η(k)), G(η(k)) are the coefficient matrices of the LPV model, η j (k) is the weight coefficient;

[0162] S2. Robust observer design: According to the obtained LPV system equation, an online observer is designed based on the robust positive invariant set to obtain the vehicle mass center side slip angle data in real time, and the conservatism is reduced by online updating the minimum robust positive invariant set:

[0163] Step S21: offline design of robust observer

[0164] Considering that the vehicle mass center side slip angle is difficult to accurately obtain, the following observer is designed for real-time state estimation:

[0165] x h (k+1)=e(η(k))x h (k)+F(η(k))u(k)+L(η(k))(y(k)-Cx h (k)) (10)

[0166] where x h is the estimated state, is the observer gain, where L q , q∈[1, 2, …, q m ] are mutually independent subsystem observation gains to be solved;

[0167] Therefore, the state observation error is defined as x e (k)=x(k)-x h (k); combining formula (9) and formula (10), the observation error system dynamics equation can be obtained as follows:

[0168] x e (k+1)=(e(η(k))L(η(k))C)x e (k)+(G(η(k))-L(η(k))H)w(k) (11)

[0169] In order to obtain better observation effect, it is necessary to limit the real-time observation error within an acceptable range at all times; considering that there is a disturbance term in formula (11), a quadratic performance function of state observation can be defined as where P eis a symmetric positive definite matrix, therefore, according to the quadratic boundedness theory, if the following inequality holds, the observation error will always be in the robust positive invariant set:

[0170]

[0171] To make formula (12) hold, the following theorem 1 is given to obtain the observer gain L q and matrix P e :

[0172] Theorem 1: for the observation system formula 11, assume that the system disturbance is bounded, i.e. If there exists matrix P e , R q , q∈[1, 2, …, q m ] and positive definite scalar θ∈(0, 1) such that the following optimization problem has a solution:

[0173]

[0174] then formula (12) always holds, and the gain of the online observer is calculated by , so as to further calculate the minimum robust positive invariant set of formula (11) where θ, Q w is a given positive definite scalar, q∈[1, 2, …, q m ] is the index of each fuzzy subsystem;

[0175] Step S22: online update of estimation error set

[0176] Through then formula (12) always holds, and the gain of the online observer is calculated by , so as to further calculate the minimum robust positive invariant set of formula (11) where θ, Q w is a given positive definite scalar,

[0177] q∈[1, 2, …, q m ] is the index of each fuzzy subsystem (formula 14) is defined As an upper bound, since θ∈(0, 1), when , it is obtained that that is, it can force the observation error to gradually decrease; when , it is obtained that which shows that the observation error will converge to the robust positive invariant set Therefore, it can be known that the set is the robust positive invariant set of the system observation error when , and correspondingly, which can be used to limit the observation error allowed boundary at k+1 time;

[0178] To obtain a better observation effect, one possible way is to obtain the minimum robust positive invariant set of observation error at each time, therefore, the following gives theorem 2 to find the minimum robust positive invariant set at k+1 time

[0179] Theorem 2: for the observation error boundary at k time wherein is a known scalar, considering all possible observation errors, parameter uncertainties and bounded input disturbances existing at k time observation system, then the optimal observation error boundary at k+1 time can be obtained by solving the following optimization problem:

[0180]

[0181] In the formula, κ1≥0 and κ2≥0 are two scalars to be solved, Λ 22 , Λ 32 , Λ 33 is the matrix element;

[0182] S3. Robust model predictive control construction: according to the designed online observer, the minimum-maximum robust predictive control model based on online observer is constructed by using linear matrix inequality:

[0183] For LPV system formula 9, after introducing the observer formula 10, the predictive control input u(i|k) at k time can be given by the following equation, wherein i≥0 is the prediction length,

[0184]

[0185] In the formula, N q (k), q=1, …, q m is the control gain to be solved at k time, in order to avoid the adverse effect of estimated action on the optimization process of robust model predictive control system, the augmented system can be constructed Therefore, combined with formula 9, formula 11 and formula 14, the closed loop prediction model of the augmented system is as follows:

