Modular distributed electric-drive heavy-load vehicle stability domain estimation method based on arc length function

Abstract

The invention discloses a modular distributed electrically-driven heavy-load vehicle stability domain estimation method based on an arc length function. The method comprises the steps that a dynamic model of a modular distributed electrically-driven heavy-load vehicle is established; estimating a Lyapunov function by using the arc length function; constructing an attraction domain through a Lyapunov function, and regarding the attraction domain as a stable domain; according to the method, the motion characteristics of the vehicle under different working conditions are reflected by constructing an accurate kinetic model; estimating a Lyapunov function by using an arc length function, and constructing an attraction domain, thereby estimating a stability domain, obtaining a stability limit boundary, and guiding the development and design of a stability control system; furthermore, for the brand-new chassis configuration of the modular distributed electric drive heavy-load vehicle, a new possibility is provided for performance optimization of the modular distributed electric drive heavy-load vehicle, all potentials of the brand-new chassis configuration of the modular distributed electric drive heavy-load vehicle are fully activated, and a guarantee is provided for the driving stability of the modular distributed electric drive heavy-load vehicle.

Description

Technical Field

[0001] The present invention relates to the field of vehicle system dynamics and control, and in particular to a method for estimating the stability domain of a modular distributed electric-driven heavy-load vehicle based on an arc-length function. Background Art

[0002] As the core vehicle of the nation's strategic equipment transportation system, heavy-haul vehicles undertake critical tasks such as strategic delivery of national defense and military equipment, transshipment of aerospace equipment, and the circulation of bulk industrial materials. According to statistics as of June 2024, my country's commercial vehicle fleet has exceeded 41.5 million, of which heavy-haul commercial vehicles account for 21.7% (over 9 million vehicles). In the military sector, these vehicles carry over 80% of major military strategic operations, including the high-mobility deployment of strategic weapons and support for field operations. In the civilian sector, they achieve an annual freight volume exceeding 19 billion tons and a turnover of 21 trillion tons on highways. Therefore, heavy-haul vehicles are crucial to national economy, people's livelihoods, and national defense security. Their technical performance is directly linked to national defense strategic capabilities and the safety of the national economy. However, the high load mass and high center of gravity of heavy-haul vehicles often lead to complex rescue procedures and high economic costs in the event of accidents such as rollovers, entrapment, or loss of stability. This phenomenon not only severely reduces cargo transportation efficiency but also poses a fatal threat to driving safety.

[0003] Current mainstream heavy-duty vehicles generally utilize a central drive shaft power distribution architecture, which suffers from inherent drawbacks such as low transmission efficiency and limited freedom of movement. Specifically, the steering kinematics of the two coaxial wheels are constrained by the structural constraints of the steering tie rods. The Ackermann geometry significantly impacts the vehicle's steering maneuverability, significantly reducing the system's freedom of movement. Consequently, the chassis flexibility of heavy-duty vehicles based on traditional Ackermann geometry is already constrained by the mechanical structure. To address this issue, modular distributed electric drive technology has emerged. This modular distributed electric drive chassis utilizes an innovative, corner-module, distributed six-wheel motor drive and six-wheel steering architecture. Compared to traditional configurations, this new chassis structure utilizes wheel-end drive, eliminating the drive shaft in the longitudinal direction and the tie rods in the transverse direction. This eliminates the geometric constraints of tie rods on steering, unleashing all degrees of freedom in the heavy-duty vehicle chassis, pushing the limits of heavy-duty vehicle mobility and providing new possibilities for optimizing its performance.

[0004] Therefore, how to fully activate the full potential of the new modular distributed electric drive configuration and ensure the driving stability of heavy-loaded vehicles is a hot issue that needs to be solved urgently. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: to provide a stability domain estimation method for modular distributed electric drive heavy-duty vehicles based on arc length function, to construct a nonlinear dynamic model of modular distributed electric drive heavy-duty vehicles according to the all-wheel drive and all-wheel steering characteristics, to estimate and optimize the stability domain of modular distributed electric drive heavy-duty vehicles based on Lyapunov nonlinear method and square sum programming theory, to obtain the stability limit boundary, and to guide the development and design of stability control systems.

