Stability domain estimation method for modular distributed electrically-driven heavy-load vehicle

Abstract

A stability domain estimation method for a modular distributed electric drive heavy-load vehicle comprises the steps that vehicle all-wheel steering and hub motor driving characteristics are considered, a modular distributed electric drive heavy-load vehicle dynamic model is constructed, a tire nonlinear model is fitted through a rational polynomial, a tire lateral force analytical expression is obtained, and a stability domain estimation result is obtained; constructing a modular distributed electrically-driven heavy-load vehicle dynamic model based on a rational polynomial; converting a positive definite problem of a dynamic rational polynomial function of the modular distributed electrically-driven heavy-load vehicle into a quadratic sum planning problem by utilizing a generalized S-process theory and a quadratic sum planning method; a V-s iterative algorithm is designed, the problem of solving a bilinear matrix inequality is solved, and based on a Lyapunov method and a nonlinear dynamics theory, the dynamic stability domain of the modular distributed electrically-driven heavy-load vehicle is estimated and optimized. Accurate estimation of the stability domain of the modular distributed electrically-driven heavy-load vehicle under different vehicle speeds, road adhesion coefficients, front / middle / rear wheel turning angles and direct yawing moments is achieved.

Description

Technical Field

[0001] The present invention relates to the field of vehicle system dynamics and control, and in particular to a stability domain estimation method for a modular distributed electric drive heavy-duty vehicle. Background Art

[0002] Heavy-duty vehicles are key to ensuring the deployment of large-scale equipment in national defense, military industry, aerospace, and other industries, and supporting the transportation of large equipment in mining, metallurgy, petrochemicals, and other industries. Therefore, heavy-duty vehicles are a major weapon of a country that is related to the national economy, people's livelihood, and national defense security. However, heavy-duty vehicles have a large load and a high center of mass. Once they are in dangerous conditions such as rollover, entrapment, and instability, rescue is difficult and costly, which seriously affects the transportation efficiency and driving stability of heavy-duty vehicles.

[0003] In the existing heavy-duty vehicle chassis configuration, all wheel power is transmitted through the central drive shaft, which has a complex structure and low transmission efficiency. At the same time, the steering movement of the wheels on both sides of the same axle is constrained by the tie rod, and the Ackerman steering trapezoid seriously restricts the maneuverability of heavy-duty vehicles, and the freedom of movement is severely limited. Therefore, the carrying capacity of heavy-duty vehicles based on the traditional fixed configuration has reached the bottleneck of mechanical structure constraints. The modular distributed electric drive chassis adopts an innovative distributed multi-wheel direct drive configuration. Compared with the chassis structure of the traditional fixed configuration, the drive shaft is eliminated longitudinally and the tie rod is eliminated laterally, releasing all the freedom of movement of the heavy-duty vehicle chassis, which can help heavy-duty vehicles break through the upper limit of their mobility and improve their handling performance. So, how to give full play to the potential advantages of the modular distributed electric drive configuration and ensure the driving stability of heavy-duty vehicles is a hot issue that needs to be solved urgently.

[0004] Therefore, the stability criterion of heavy-duty vehicles, namely the estimation of the dynamic stability domain, needs to be comprehensively renewed and reconstructed according to the modular distributed electric drive configuration to guide and guarantee the development and design of the stability control system of modular distributed electric drive heavy-duty vehicles. 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, to construct a nonlinear dynamic model of modular distributed electric drive heavy-duty vehicles according to the all-wheel steering characteristics, to estimate and optimize the stability domain of modular distributed electric drive heavy-duty vehicles based on the Lyapunov nonlinear method and the square sum programming theory, to obtain the stability limit boundary, and to guide the development and design of the stability control system.

[0006] In order to solve the above technical problems, the present invention provides a stability domain estimation method for a modular distributed electric drive heavy-duty vehicle, comprising the following steps:

[0007] 1. Considering the vehicle's all-wheel steering and hub motor drive characteristics, a modular distributed electric drive heavy-load vehicle dynamics model is constructed. The tire nonlinear model is fitted with rational polynomials to obtain the analytical expression of the tire lateral force. Finally, a modular distributed electric drive heavy-load vehicle dynamics model based on rational polynomials is constructed.

[0008] 2. Using the generalized S-procedure theory and the sum-of-squares programming method, the positive definite problem of rational polynomial function of modular distributed electric drive heavy-duty vehicle dynamics is transformed into a sum-of-squares programming problem.