[0186] ξ(i+1|k)=Π(i,k)ξ(i|k)+Ξ(i,k)ω(k+i),i≥0 (17)

[0187] Wherein:

[0188]

[0189] For augmented system formula (17), the minimum-maximum based robust predictive control model at each time k is constructed, wherein

[0190]

[0191] where Y is the performance index, S = diag{S1, S2} is a matrix with S1 > 0, S2 > 0, T > 0 and U > 0 are weight matrices, Ω represents the set of uncertain systems, is the maximum control input according to the actual physical constraints or for safety considerations, represents the maximum allowed system state, Φ is a general constant matrix;

[0192] Therefore, it can be seen that formula 19 represents the state constraints of the augmented system, formula 20 is the quadratic bounded condition that satisfies the performance index, formula 21 is the input constraint, and formula 22 represents the state constraints of the original system formula 9, so the optimization problem is to solve the optimization problem with uncertainty and multiple state and input constraints at each time k, so that i is minimized;

[0193] S4. Vehicle stability domain construction: based on the vehicle dynamics equation and the magic formula tire model, a compound differential equation is formed, according to the compound differential equation, the predetermined longitudinal velocity, the front wheel steering angle and the road surface friction coefficient, the phase trajectory is drawn, the stable point and the saddle point are calculated by searching for the equilibrium solution, and the vehicle longitudinal velocity, the front wheel steering angle and the road surface friction coefficient are changed to obtain vehicle parameters in different working conditions, and the vehicle stability domain boundary is obtained by parameter fitting:

[0194] According to the compound differential equation composed of formula 1 and formula 2, β-γ phase trajectory can be drawn according to the predetermined longitudinal velocity, front wheel steering angle and road surface friction coefficient, then based on the bifurcation stability theory of phase trajectory, the stable point and the saddle point can be calculated by searching for the equilibrium solution, by changing the vehicle driving conditions, the vehicle stability state and data under different working conditions can be obtained, and by parameter fitting method, the following vehicle dynamic stability domain boundary can be obtained:

[0195] -Ψ1≤φ1β+ζ1γ≤Ψ1

[0196] -Ψ2≤φ2β+ζ2γ≤Ψ2 (23)

[0197] In the formula, φ1, ζ1, ψ1, φ2, ζ2, Ψ2 are fitting parameters;

[0198] Considering the physical constraints of the actual steering system and the four-wheel independent drive system, the limit of the control input is set as follows:

[0199]

[0200] In the formula, and are the maximum front wheel steering angle and the maximum additional yaw moment, respectively;

[0201] S5. Four-wheel torque optimal distribution: design the optimization objective function, according to the expected additional yaw moment obtained, combined with the longitudinal expected vehicle speed, and solve the optimal torque distribution strategy objective function, so as to optimize the four-wheel torque distribution of the four-wheel independent drive electric vehicle:

[0202] In order to further ensure the stability of the vehicle, the optimal torque distribution strategy is adopted to optimize the four-wheel torque distribution of the four-wheel independent drive electric vehicle. In addition to considering the total adhesion coefficient utilization rate of the four wheels as small as possible, in order to make the vehicle run more smoothly, the average deviation of the adhesion coefficient utilization rate between different wheels is also considered. Therefore, the optimization problem objective function is designed as:

[0203]

[0204] In the formula, J is the performance index, represents the adhesion rate utilization rate of a single wheel, τ = fl, fr, rl, rr is the label of each wheel; is a given scalar to adjust the weight distribution;

[0205] The optimization problem of formula (25) can be converted into a standard quadratic programming problem, so that the built-in QP function of Matlab can be used for solving. The equality and inequality constraints of the QP problem are as follows:

[0206]

[0207] In the formula, ΔM z is the additional yaw moment, F x , F y , F z is the longitudinal, lateral and vertical force of the tire, τ = fl, fr, rl, rr represents different wheels, μ is the road adhesion coefficient, l f is the front track, T max is the maximum output torque of a single wheel, r ω is the equivalent wheel rolling radius, t ω is the left and right wheel width of the vehicle.