[0006] Technical solution: To achieve the above-mentioned purpose, the technical solution adopted by the present invention is:

[0007] A modular distributed electric drive heavy-load vehicle stability domain estimation method based on arc length function includes the following steps:

[0008] S1. Establish an integrated model. The process is as follows:

[0009] S1.1. Construct a vehicle dynamics model: Let i∈{f,m,r} represent the front, middle, and rear axles of a three-axle heavy-duty vehicle, and j∈{l,s} represent the left and right wheels on the same axle. Obtain the vehicle mass m and the distance l from the corresponding axle to the center of mass of the heavy-duty vehicle. i 、Wheelbase b w , wheel angle δ of the corresponding axis i , vehicle longitudinal speed v x , vehicle lateral speed v y , the vehicle yaw angular velocity γ, and the three-degree-of-freedom dynamic model of the modular distributed electric drive three-axle heavy-duty vehicle is established. Its dynamic equations are as follows:

[0010]

[0011] M z =b w Σ(F xil cosδ i -F yil sinδ i +F xis cosδ i -F yis sinδ i )

[0012] Where: is the derivative of the vehicle's longitudinal velocity, is the derivative of the vehicle's lateral velocity, is the derivative of the vehicle's yaw rate, F xij is the corresponding tire longitudinal force, F yij is the corresponding tire lateral force, I z is the vehicle's moment of inertia, M z is the direct yaw moment;

[0013] S1.2. Introduce rational polynomials to approximate tire nonlinear characteristics and fit the tire lateral force F yij :

[0014]

[0015] Where: F zij is the vertical load on the tire, μ ij is the road adhesion coefficient corresponding to the ground contacted by the tire, q1, q2, q3, q4, q5 are the rational polynomial coefficients in the fitted tire model, α ij is the tire slip angle of the corresponding tire; n ij and d ij Respectively represent the numerator and denominator in the tire lateral force formula;

[0016] S1.3, Based on the rational polynomial model and F yij , derive and calculate α ij :

[0017]

[0018] Where: β represents the vehicle's center of mass sideslip angle;

[0019] S1.4. Combining the rational polynomial tire model with the vehicle dynamics model yields a modular distributed electric drive heavy-duty vehicle dynamics model that integrates the rational polynomial characteristics of the tire:

[0020]

[0021] in:

[0022]

[0023] D(x,u)=d f d m d r

[0024] Where: state quantity x = [βγ] T , control input u=[δ f δ m δ r M z ] T ;

[0025] S2. Use the arc length function to construct the Lyapunov function. The process is as follows:

[0026] S2.1. Define the arc length function: Assuming the origin is the asymptotically stable equilibrium point of the heavy-load vehicle nonlinear system, the arc length function L(x(t)) is defined as:

[0027]

[0028] Where: f(x(t)) is the state equation of the heavy-duty vehicle nonlinear system at time t;

[0029] S2.2. Construct the Lyapunov function and use the arc length function as the Lyapunov function V(x), which is expressed as:

[0030] V(x)=L(x)

[0031] S3. Construct the attraction domain and estimate the stability domain. The process is as follows:

[0032] S3.1. Construct the attraction domain D through the Lyapunov function and regard it as a stable domain. The attraction domain D represents the set of all initial states that can converge to the equilibrium point:

[0033]

[0034] S3.2. Optimization Problem Solving: Solve a nonlinear constrained optimization problem To estimate the domain of attraction, the constraints are as follows:

[0035]

[0036] Where c represents the level set parameter. The larger the level set, the better the estimation of the attraction domain.

[0037] S3.3. Input the independent variables including vehicle speed, road adhesion coefficient, three-axis tire angle and direct yaw moment, and estimate the attraction domain under the corresponding working condition, which is equivalent to the stability domain of the modular distributed electric drive heavy-duty vehicle under this working condition, thereby realizing the estimation of the stability domain of the heavy-duty vehicle.

[0038] In a preferred embodiment, the vehicle dynamics model established in S1.1 includes three degrees of freedom: longitudinal, lateral, and yaw. When constructing the vehicle dynamics model, the characteristics of the all-wheel steering system are considered, and the hub motor dynamics analysis is introduced.