[0009] 3. Design a Vs iterative algorithm to solve the problem of solving bilinear matrix inequalities. Based on the Lyapunov method and nonlinear dynamics theory, estimate and optimize the stability domain of modular distributed electric drive heavy-load vehicle dynamics, and accurately estimate the stability domain of modular distributed electric drive heavy-load vehicles under different vehicle speeds, road adhesion coefficients, front / middle / rear wheel angles and direct yaw moments.

[0010] Furthermore, in step 1, considering the vehicle's all-wheel steering and wheel hub motor drive characteristics, the modular distributed electric drive heavy-duty vehicle dynamics model is constructed, including the following contents:

[0011] According to Newton's laws of motion, considering the all-wheel steering and wheel hub motor drive characteristics, taking a three-axle heavy-duty vehicle as an example, the dynamic equations of the three degrees of freedom of longitudinal, lateral and yaw can be obtained, as follows: Figure 2 shown.

[0012]

[0013] Among them, ●∈{f,m,r} represents the front, middle and rear axles, ◇∈{l,r} represents the left and right wheels, m represents the vehicle mass, v x represents the longitudinal velocity of the center of mass, γ represents the vehicle yaw rate, v y is the lateral velocity of the center of mass, F x·◇ Indicates the longitudinal force of the shaft and wheel, F y·◇ Indicates the lateral force of the shaft and wheel, I z represents the vehicle's moment of inertia, l · Indicates the wheelbase of the axle, b w Indicates wheelbase, M z represents the direct yaw moment.

[0014] The tire lateral force is generally obtained by fitting the tire lateral force and the tire sideslip angle data. Commonly used tire models include the magic tire formula, the Fiala tire formula, etc. The method of the present invention is to construct a rational polynomial and fit the tire lateral force-tire sideslip angle data by a nonlinear least squares method.

[0015]

[0016] Among them, F z·◇ is the vertical load of the shaft and wheel, μ ·◇ is the road adhesion coefficient of the axle and wheel, α ·◇ is the wheel slip angle, q1, q2, q3, q4, q5 are the fitting coefficients of the rational polynomial, and for simplicity, the numerator and denominator of the tire lateral force are replaced by variables n ·∑ and d ·◇ .

[0017] Using the measured data in TruckSim software, the fitting results based on rational polynomials and the magic tire formula are given under vertical loads of 7.4 kN, 14.7 kN, and 29.4 kN, as shown in the figure. Figure 3 shown.

[0018] We give the expression of tire slip angle as follows:

[0019]

[0020] Among them, α f , α m , α r are the tire slip angles of the front, middle and rear wheels respectively, and β is the vehicle’s center of mass slip angle.

[0021] According to equations (1)-(3), a modular distributed electric drive heavy-duty vehicle dynamics model based on rational polynomials can be constructed:

[0022]

[0023] in,

[0024]

[0025] D(x,u)=d f d m d r (18)

[0026] Where x = [βγ] T is the state variable, u=[δ f δ m δ r M z ] T is the control input.

[0027] Furthermore, in step 2, the generalized S-procedure theory and the sum-of-squares programming method are used to transform the positive definite problem of the rational polynomial function of the modular distributed electric drive heavy-duty vehicle dynamics into a sum-of-squares programming problem.

[0028] First, the definition of the generalized S-procedure is given. Its purpose is to transform some non-convex constraints into linear matrix inequality constraints. N}, if there exists {s1,s2,...,s N}∈S x Make So

[0029]

[0030] Secondly, the definition of the sum of squares is given. Its purpose is to transform a polynomial sum of squares problem into a feasibility problem of linear matrix inequalities. For a multivariate polynomial p(x) with n real variables, where x is a component {x1,x2,...,x n}. If there exists a polynomial f i (x) such that: Then the multivariate polynomial p(x) is called a sum of squares. So, if p(x) is a sum of squares, it can be written as

[0031]

[0032] Among them, Q0>0 is the Gram matrix. Therefore, if there is λ i Make Then p(x) is the sum of squares, which is a linear matrix inequality feasibility problem.

[0033] According to Lyapunov stability theory, for autonomous nonlinear systems x is the state vector, and f is the local Lipschitz function that describes the system dynamics. The local stability condition of the system is that there exists a continuously differentiable function V such that the following two conditions hold: (1) for all x≠0, V(x)>0 and V(0)=0; (2) Right now In addition, if Then the equilibrium point is locally asymptotically stable.