[0208] See Fig. 2It can be known that the real-time vehicle mass center side slip angle can be obtained by a robust observer based on a robust positive invariance set, and a robust model predictive control based on the observer is proposed, the observer gain running online is obtained by offline calculation, the minimum allowable observation error can be obtained by online refreshing, then a minimum-maximum robust model predictive optimization problem is constructed, the state constraints based on phase plane stability and the input saturation constraints caused by physical characteristics are processed according to the robust positive invariance set theory, and finally the optimal torque distribution is carried out to realize the intervention of additional yaw moment and longitudinal speed tracking.

[0209] In summary, the present application comprehensively considers various uncertain disturbances in the vehicle driving process, designs a minimum-maximum robust model predictive control architecture, and enhances the robustness of the path tracking control system; at the same time, an online observer based on the minimum robust positive invariance set is designed to realize the real-time and accurate acquisition of key vehicle parameters without increasing the hardware cost; in addition, the present application designs an active front wheel steering and torque vectoring cooperative control method to realize the coordinated operation between the steering system and the four-wheel drive system, enhances the operation stability and path tracking accuracy of the distributed drive electric vehicle under different driving conditions, and improves the safety of the vehicle road driving.

[0210] Embodiment two:

[0211] The embodiment provides a distributed drive electric vehicle path tracking control system based on a vehicle stability domain, which is used for realizing the distributed drive electric vehicle path tracking control method described in embodiment one, and comprises:

[0212] A model construction module is used for receiving vehicle parameter information, constructing a vehicle dynamics model and a magic formula tire model according to the vehicle parameter information, and constructing a vehicle-road system model for trajectory tracking control based on the vehicle dynamics model and the magic formula tire model, so as to construct an LPV system equation.

[0213] An observer design module is used for designing an online observer based on a robust positive invariance set according to the obtained LPV system equation, for real-time acquisition of vehicle mass center side slip angle data, and for reducing the conservativeness by online updating of the minimum robust positive invariance set.

[0214] A prediction control module is used for constructing a minimum-maximum robust prediction control model based on the online observer by using a linear matrix inequality according to the designed online observer.

[0215] The stable region boundary derivation module is configured to construct a compound differential equation based on a vehicle dynamics equation and a magic formula tire model, draw a phase trajectory according to the compound differential equation, a predetermined longitudinal velocity, a front wheel steering angle and a road surface friction coefficient, calculate stable points and saddle points by searching for a balance solution, and obtain vehicle parameters in different working conditions by changing the longitudinal velocity, the front wheel steering angle and the road surface friction coefficient, and obtain the vehicle stable region boundary by parameter fitting.

[0216] The optimization module is configured to design an optimization objective function, solve the optimization objective function by using an optimal torque distribution strategy objective function according to the obtained expected additional yaw moment and a longitudinal expected vehicle speed, and thus optimize four-wheel torque distribution of the four-wheel independent drive electric vehicle.

[0217] Specifically, the model construction module, the observer design module, the prediction control module, the stable region boundary derivation module and the optimization module can be embedded into a computer processing system. The computer can complete the task of enhancing vehicle driving tracking control by calling the modules according to the distributed drive electric vehicle path tracking control method provided above. The model construction module, the observer design module, the prediction control module, the stable region boundary derivation module and the optimization module can perform operations according to the specific steps given in the distributed drive electric vehicle path tracking control method.

[0218] It should be noted that the division of each module of the above system is only a logical function division. In actual implementation, all or part of the modules can be integrated into one physical entity, or can be physically separated. These modules can all be implemented in the form of software called by a processing element; or all can be implemented in the form of hardware; or part of the modules can be implemented in the form of software called by a processing element, and part of the modules can be implemented in the form of hardware. For example, the model construction module can be a separately established processing element, or can be integrated into a chip of the above device. In addition, the model construction module can also be stored in the form of program code in the memory of the above device, and the function of the model construction module can be called and executed by a processing element of the above device. The implementation of other modules is similar. In addition, all or part of the modules can be integrated together or independently implemented. The processing element described herein can be an integrated circuit having a signal processing capability. In the implementation process, each step of the above method or each of the above modules can be completed by an integrated logic circuit of hardware or an instruction in the form of software in the processing element.