[0039] In a preferred embodiment, in S1.2, the rational polynomial coefficients q1, q2, q3, q4, and q5 are obtained by fitting the trucksim simulation experiment, and μ ij Experience value.

[0040] In a preferred embodiment, in S1.3, the turning angles of the left and right wheels on the same axle of the front, middle and rear axles are the same, and the distances l from the front, middle and rear axles to the center of mass are measured. f 、l m 、l r And the wheel angles δ on the front, middle and rear axles f , δ m , δ r, substitute the following expression to calculate the tire side slip angle α of the left and right wheels on the front, middle and rear axles f , α m , α r ;

[0041]

[0042] In a preferred embodiment, in S2.1, the process of obtaining the arc length function is as follows:

[0043] Assume that the origin is the asymptotically stable equilibrium point of the heavy-load vehicle nonlinear system, and set Represents its domain of attraction, then the length element of the phase trajectory at time τ is defined as:

[0044]

[0045] Where: dx i (τ) = f i ((x(τ)))dτ;

[0046] For any point x(t)∈Ω, the arc length function of the heavy-duty vehicle nonlinear system is expressed as L(x(t)) and is expressed as follows:

[0047]

[0048] The nonlinear system of the heavy-load vehicle is at the origin at time t, so the phase trajectory length is zero at any time, that is,

[0049] L(0)=0

[0050] Derive the derivative of the arc length function:

[0051]

[0052] Where:

[0053] In a preferred embodiment, the arc length function L(x(t)) represents the sum of the length differential elements on the phase trajectory curve from τ = t to τ = ∞;

[0054] The arc length function is a positive definite function, and its derivative is a negative definite function.

[0055] In a preferred embodiment, the arc length function is approximated as a Lyapunov function in Ω.

[0056] In a preferred embodiment, the arc length function approximates the H(V) associated with its quadratic term coefficient and time derivative. n (x)) and A symmetric matrix satisfies the following constraints:

[0057] The real part of the eigenvalue of H(V(x)) is positive definite;

[0058] The real part of the eigenvalue of is negative;

[0059] After root test, V and There are no other roots around the origin.

[0060] Beneficial effects of the present invention:

[0061] By constructing a precise dynamic model, the vehicle's motion characteristics under different working conditions are reflected; the arc-length function is used to estimate the Lyapunov function and construct the attraction domain; the size of the attraction domain is determined by optimization methods, and thus the stability domain is estimated, and the stability limit boundary can be obtained to guide the development and design of the stability control system; further targeting the new chassis configuration of modular distributed electric drive heavy-duty vehicles, new possibilities are provided for its performance optimization, fully activating the full potential of the new modular distributed electric drive configuration, and achieving accurate estimation of the stability domain under different vehicle speeds, different road adhesion coefficients, different three-axle tire angles and different direct yaw moment conditions, providing guarantee for the driving stability of modular distributed electric drive heavy-duty vehicles. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a flow chart of the stability region estimation based on the arc length function of the present invention.

[0063] Figure 2 Schematic diagram of the modular distributed electric drive three-axle heavy-load vehicle dynamics model established for the present invention.

[0064] Figure 3 Schematic diagram of tire fitting results based on rational polynomials.

[0065] Figure 4 Schematic diagram of the results before fitting the Lyapunov function estimated based on the arc length function.

[0066] Figure 5 Schematic diagram of the results of fitting the Lyapunov function estimated based on the arc length function.

[0067] Figure 6 A comparison chart of the stability domain estimation results of a modular distributed electric drive heavy-load vehicle under different vehicle speed conditions.

[0068] Figure 7 A comparison chart of the stability domain estimation results of a modular distributed electric drive heavy-load vehicle under different road adhesion conditions.