[0034] According to the theory of attraction domain of nonlinear systems, it is assumed that γ>0 and there exists a continuous differentiable function V such that: (1) for all x≠0, V(x)>0 and V(0)=0; (2) is bounded; (3) Then, for all x0∈Μ V,γ , the solution ξ(x0,t) of the nonlinear system exists on [0,∞], and for t≥0, Μ V,γ is the invariant set of the attraction domain of the nonlinear system at the equilibrium point.

[0035] According to the above theory, a modular distributed electric drive heavy-duty vehicle stability domain estimation method is constructed based on the nonlinear dynamic system (4).

[0036] For the rational polynomial modular distributed electric drive heavy-duty vehicle dynamics system (4), that is, The stability region around its equilibrium point can be estimated by finding the Lyapunov function V that maximizes β, namely:

[0037] max β (21)

[0038]

[0039] q1(x)(s(x)-β)-(V(x)-γ)∈∑[x] (23)

[0040]

[0041] Constraint (10) satisfies the stability condition of the Lyapunov function, ensuring the positive definiteness of V(x); in constraint (11), s(x) is a given shape function, ensuring Constraint (12) Force Negative determination.

[0042] Furthermore, in step 3, a Vs iteration algorithm is designed to solve the bilinear matrix inequality problem, estimate and optimize the stability domain of the modular distributed electric drive heavy-duty vehicle dynamics, including the following:

[0043] The process of solving bilinear matrix inequality by Vs iteration method is as follows:

[0044] (4) Step γ: Initialize V and maximize γ by finding q2(x) such that constraint (12) holds.

[0045] (5) β step: Keep V, γ, and q2(x) fixed and maximize β by finding q1(x) such that constraint (11) holds;

[0046] (6) Step V: Keep γ, β, q1(x), q2(x) fixed, and find V such that (10)-(12) hold.

[0047] The above steps can be programmed through the free open source mathematical optimization toolbox YALMIP and the solver MOSEK to obtain the stability domain of the modular distributed electric drive heavy-duty vehicle under different vehicle speeds, road adhesion coefficients, front / middle / rear wheel angles and direct yaw moments.

[0048] Beneficial effects of the present invention: The present invention is aimed at the new chassis configuration of modular distributed electric drive heavy-duty vehicles, and uses Lyapunov stability theory, nonlinear system theory, square sum programming theory and Vs iterative solution of bilinear matrix inequality method to invent a stability domain estimation method, which can realize stability domain estimation under different vehicle speeds, road adhesion coefficients, front / middle / rear wheel angles and direct yaw moments, and guide and guarantee the development and design of modular distributed electric drive heavy-duty vehicle stability control system. In addition, the modular distributed electric drive heavy-duty vehicle stability domain estimation method of the present invention can be applied in the fields of aerospace and power systems, and has good cross-industry application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is a flow chart of the stability region estimation of the present invention;

[0050] Figure 2 It is a modular distributed electric drive all-wheel steering three-axle heavy-load vehicle dynamics model established by the present invention;

[0051] Figure 3 It is the tire fitting result based on rational polynomial;

[0052] Figure 4 It is the estimation result of the stability domain of modular distributed electric drive heavy-load vehicle at different vehicle speeds;

[0053] Figure 5 It is the estimation result of the stability domain of modular distributed electric drive heavy-duty vehicle under different road adhesion;

[0054] Figure 6 It is the stability domain estimation result of the modular distributed electric drive heavy-load vehicle under different front wheel turning angles. DETAILED DESCRIPTION

[0055] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0056] Figure 1The present invention is a stability domain estimation flow chart, which includes three parts: first, considering the vehicle's all-wheel steering and hub motor driving characteristics, constructing a modular distributed electric drive heavy-load vehicle dynamics model, fitting the tire nonlinear model through rational polynomials, obtaining the tire lateral force analytical expression, and finally constructing a modular distributed electric drive heavy-load vehicle dynamics model based on rational polynomials; second, using the generalized S-procedure theory and the square sum planning method, the positive definite problem of the rational polynomial function of the modular distributed electric drive heavy-load vehicle dynamics is converted into a square sum planning problem; third, designing a Vs iterative algorithm to solve the problem of solving bilinear matrix inequalities, based on the Lyapunov method and nonlinear dynamics theory, estimating and optimizing the stability domain of the modular distributed electric drive heavy-load vehicle dynamics, and realizing accurate estimation of the stability domain of the modular distributed electric drive heavy-load vehicle under different vehicle speeds, road adhesion coefficients, front / middle / rear wheel angles and direct yaw moments.