[0219] For example, the above modules can be one or more integrated circuits configured to implement the above methods, such as one or more Application Specific Integrated Circuits (ASICs), or one or more Digital Signal Processors (DSPs), or one or more Field Programmable Gate Arrays (FPGAs), etc. For another example, when a certain module above is implemented in the form of a processing element scheduling code, the processing element can be a general-purpose processor, such as a Central Processing Unit (CPU) or other processor capable of invoking code. For another example, the modules can be integrated together to implement a system-on-a-chip (SOC).

[0220] Embodiment Three

[0221] The application provides a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, the memory stores a computer program capable of running on the processor, and when the processor loads and executes the computer program, the distributed drive electric vehicle path tracking control method is adopted.

[0222] It should be noted that the terminal device can be a computer device such as a desktop computer, a notebook computer, or a cloud server, and the terminal device includes but is not limited to a processor and a memory. For example, the terminal device can further include an input / output device, a network access device, a bus, etc.

[0223] Further, the processor can be a Central Processing Unit (CPU), and of course, according to actual use cases, other general-purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), ready-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. can also be used. The general-purpose processor can be a microprocessor or any conventional processor, and the present application does not limit it.

[0224] It is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting; it is not intended that the scope of the application be limited to the detailed description contained herein or the specific examples given herein, but rather that the scope of the application be determined by the appended claims, and their equivalents.

[0225] Those of ordinary skill in the art will appreciate that the above described terms are to be construed in accordance with their ordinary meanings in the present invention. When an element is referred to as being "connected", "coupled", "fixed", or "attached" to another element, it can be directly connected, coupled, fixed, or attached to the other element, or intervening elements can be present. When an element is referred to as being "connected" to another element, it can be directly connected to the other element, or intervening elements can be present. The terms "vertical", "horizontal", "upper", "lower", "left", "right", and similar terms as used herein are for descriptive purposes only and not meant to be limiting.

[0226] While embodiments of the application have been shown and described, it is to be understood that various modifications, substitutions, combinations, and variations can be made therein and by those of ordinary skill in the art without departing from the spirit and scope of the present application, which is defined by the following claims and their equivalents.

[0227] In the description of the specification, reference can be made to terms such as "one embodiment", "an example", "a specific example", etc. which indicates that the particular feature, structure, material, or characteristic being described is included in at least one embodiment or example of the present disclosure. The illustrative appearances of such terms in various places of the specification are not necessarily referring to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

Claims

1. A distributed drive electric vehicle path tracking control method, characterized in that: The following steps are involved: Receiving vehicle parameter information, constructing a vehicle dynamics model and a magic formula tire model according to the vehicle parameter information, and constructing a vehicle-road system model for trajectory tracking control based on the vehicle dynamics model and the magic formula tire model, thereby constructing an LPV system equation; According to the obtained LPV system equation, an online observer is designed based on the robust positive invariant set to obtain the vehicle center of mass sideslip angle data in real time, and the conservatism is reduced by online updating of the minimum robust positive invariant set. According to the designed online observer, a minimum-maximum robust predictive control model based on the online observer is constructed using linear matrix inequality. A complex differential equation is constructed based on the vehicle dynamics equation and the magic formula tire model. The β-γ phase trajectory is plotted based on the complex differential equation, the predetermined longitudinal speed, the front wheel steering angle, and the road friction coefficient. The stable point and saddle point are calculated by searching for the equilibrium solution. The vehicle parameters under different operating conditions are obtained by changing the vehicle longitudinal speed, the front wheel steering angle, and the road friction coefficient. The vehicle stability domain boundary is obtained through parameter fitting. An optimization objective function is designed. According to the obtained expected additional yaw moment and the expected longitudinal vehicle speed, the optimal torque distribution strategy objective function is adopted to solve the problem, thereby optimizing the four-wheel torque distribution of the four-wheel independent drive electric vehicle.