[0069] Figure 8 A comparison chart of the stability domain estimation results of a modular distributed electric drive heavy-load vehicle under different front wheel turning angle conditions. DETAILED DESCRIPTION

[0070] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0071] like Figure 1 The method for estimating the stability region of a modular distributed electric drive heavy-load vehicle based on an arc length function includes the following steps:

[0072] S1. Establish an integrated model. Considering the characteristics of the all-wheel steering system, introduce the dynamic analysis of the hub motor, and establish a modular distributed electric drive heavy-duty vehicle dynamic model. By introducing the rational polynomial approximation method to parameterize the nonlinear characteristics of the tire, an explicit analytical expression for the lateral force is derived. Finally, a modular distributed electric drive heavy-duty vehicle dynamic model is established that integrates the rational polynomial characteristics of the tire. The specific process is as follows:

[0073] S1.1. Consider the characteristics of the all-wheel steering system and introduce the dynamic analysis of the hub motor to build a vehicle dynamics model:

[0074] Let i∈{f,m,r} represent the front, middle and rear axles of a three-axle heavy-duty vehicle, and j∈{l,r} represent the left and right wheels on the same axle. Then, we can obtain the vehicle mass m and the distance l from the corresponding axle to the center of mass of the heavy-duty vehicle. i 、Wheelbase b w , wheel angle δ of the corresponding axis i , vehicle longitudinal speed v x , vehicle lateral speed v y , the vehicle yaw angular velocity γ, and establish a three-degree-of-freedom dynamic model of a modular distributed electric drive three-axle heavy-duty vehicle, including the longitudinal, lateral and yaw degrees of freedom, such as Figure 2 As shown, the dynamic equations of the vehicle dynamics model are as follows:

[0075]

[0076] Where: is the derivative of the vehicle's longitudinal velocity, is the derivative of the vehicle's lateral velocity, is the derivative of the vehicle's yaw rate, F xij is the corresponding tire longitudinal force, F yij is the corresponding tire lateral force, I z is the vehicle's moment of inertia, M z is the direct yaw moment.

[0077] S1.2. Introduce rational polynomials to approximate tire nonlinear characteristics and fit the tire lateral force F yij :

[0078]

[0079] Where: F zijis the vertical load on the tire, μ ij is the road adhesion coefficient corresponding to the ground contacted by the tire, q1, q2, q3, q4, q5 are the rational polynomial coefficients in the fitted tire model, α ij is the side slip angle of the corresponding tire.

[0080] The rational polynomial coefficients q1, q2, q3, q4, and q5 are obtained by fitting the trucksim simulation experiment, and μ ij Empirical values can be obtained by estimation.

[0081] By variable substitution, n ij and d ij They represent the numerator and denominator in the tire lateral force formula respectively.

[0082] S1.3, Based on the rational polynomial model and F yij , derive and calculate α ij :

[0083]

[0084] Where: β represents the sideslip angle of the vehicle's center of mass.

[0085] Since the left and right wheels on the same axle have the same turning angle, the distance l from the front, middle and rear axles to the center of mass is measured. f 、l m 、l r And the wheel angles δ on the front, middle and rear axles f , δ m , δ r , substitute the following expression to calculate the tire side slip angle α of the left and right wheels on the front, middle and rear axles f , α m , α r ;

[0086]

[0087] S1.4, simultaneous equations (1)-(3), combine the rational polynomial tire model with the vehicle dynamics model to obtain a modular distributed electric drive heavy-duty vehicle dynamics model that integrates the rational polynomial characteristics of the tire:

[0088]

[0089] in:

[0090]

[0091] D(x,u)=d f d m d r (6)

[0092] Where: state quantity x = [βγ] T , control input u=[δ f δ m δ r M z ] T .

[0093] S2. Use the arc length function to construct the Lyapunov function. The process is as follows:

[0094] S2.1. Define the arc length function: Assuming the origin is the asymptotically stable equilibrium point of the heavy-load vehicle nonlinear system, the arc length function L(x(t)) is defined as:

[0095]

[0096] Where: f(x(t)) is the state equation of the heavy-duty vehicle nonlinear system at time t;

[0097] Assume that the origin is the asymptotically stable equilibrium point of the heavy-load vehicle nonlinear system, and set Represents its domain of attraction, then the length element of the phase trajectory at time τ is defined as:

[0098]

[0099] Where: dx i (τ) = f i ((x(τ)))dτ.