[0057] First, considering the vehicle's all-wheel steering and wheel hub motor drive characteristics, the construction of a modular distributed electric drive heavy-duty vehicle dynamics model includes the following:

[0058] According to Newton's laws of motion, considering the all-wheel steering and wheel hub motor drive characteristics, taking a three-axle heavy-duty vehicle as an example, the dynamic equations of the three degrees of freedom of longitudinal, lateral and yaw can be obtained, as follows: Figure 2 shown.

[0059]

[0060] Among them, ·∈{f,m,r} represents the front, middle and rear axles, ·◇∈{l,r} represents the left and right wheels, m represents the vehicle mass, v x represents the longitudinal velocity of the center of mass, γ represents the vehicle yaw rate, v y is the lateral velocity of the center of mass, F x·◇ Indicates the longitudinal force of the shaft and wheel, F y·◇ Indicates the lateral force of the shaft and wheel, I z represents the vehicle's moment of inertia, l · Indicates the wheelbase of the axle, b w Indicates wheelbase, M z represents the direct yaw moment.

[0061] The tire lateral force is generally obtained by fitting the tire lateral force and the tire sideslip angle data. Commonly used tire models include the magic tire formula, the Fiala tire formula, etc. The method of the present invention is to construct a rational polynomial and fit the tire lateral force-tire sideslip angle data by a nonlinear least squares method.

[0062]

[0063] Among them, Fz·◇ is the vertical load of the shaft and wheel, μ ·◇ is the road adhesion coefficient of the axle and wheel, α ·◇ is the wheel slip angle, q1, q2, q3, q4, q5 are the fitting coefficients of the rational polynomial, and for simplicity, the numerator and denominator of the tire lateral force are replaced by variables n ·◇ and d ·◇ .

[0064] Using the measured data in TruckSim software, the fitting results based on rational polynomials and the magic tire formula are given under vertical loads of 7.4 kN, 14.7 kN, and 29.4 kN, as shown in the figure. Figure 3 shown.

[0065] We give the expression of tire slip angle as follows:

[0066]

[0067] Among them, α f , α m , α r are the tire slip angles of the front, middle and rear wheels respectively, and β is the vehicle’s center of mass slip angle.

[0068] According to equations (13)-(15), a modular distributed electric drive heavy-duty vehicle dynamics model based on rational polynomials can be constructed:

[0069]

[0070] in,

[0071]

[0072] D(x,u)=d f d m d r (30)

[0073] Where x = [βγ] T is the state variable, u=[δ f δ m δ r M z ] T is the control input.

[0074] Second, the generalized S-procedure theory and the sum-of-squares programming method are used to transform the positive definite problem of rational polynomial functions of modular distributed electric drive heavy-duty vehicle dynamics into a sum-of-squares programming problem.

[0075] First, the definition of the generalized S-procedure is given. Its purpose is to transform some non-convex constraints into linear matrix inequality constraints. N}, if there exists {s1,s2,...,s N}∈S x Make So

[0076]

[0077] Secondly, the definition of the sum of squares is given. Its purpose is to transform a polynomial sum of squares problem into a feasibility problem of linear matrix inequalities. For a multivariate polynomial p(x) with n real variables, where x is a component {x1,x2,...,x n}. If there exists a polynomial f i (x) such that: Then the multivariate polynomial p(x) is called a sum of squares. So, if p(x) is a sum of squares, it can be written as

[0078]

[0079] Among them, Q0>0 is the Gram matrix. Therefore, if there is λ i Make Then p(x) is the sum of squares, which is a linear matrix inequality feasibility problem.

[0080] According to Lyapunov stability theory, for autonomous nonlinear systems x is the state vector, and f is the local Lipschitz function that describes the system dynamics. The local stability condition of the system is that there exists a continuously differentiable function V such that the following two conditions hold: (1) for all x≠0, V(x)>0 and V(0)=0; (2) Right now In addition, if Then the equilibrium point is locally asymptotically stable.

[0081] According to the theory of attraction domain of nonlinear systems, it is assumed that γ>0 and there exists a continuous differentiable function V such that: (1) for all x≠0, V(x)>0 and V(0)=0; (2) is bounded; (3) Then, for all x0∈Μ V,γ , the solution ξ(x0,t) of the nonlinear system exists on [0,∞], and for t≥0, Μ V,γ is the invariant set of the attraction domain of the nonlinear system at the equilibrium point.