2. The distributed drive electric vehicle path tracking control method according to claim 1, characterized in that: The vehicle parameter information includes front wheel angle, longitudinal speed, center of mass sideslip angle, yaw angular velocity, additional yaw moment and tire lateral force, and the vehicle parameter information is collected by a rotation angle sensor, a gyroscope and a tire six-component force tester respectively.

3. The distributed drive electric vehicle path tracking control method according to claim 1, characterized in that: The vehicle dynamics model and magic formula tire model are constructed based on the vehicle parameter information, as follows: (31) Focusing on the trajectory tracking control of distributed drive electric vehicles, the vehicle dynamics equation is described as follows: Where m is the vehicle mass, l z is the yaw moment of inertia, l f and l r are the lengths from the vehicle's center of mass to the front and rear axles, v x is the vehicle longitudinal velocity, β and γ are the sideslip angle and yaw rate of the center of mass, respectively, δ f is the front wheel angle, ΔM z is the additional yaw moment, F yf and F yr are the front and rear wheel lateral forces respectively; (32) A magic formula tire model is constructed to characterize the longitudinal force and lateral force of the tire. The lateral force of the tire can be calculated by the following formula: Where α n , (n=f, r) is the tire side slip angle, a0~a 13 are the fitting parameters, BCD y =a3sin[2arctan(F z / a4)],E y =a6F z +a7 S hy =a8F z +a9+a 10 χ,S vy =a 11 F z χ+a 12 F z +a 13 . Perform offline linearization on each slip angle: F yf =K f a f ,F yr =K r a r (3) Where K n , n = f, r is the equivalent tire cornering stiffness; Introducing the adjustment factor ε f and ε r , so K n Expressed as: K f =e f C f ,K r =e r C r (14) Where C f and C r are the cornering stiffness values ​​of the front and rear wheels in the approximately linear region, respectively; (33) A deviation tracking model is constructed based on the kinematic relationship between the vehicle and the road, specifically: Where ρ r is the road curvature, e y and They are lateral tracking deviation and heading angle deviation, l p is the preview distance; Combining formulas (1) to (5), the vehicle-road system model for trajectory tracking control is obtained as follows: y(t)=Cx(t)+Hw(t) (6) In the formula is the state vector, u=[δ f ΔM z ] T is the control input, w=ρ r is the system disturbance, H 2×1 It is a constant matrix introduced to describe the unknown disturbance in the measurement output process.

4. The distributed drive electric vehicle path tracking control method according to claim 3, characterized in that: Construct the LPV system equation as follows: (41) All time-varying terms in formula (6) are linearly stripped off to define the variable parameters σ1~σ7 of the LPV system: The maximum and minimum values ​​of σ1, σ3 and σ5 are all reached synchronously, which is exactly opposite to the maximum and minimum values ​​of σ7. Similarly, the maximum and minimum values ​​of σ2, σ4 and σ6 are also reached synchronously. (42) Redefine the following four LPV system variable parameters λ1~λ4 as follows: λ1=[σ 1min ,s 2min ,s 3min ,s 4min ,s 5min ,s 6min ,s 7max ], λ2=[σ 1max ,s 2min ,s 3max ,s 4min ,s 5max ,s 6min ,s 7min ], λ3=[σ 1min ,s 2max ,s 3min ,s 4max ,s 5min ,s 6max ,s 7max ], λ4=[σ 1max ,s 2max ,s 3max ,s 4max ,s 5max ,s 6max ,s 7min ], (7) The linear and nonlinear terms of the coefficient matrix of formula (6) are stripped using variable parameters λ1 to λ4, and the following coefficient matrix is ​​obtained: in: Combining formula (6) and formula (8), the zero-order hold method is used to discretize the model to obtain the discretized LPV system model: x(k+1)=E(η(k))x(k)+F(η(k))u(k)+G(η(k))w(k) y(k)=Cx(k)+Hw(k) (9) Among them, T s is the sampling period, Weight coefficient η j (k)≥0, (j=1, 2, 3, 4) satisfies And it can be defined as: Where x(k), u(k), w(k) and y(k) are the discrete forms of the state vector, control input, system disturbance, and output vector, respectively. is the coefficient matrix of the discretized vehicle-road system model in formula (6), E(η(k)), F(η(k)), G(η(k)) is the coefficient matrix of the LPV model, η j (k) is the weight coefficient.