[0100] For any point x(t)∈Ω, the arc length function of the heavy-duty vehicle nonlinear system is represented by L(x(t)). The arc length function L(x(t)) represents the sum of the length differential elements on the phase trajectory curve from τ=t to τ=∞, and the expression is as follows:

[0101]

[0102] From the system definition of formula (4), it can be seen that if the heavy-load vehicle nonlinear system is at the origin at time t, then the phase trajectory length is zero at any time, that is,

[0103] L(0)=0(9)

[0104] According to equations (4), (7), and (8), the derivative of the arc length function can be written as:

[0105]

[0106] Where: From formula (10), we can see that the arc length function is a positive definite function, and it can also be proved that its derivative is negative definite.

[0107]

[0108] Therefore, assuming x(t) = 0 and Δt → 0, we can obtain:

[0109]

[0110] Since the partial derivative of f(·) in Equation (4) exists and is continuous, according to Equations (42) and (12), we can conclude that the arc-length function is also a continuous derivative function. Furthermore, from Equations (9), (10), and (12), we can conclude that the arc-length function is a Lyapunov function in Ω.

[0111] Assume that the system state x∈Ω can be initialized at t=0. For each c greater than 0, the equal-length set is defined as follows:

[0112] Γ c ={x∈Ω|L(x)=c}(13)

[0113] That is: equal length set Γ c is the set of state points whose arc length function is c.

[0114] Based on this, we propose the theorem: In the system proposed by formula (4), for any bounded c that satisfies c>0, the equal-length set Γ c Not null.

[0115] The proof is as follows: Assume yes The maximum bounded value of . Since the origin is asymptotically stable, And there is a Make Γ c Not empty. Since the system has only one equilibrium point in Ω and is consistent with formula (12), for each The state satisfies L(x(t))=c. At the same time, for any state satisfying t1<t, x(t1)≠x(t), the following relationship exists:

[0116]

[0117] Since f(x(τ))=0,(x(t1))>c, Not satisfied The maximum bounded value of , so for any bounded c greater than 0, the equal-length sets Not empty. The maximal Lyapunov function converges the arc-length function to infinity by approximating the boundary of the region of attraction. Based on this fact, and considering that the arc-length function is a Lyapunov function, it can be found that the arc-length function inherits all the properties of the maximal Lyapunov function. Based on this problem and the characteristics of the maximal Lyapunov function, the arc-length function can represent a larger region of attraction for dynamic nonlinear systems.

[0118] The above arc length function is estimated by numerical methods. For this purpose, two procedures are considered. In the first procedure, the arc length function of all considered state points is calculated by discretizing the system described by equation (4) and equation (10), which are the nodes of the grid around the origin. This procedure is the main process of assigning length attributes to state space points using numerical methods. In the next step, the parameter model is approximated by the least squares (LS) method using the set of state points and their corresponding lengths. As can be seen from the above, the arc length function is a kind of maximal Lyapunov function. In order to use the Lyapunov function, a polynomial form with a certain degree like V(x) is used as a truncated structure of the rational function. Since there is no prior knowledge about the correct degree of the arc length function, the approximate arc length function must satisfy the following three constraints:

[0119] The real part of the eigenvalue of H(V(x)) is positive definite; it ensures that V has a certain positive area around the origin;

[0120] The real part of the eigenvalue of is negative; ensure It has a certain negative area around the origin;

[0121] After the root test using the homotopy concept, V and There are no other roots around the origin.

[0122] Then calculate the arc length function. First initialize the parameters Δt, Δx, t max , r0, represents the distance between each grid point, and is the maximum time threshold for ignoring trajectories that do not approach the origin within a certain time. The minimum distance threshold is used to terminate the length calculation process of a certain state and discretize the system using the step time. The required calculation accuracy and speed are adjusted by controlling the parameters (Δx and Δt). Since the approach of the edge of the attraction domain will lead to the concentration of the length profile of the similar trajectory, Δx and Δt are reduced by constructing the distance from the origin. In this regard, the initialized Δx decreases radially, and Δt is defined as:

[0123] Where: p = x T x is the radial distance of the state, and p0 is the threshold distance.