[0082] According to the above theory, a modular distributed electric drive heavy-duty vehicle stability domain estimation method is constructed based on the nonlinear dynamic system (16).

[0083] For the rational polynomial modular distributed electric drive heavy-duty vehicle dynamics system (16), The stability region around its equilibrium point can be estimated by finding the Lyapunov function V that maximizes β, namely:

[0084] max β (33)

[0085]

[0086] q1(x)(s(x)-β)-(V(x)-γ)∈∑[x] (35)

[0087]

[0088] Constraint (22) satisfies the stability condition of the Lyapunov function, ensuring the positive definiteness of V(x); in constraint (23), s(x) is a given shape function, ensuring Constraint (24) Force Negative determination.

[0089] Third, design the Vs iteration algorithm to solve the bilinear matrix inequality problem, estimate and optimize the stability domain of modular distributed electric drive heavy-duty vehicle dynamics, including the following:

[0090] The process of solving bilinear matrix inequality by Vs iteration method is as follows:

[0091] (1) Step γ: Initialize V and maximize γ by finding q2(x) such that constraint (24) holds.

[0092] (2) β step: keep V, γ, q2(x) fixed, and maximize β by finding q1(x) such that constraint (23) holds;

[0093] (3) Step V: Keep γ, β, q1(x), q2(x) fixed, and find V such that (22)-(24) hold.

[0094] The above steps can be programmed through the free open source mathematical optimization toolbox YALMIP and the solver MOSEK to obtain the stability domain of the modular distributed electric drive heavy-duty vehicle under different vehicle speeds, road adhesion coefficients, front / middle / rear wheel angles and direct yaw moments.

[0095] Figure 4The influence of vehicle speed change on the estimation of the stability domain of modular distributed electric drive heavy-duty vehicles is described. The results show that the stability domain gradually decreases with the increase of vehicle speed (10m / s, 15m / s, 20m / s).

[0096] Figure 5 The influence of the road adhesion coefficient change on the estimation of the stability domain of the modular distributed electric drive heavy-duty vehicle is described. The results show that with the increase of the road adhesion coefficient (μ=0.8, μ=1.0, μ=1.2), the stability domain gradually increases.

[0097] Figure 6 The influence of the front wheel steering angle change on the estimation of the stability domain of the modular distributed electric drive heavy-duty vehicle is described. The results show that with the change of the front wheel steering (-10°, 0°, 10°), the stability domain no longer expands proportionally and presents irregular changes. Among them, -10° and 10° are approximately symmetrical relative to the origin.

Claims

1. A stability region estimation method for modular distributed electric drive heavy-duty vehicles, characterized by: The following steps are involved: (1) Considering the vehicle's all-wheel steering and wheel hub motor drive characteristics, a modular distributed electric drive heavy-duty vehicle dynamics model is constructed. The tire nonlinear model is fitted with rational polynomials to obtain an analytical expression for the tire lateral force. Finally, a modular distributed electric drive heavy-duty vehicle dynamics model based on rational polynomials is constructed. (2) Using the generalized S-procedure theory and the sum-of-squares programming method, the positive definite problem of the rational polynomial function of modular distributed electric drive heavy-duty vehicle dynamics is transformed into a sum-of-squares programming problem; (3) Design a Vs iterative algorithm to solve the problem of solving bilinear matrix inequalities. Based on the Lyapunov method and nonlinear dynamics theory, estimate and optimize the stability domain of modular distributed electric drive heavy-duty vehicles, and accurately estimate the stability domain of modular distributed electric drive heavy-duty vehicles under different vehicle speeds, road adhesion coefficients, front / middle / rear wheel angles, and direct yaw moments.