5. The distributed drive electric vehicle path tracking control method according to claim 4, characterized in that: According to the obtained LPV system equation, an online observer is designed based on the robust positive invariant set to obtain the vehicle center of mass sideslip angle data in real time. The conservatism is reduced by updating the minimum robust positive invariant set online, as follows: (51) Online observer performs real-time state estimation: x h (k+1)=E(η(k))x h (k)+F(η(k))u(k)+L(η(k))(y(k)-Cx h (k)) (10) Where x h is the estimated state, is the observer gain, where L q ,q∈[1,2,…,q m ] are independent observation gains of the subsystems to be solved; Therefore, the state observation error is defined as x e (k) = x(k) - x h (k); Combining Formula 9 and Formula 10, the dynamic equation of the observation error system can be obtained as follows: x e (k+1)=(E(η(k))-L(η(k))C)x e (k)+(G(η(k))-L(η(k))H)w(k) (11) Define the quadratic performance function of the state observation Among them, P e is a symmetric positive definite matrix; According to the quadratic boundedness theory, if the following inequality holds, the observation error will always be in the robust positive invariant set: For the observation system formula (11), it is assumed that the system disturbance is bounded, that is, Assume that there is a matrix P e , R q ,q∈{1,2,…,q m ], and a positive definite scalar θ∈(0,1), then the following optimization problem has a solution: Then formula (12) always holds true, and the gain of the online observer is given by L q =P e -1 R q Calculated, and then further calculated to get the minimum robust positive invariant set of formula (11) where θ, Q w is a given positive definite scalar, q∈{1, 2,…, q m ] is the label of each fuzzy subsystem; (52) Robust positive invariant set online update: (52.1) Introducing a known scalar Make Established, of which is obtained by solving the optimization problem of formula (13); according to You can get: definition As an upper bound, since θ∈(0,1), when When That is, it can force the observation error to gradually decrease; when When Then the observation error will converge to the robust positive invariant set Therefore, the set for When , the robust positive invariant set of the system observation error; (52.2) Accordingly, It can be used to limit the allowable boundary of observation error at time k+1; Find the minimum robust positive invariant set at time k+1 The details are as follows: The observation error bound at time k is in is a known scalar, the optimal observation error bound at time k+1 By solving the following optimization problem: Where κ1≥0 and κ2≥0 are two scalars to be solved, Λ 22 , Λ 32 , Λ 33 are matrix elements.

6. The distributed drive electric vehicle path tracking control method according to claim 5, characterized in that: According to the designed online observer, a robust Min-Max predictive control model based on the online observer is constructed using linear matrix inequality, as follows: (61) For the LPV system formula (9), after introducing the observer formula (10), the predicted control input u(i|k) at time k is given by the following equation, where i ≥ 0 is the prediction length: Where N q (k),q=1,…,q m is the control gain at time k to be determined; (62) Building an augmented system Combining formula (9), formula (11) and formula (14), the closed-loop prediction model of the augmented system is obtained as follows: ξ(i+1|k)=Π(i,k)ξ(i|k)+Ξ(i,k)w(k+i),i≥0 (17) in: For the augmented system formula (17), a robust predictive control model based on minimum-maximum control is constructed at each time k, where Where γ is the performance index, the matrix S = diag{S1, S2}, where S1>0, S2>0, T>0 and U>0 are weight matrices, and Ω represents the set of uncertain systems. It is the maximum control input based on actual physical constraints or for safety considerations. represents the maximum allowed system state, and Φ is a general constant matrix.