[0124] Then, by performing a simple search within the desired region around the equilibrium point, all expected points with trajectory paths that enter the origin are detected, and the corresponding lengths with respect to the selected point are calculated. All points within the estimated attraction domain then have length properties. Therefore, contours of equal length can be displayed based on these properties. By performing a simple least squares fit on these contours and considering L(0) = 0, an arc length function can be derived for the system as an estimate of the Lyapunov function.

[0125] To do this, consider a polynomial function that contains no linear terms.

[0126] As mentioned above, the iterative arc length function can eventually select a maximized attraction domain. The steps are as follows: First, set the initialization parameters, such as the maximum and minimum orders of the polynomial, the initial region, and the initial hypervolume. For each approximate arc length function that meets the requirements, calculate the H(V) related to its quadratic term coefficient and time derivative. n (x)) and Symmetric matrix. A root check is then performed to verify that the origin is relative to V n The isolation of the function is then determined using the Bertini solver to generate points that are connected to form visual curves and surfaces. Bertini_real is then used to ensure that the candidate function and its derivatives have no roots around the origin except the equilibrium point itself. The corresponding hypervolume is then calculated and saved, and the approximate V n (x) Estimate the attraction domain. Finally, the arc length function with the largest hypervolume will be selected from the candidate functions.

[0127] S2.2. Construct the Lyapunov function and use the arc length function as the Lyapunov function V(x), which is expressed as:

[0128] V(x)=L(x)

[0129] Khalil and Grizzle proposed the following theorem in 1996:

[0130] A closed set containing the origin as an equilibrium point is The domain of attraction of the origin of the system can be approximated, and if the equilibrium point is non-zero, it can be used Instead, It is a non-zero equilibrium point;

[0131] 1. The constant set Ω of the system;

[0132] 2. For all x that satisfies x∈Ω except x=0, we can find a positive definite function V(x) such that It is negatively definite.

[0133] The sublevel set V(c) of the Lyapunov function V(x) can be defined as

[0134] V(c)={x∈X:0≤V(x)≤c} (15)

[0135] According to the above theorem, if the derivative of the Lyapunov function is everywhere negative in the sublevel set, then any sublevel set of candidate Lyapunov functions that satisfies the local asymptotic stability of the equilibrium point can be an estimate of the attraction domain. However, this theorem only gives an estimate of the attraction domain, which can actually be much larger than Ω. The theorem does not provide information on how to choose or create the Lyapunov function V(x).

[0136] Therefore, in the present invention, the arc length function is used to estimate the Lyapunov function. From formula (15), it can be seen that the larger the level set c is, the better the attraction domain is estimated. Therefore, by solving a nonlinear constrained optimization problem to estimate the domain of attraction. The constraints are as follows: c>0. The estimated attraction domain is the stability domain of the modular distributed electric drive heavy-duty vehicle under this working condition, and ultimately the estimation of the stability domain of the heavy-duty vehicle is achieved.

[0137] Specifically, refer to the following process: S3, construct the attraction domain and estimate the stability domain. The attraction domain is estimated using the Lyapunov function method. For the heavy-duty vehicle dynamics system under study, if x* is the stable equilibrium point of the closed-loop system, and x(t,x0) represents the solution of the system under these initial conditions at time t, then the attraction domain can be defined as:

[0138]

[0139] S3.1. Construct the attraction domain D through the Lyapunov function and regard it as a stable domain. The attraction domain D represents the set of all initial states that can converge to the equilibrium point:

[0140]

[0141] S3.2. Optimization Problem Solving: Solve a nonlinear constrained optimization problem To estimate the domain of attraction, the constraints are as follows:

[0142]

[0143] Where c represents the level set parameter. The larger the level set, the better the estimation of the attraction domain.

[0144] S3.3. Input the independent variables including vehicle speed, road adhesion coefficient, three-axis tire angle and direct yaw moment, and estimate the attraction domain under the corresponding working condition, which is equivalent to the stability domain of the modular distributed electric drive heavy-duty vehicle under this working condition, thereby realizing the estimation of the stability domain of the heavy-duty vehicle.

[0145] In the embodiment given in the present invention, the simulation experiment is carried out using TruckSim software to fit the vertical load F zij The fitting results of the rational polynomial coefficients and the magic tire formula are as follows: Figure 3 shown.