2. The stability region estimation method for modular distributed electric drive heavy-duty vehicles according to claim 1 is characterized in that: In step (1), considering the vehicle's all-wheel steering and wheel hub motor drive characteristics, the modular distributed electric drive heavy-duty vehicle dynamics model is constructed, including the following contents: Establish the dynamic equations of the longitudinal, lateral and yaw degrees of freedom of a modular distributed electric drive three-axle heavy-duty vehicle Among them, ·∈{f,m,r} represents the front, middle and rear axles, ◇∈{l,r} represents the left and right wheels, m represents the vehicle mass, v x represents the longitudinal velocity of the center of mass, γ represents the vehicle yaw rate, v y is the lateral velocity of the center of mass, F x·◇ Indicates the longitudinal force of the shaft and wheel, F y·◇ Indicates the lateral force of the shaft and wheel, I z represents the vehicle's moment of inertia, l · Indicates the wheelbase of the axle, b w Indicates wheelbase, M z represents the direct yaw moment, δ · Indicates the wheel steering angle of the axis. The left and right wheel steering angles of the axis are the same. The lateral force of the tire is: Among them, F z·◇ is the vertical load of the shaft and wheel, μ ·◇ is the road adhesion coefficient of the axle and wheel, α ·◇ is the wheel slip angle, q1, q2, q3, q4, q5 are the fitting coefficients of the rational polynomial, and the numerator and denominator of the tire lateral force are replaced by variables n ·◇ and d ·◇ ; The expression of tire slip angle is as follows: Among them, α f , α m , α r are the tire slip angles of the front, middle and rear wheels respectively, and β is the vehicle’s center of mass slip angle; According to equations (1)-(3), a modular distributed electric drive heavy-duty vehicle dynamics model based on rational polynomials is constructed: in, D(x,u)=d f d m d r (6) Where x = [βγ] T is the state variable, u=[δ f δ m δ r M z ] T is the control input.

3. The stability region estimation method for modular distributed electric drive heavy-duty vehicles according to claim 2 is characterized in that: In step 2, the generalized S-procedure theory and the sum-of-squares programming method are used to transform the positive definite problem of the rational polynomial function of modular distributed electric drive heavy-duty vehicle dynamics into a sum-of-squares programming problem, including: First, we give the definition of the generalized S-procedure, which transforms the problem of non-convex constraints into linear matrix inequality constraints. For a given set {p0,p1,...,p N }, if there exists {s1,s2,...,s N }∈S x Make So Secondly, given the definition of the sum of squares, a polynomial sum of squares problem is transformed into a feasibility problem of linear matrix inequalities. For a multivariate polynomial p(x) with n real variables, where x is the component {x1, x2, ..., x n }, if there exists a polynomial f i (x) such that: Then the multivariate polynomial p(x) is called the sum of squares. So, if p(x) is the sum of squares, it can be written as Among them, Q0>0 is the Gram matrix, so if there is λ i Make Then p(x) is the sum of squares, which is a linear matrix inequality feasibility problem; According to Lyapunov stability theory, for autonomous nonlinear systems x is the state vector, f is the local Lipschitz function describing the system dynamics. The local stability condition of the system is that there exists a continuously differentiable function V such that the following two conditions hold: (1) for all x≠0, V(x)>0 and V(0)=0; (2) Right now In addition, if Then the equilibrium point is locally asymptotically stable; According to the theory of attraction domain of nonlinear systems, it is assumed that γ>0 and there exists a continuous differentiable function V such that: (1) for all x≠0, V(x)>0 and V(0)=0; (2) is bounded; (3) Then, for all x0∈Μ V,γ , the solution ξ(x0,t) of the nonlinear system exists on [0,∞], and for t≥0, Μ V,γ is the invariant set of the nonlinear system attraction domain at the equilibrium point, According to the above theory, a modular distributed electric drive heavy-duty vehicle stability domain estimation method is constructed based on the nonlinear dynamic system (4); For the rational polynomial modular distributed electric drive heavy-duty vehicle dynamics system (4), that is, The stability region around its equilibrium point can be estimated by finding the Lyapunov function V that maximizes β, namely: max β (9) q1(x)(s(x)-β)-(V(x)-γ)∈∑[x] (11) Constraint (10) satisfies the stability condition of the Lyapunov function, ensuring the positive definiteness of V(x); in constraint (11), s(x) is a given shape function, ensuring Constraint (12) Force Negative determination.

4. The stability region estimation method for modular distributed electric drive heavy-duty vehicles according to claim 3 is characterized in that: In step 3, the Vs iterative algorithm is designed to solve the bilinear matrix inequality problem, estimate and optimize the stability domain of the modular distributed electric drive heavy-duty vehicle dynamics, including the following: The process of solving bilinear matrix inequality by Vs iteration method is as follows: (1) Step γ: Initialize V and maximize γ by finding q2(x) such that constraint (12) holds. (2) β step: Keep V, γ, and q2(x) fixed and maximize β by finding q1(x) such that constraint (11) holds. (3) Step V: Keep γ, β, q1(x), q2(x) fixed, and find V such that (10)-(12) hold.

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