7. The distributed drive electric vehicle path tracking control method according to claim 6, characterized in that: The β-γ phase trajectory is drawn, the stable point and saddle point are calculated by searching the equilibrium solution, and the vehicle stability region boundary is obtained by parameter fitting according to the vehicle parameters under different working conditions, as follows: (71) According to the composite differential equation composed of formula (1) and formula (2), the β-γ phase trajectory is drawn according to the predetermined longitudinal speed, front wheel steering angle and road friction coefficient, and then the stable point and saddle point are calculated by searching for the equilibrium solution based on the phase trajectory bifurcation stability theory; (72) By changing the vehicle driving conditions, the vehicle stability status and data under different conditions are obtained. By using the parameter fitting method, the following vehicle dynamic stability region boundary is calculated: -Ψ1≤φ1β+ζ1γ≤Ψ1 -Ψ2≤φ2β+ζ2γ≤Ψ2 (23) Where φ1, ζ1, Ψ1, φ2, ζ2, Ψ2 are fitting parameters; Considering the physical constraints of the actual steering system and the four-wheel independent drive system, the limits of the control input are set as follows: Where, and are the maximum front wheel steering angle and the maximum additional yaw moment respectively.

8. The distributed drive electric vehicle path tracking control method according to claim 7, characterized in that: The optimization objective function is designed. Based on the expected additional yaw moment and the expected longitudinal vehicle speed, the optimal torque distribution strategy objective function is used to solve the problem, thereby optimizing the four-wheel torque distribution of the four-wheel independent drive electric vehicle. The details are as follows: (81) The objective function of the optimization problem is designed as: Where J is the performance index, represents the utilization rate of adhesion of a single wheel, τ = fl, fr, rl, rr is the number of each wheel; is a given scalar used to adjust the weight distribution; (82) The optimization problem of formula (25) is transformed into a standard quadratic programming problem and solved using the built-in QP function in Matlab. The equality and inequality constraints of the QP problem are as follows: Where ΔM z is the additional yaw moment, F x , F y , F z is the longitudinal, lateral and vertical force of the tire, τ=fl, fr, rl, rr represent different wheels, μ is the road adhesion coefficient, l f is the front wheelbase, T max is the maximum output torque of a single wheel, r ω is the equivalent wheel rolling radius, t ω The width of the left and right wheels of the vehicle.

9. A distributed drive electric vehicle path tracking control system based on a vehicle stability domain, used to implement the distributed drive electric vehicle path tracking control method according to any one of claims 1 to 8, characterized in that: include: a model building module for receiving vehicle parameter information, constructing a vehicle dynamics model and a magic formula tire model according to the vehicle parameter information, and constructing a vehicle-road system model for trajectory tracking control based on the vehicle dynamics model and the magic formula tire model, thereby constructing an LPV system equation; The observer design module is used to design an online observer based on the obtained LPV system equation and the robust positive invariant set to obtain the vehicle center of mass sideslip angle data in real time and reduce conservatism by online updating the minimum robust positive invariant set; A predictive control module is used to construct a minimum-maximum robust predictive control model based on the designed online observer using linear matrix inequalities; The stability region boundary derivation module is used to construct a complex differential equation based on the vehicle dynamics equation and the magic formula tire model. The bg phase trajectory is plotted based on the complex differential equation, the predetermined longitudinal speed, the front wheel steering angle, and the road friction coefficient. The stability point and saddle point are calculated by searching for the equilibrium solution. The vehicle parameters under different working conditions are obtained by changing the vehicle longitudinal speed, the front wheel steering angle, and the road friction coefficient. The vehicle stability region boundary is obtained through parameter fitting. The optimization module is used to design the optimization objective function. According to the obtained expected additional yaw moment and the expected longitudinal vehicle speed, the optimal torque distribution strategy objective function is used to solve the problem, thereby optimizing the four-wheel torque distribution of the four-wheel independent drive electric vehicle.

10. A terminal device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that: The memory stores a computer program that can be run on the processor. When the processor loads and executes the computer program, the path tracking control method of the distributed drive electric vehicle according to any one of claims 1 to 8 is adopted.

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