[0146] Figure 4 and Figure 5 An example of the Lyapunov function constructed using the arc length function mentioned in the present invention is given. Figure 4 are the discrete points before fitting, Figure 5 is the continuous Lyapunov function after fitting.

[0147] Reference Figure 6 The comparative results in this figure illustrate the impact of different vehicle speeds on the stability region of a modular distributed electric heavy-duty vehicle, as determined using the stability region estimation algorithm proposed in this paper. The results show that as the vehicle speed increases from 10 m / s to 20 m / s, the stability region decreases.

[0148] Reference Figure 7 The comparative results in this figure describe the impact of different road adhesion coefficients on the stability range of modular distributed electric drive heavy-duty vehicles. The results show that as the road adhesion coefficient gradually increases from 0.6 to 1.0, the stability range gradually increases;

[0149] Reference Figure 8 The comparative results in this figure illustrate the impact of different front wheel steering angles on the stability domain of a modular distributed electric heavy-duty vehicle. The results show that as the front wheel steering angles change (-10°, 0°, and 10°), the stability domain is not completely centrosymmetrical and exhibits a certain degree of offset.

[0150] In summary, the following conclusions are drawn for the estimation of the stability domain of modular distributed electric heavy-duty vehicles based on arc length function:

[0151] At high speeds, a vehicle is more susceptible to external disturbances and may lose stability. As speed increases, the stability range decreases. A high adhesion coefficient provides greater grip, making it easier for the vehicle to maintain stability. As the road adhesion coefficient increases, the stability range increases. Large front wheel angles increase the vehicle's tendency to skid, and changes in front wheel angle can cause the stability range to shift. Appropriate yaw moment can improve vehicle stability, but excessive yaw moment can lead to instability.

[0152] Through the above steps, the stability domain estimation under different vehicle speeds, different road adhesion coefficients, different three-axle wheel angles, and different direct yaw moment conditions is achieved, providing guarantee for the driving stability of modular distributed electric drive heavy-duty vehicles.

[0153] The preferred embodiments of the present invention are described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the scope of protection of the present invention.

Claims

1. A modular distributed electric drive heavy-load vehicle stability region estimation method based on arc length function, characterized by: The following steps are involved: S1. Establish an integrated model. The process is as follows: S1.

1. Construct a vehicle dynamics model: Let i∈{f,m,r} represent the front, middle, and rear axles of a three-axle heavy-duty vehicle, and j∈{l,s} represent the left and right wheels on the same axle. Obtain the vehicle mass m and the distance l from the corresponding axle to the center of mass of the heavy-duty vehicle. i 、Wheelbase b w , wheel angle δ of the corresponding axis i , vehicle longitudinal speed v x , vehicle lateral speed v y , the vehicle yaw angular velocity γ, and the three-degree-of-freedom dynamic model of the modular distributed electric drive three-axle heavy-duty vehicle is established. Its dynamic equations are as follows: M z =b w ∑(F xil cosδ i -F yil sinδ i +F xis cosδ i -F yis sinδ i ) Where: is the derivative of the vehicle's longitudinal velocity, is the derivative of the vehicle's lateral velocity, is the derivative of the vehicle's yaw rate, F xij is the corresponding tire longitudinal force, F yij is the corresponding tire lateral force, I z is the vehicle's moment of inertia, M z is the direct yaw moment; S1.

2. Introduce rational polynomials to approximate tire nonlinear characteristics and fit the tire lateral force F yij : Where: F zij is the vertical load on the tire, μ ij is the road adhesion coefficient corresponding to the ground contacted by the tire, q1, q2, q3, q4, q5 are the rational polynomial coefficients in the fitted tire model, α ij is the tire slip angle of the corresponding tire; n ij and d ij Respectively represent the numerator and denominator in the tire lateral force formula; S1.3, Based on the rational polynomial model and F yij , derive and calculate α ij : Where: β represents the vehicle's center of mass sideslip angle; S1.

4. Combining the rational polynomial tire model with the vehicle dynamics model yields a modular distributed electric drive heavy-duty vehicle dynamics model that integrates the rational polynomial characteristics of the tire: in: D(x,u)=d f d m d r Where: state quantity x = [β γ] T , control input u=[δ f δ m δ r M z ] T ; S2. Use the arc length function to construct the Lyapunov function. The process is as follows: S2.

1. Define the arc length function: Assuming the origin is the asymptotically stable equilibrium point of the heavy-load vehicle nonlinear system, the arc length function L(x(t)) is defined as: Where: f(x(t)) is the state equation of the heavy-duty vehicle nonlinear system at time t; S2.

2. Construct the Lyapunov function and use the arc length function as the Lyapunov function V(x), which is expressed as: V(x)=L(x) S3. Construct the attraction domain and estimate the stability domain. The process is as follows: S3.

1. Construct the attraction domain D through the Lyapunov function and regard it as a stable domain. The attraction domain D represents the set of all initial states that can converge to the equilibrium point: S3.

2. Optimization Problem Solving: Solve a nonlinear constrained optimization problem To estimate the domain of attraction, the constraints are as follows: Where c represents the level set parameter. The larger the level set, the better the estimation of the attraction domain. S3.

3. Input the independent variables including vehicle speed, road adhesion coefficient, three-axis tire angle and direct yaw moment, and estimate the attraction domain under the corresponding working condition, which is equivalent to the stability domain of the modular distributed electric drive heavy-duty vehicle under this working condition, thereby realizing the estimation of the stability domain of the heavy-duty vehicle.

2. The arc-length function-based modular distributed electric drive heavy-duty vehicle stability region estimation method according to claim 1, characterized in that: The vehicle dynamics model established in S1.1 includes three degrees of freedom: longitudinal, lateral, and yaw. When constructing the vehicle dynamics model, the characteristics of the all-wheel steering system are considered, and the hub motor dynamics analysis is introduced.

3. The arc-length function-based modular distributed electric heavy-duty vehicle stability region estimation method according to claim 1, characterized in that: In S1.2, the rational polynomial coefficients q1, q2, q3, q4, and q5 are obtained by fitting the trucksim simulation experiment, and μ ij Experience value.

4. The arc-length function-based modular distributed electric heavy-duty vehicle stability region estimation method according to claim 1, characterized in that: In S1.3, the left and right wheels on the same axle of the front, center, and rear axles have the same turning angle. Measure the distance l from the front, center, and rear axles to the center of mass. f 、l m 、l r And the wheel angles δ on the front, middle and rear axles f , δ m , δ r , substitute the following expression to calculate the tire side slip angle α of the left and right wheels on the front, middle and rear axles f , α m , α r ; 5. The method for estimating the stability region of a modular distributed electric heavy-duty vehicle based on an arc length function according to claim 1, characterized in that: In S2.1, the process of obtaining the arc length function is as follows: Assume that the origin is the asymptotically stable equilibrium point of the heavy-load vehicle nonlinear system, and set Represents its domain of attraction, then the length element of the phase trajectory at time τ is defined as: where: dx i τ) = f i ((x(τ))) dτ; For any point x(t)∈Ω, the arc length function of the heavy-duty vehicle nonlinear system is expressed as L(x(t)) and is expressed as follows: The nonlinear system of the heavy-load vehicle is at the origin at time t, so the phase trajectory length is zero at any time, that is, L(0)＝0 Derive the derivative of the arc length function: Where:

6. The arc-length function-based modular distributed electric heavy-duty vehicle stability region estimation method according to claim 5, characterized in that: The arc length function L(x(t)) represents the sum of the length differential elements on the phase trajectory curve from τ = t to τ = ∞; The arc length function is a positive definite function, and its derivative is a negative definite function.

7. The arc-length function-based modular distributed electric heavy-duty vehicle stability region estimation method according to claim 6, characterized in that: The arc length function is approximated by a Lyapunov function in Ω.

8. The arc-length function-based modular distributed electric heavy-duty vehicle stability region estimation method according to claim 7, characterized in that: The approximate arc length function calculates H(V) related to its quadratic term coefficient and time derivative n (x)) and A symmetric matrix satisfies the following constraints: The real part of the eigenvalue of H(V(x)) is positive definite; The real part of the eigenvalue of is negative; After root test, V and There are no other roots around the origin.

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