A vehicle stability analysis method based on central manifold dimensionality reduction

Abstract

The present invention discloses a vehicle stability analysis method based on central manifold dimensionality reduction, comprising: establishing a vehicle dynamics model, a wheel dynamics model, and a magic formula tire model; establishing a vehicle lateral and longitudinal coupled five-degree-of-freedom nonlinear dynamics system model; performing dimensionality reduction processing on the nonlinear dynamics system based on central manifold theory to obtain a nonlinear dynamics system model after dimensionality reduction; drawing a phase plane trajectory diagram of the nonlinear dynamics system to determine the equilibrium state in the vehicle's steering and braking integration; and controlling vehicle stability based on unstable regions, stable regions, and instability boundaries. The method establishes a connection between vehicle braking and steering stability, revealing the nonlinear dynamics mechanism by which braking torque, front wheel angle, and road adhesion coefficient affect handling stability; shortening the nonlinear dynamics stability analysis cycle, improving real-time performance, and increasing analysis accuracy; reflecting the system's equilibrium state, and being able to evaluate the impact of initial conditions and parameter changes on system motion.

Description

Technical Field

[0001] The present invention relates to a vehicle stability analysis method based on central manifold dimensionality reduction, belonging to the technical field of intelligent vehicle stability control. Background Art

[0002] Most current research on integrated steering and braking focuses solely on vehicle stability control under small-angle conditions. However, at high speeds and large angles, the dynamic characteristics of the vehicle system undergo fundamental changes. The tires enter a highly nonlinear regime, and the slip angle no longer conforms to a linear relationship. The lateral force and slip angle exhibit a strong nonlinear characteristic, making the tires unable to provide sufficient reaction force to overcome the vehicle's centrifugal force, making the vehicle susceptible to instability. Therefore, a method for integrated steering and braking stability control that accounts for tire nonlinearity and is tailored to high-speed, large-angle conditions is needed.

[0003] The traditional nonlinear analysis method of integrated steering and braking stability cannot fully reflect the high-order and complex steering and braking process of the vehicle. The Lyapunov stability analysis method of high-order nonlinear systems has an extremely complex Lyapunov function construction process, a long analysis cycle, and poor real-time performance.

[0004] Patent publication number CN 108909703 A discloses a method for determining the instability controllable domain for autonomous driving emergency avoidance. This method constructs a vehicle instability controllable domain calculation system model and performs central manifold dimensionality reduction on the system model. However, it cannot explain the instability mechanism of high-speed, large-angle vehicles during steering and braking. Furthermore, it does not provide a specific vehicle control method, and cannot solve the vehicle stability control problem during steering and braking. Summary of the Invention

[0005] Purpose of the invention: In response to the deficiencies in the prior art, the present invention provides a vehicle stability analysis method based on central manifold dimensionality reduction. The present invention analyzes the lateral and longitudinal stability of the vehicle through central manifold theory to solve the problem of complex control of the vehicle under the influence of nonlinear changes in tires at high speeds and large turning angles.

[0006] Technical solution: A vehicle stability analysis method based on central manifold dimensionality reduction, including the following steps:

[0007] Step 1: Establish vehicle dynamics model, wheel dynamics model and magic formula tire model;

[0008] Step 2: Based on the model in step 1, a nonlinear dynamic system model of the vehicle with five degrees of freedom coupled in the longitudinal and lateral directions is established;

[0009] Step 3: Based on the central manifold theory, the nonlinear dynamic system is subjected to dimensionality reduction processing to obtain a nonlinear dynamic system model after dimensionality reduction;

[0010] Step 4: Based on the dimensionality reduction model obtained in step 3, draw the phase plane trajectory diagram of the nonlinear dynamic system to determine the equilibrium state of the vehicle steering and braking integration;

[0011] Step 5: Control vehicle stability based on the unstable region, stable region, and instability boundary in step 4.

[0012] Preferably, the specific steps of step 1 are:

[0013] Based on the fact that tires enter the nonlinear region under high-speed and large-angle conditions, the automobile tire force model adopts a nonlinear tire model. The influence of braking torque and steering angle is considered at the same time, and the influence of Ackerman steering structure is ignored. The dynamic equation of vehicle steering and braking integration including lateral motion, longitudinal motion and yaw motion is established:

[0014] The vehicle dynamics model is established based on the three-degree-of-freedom vehicle system dynamics model:

[0015]

[0016] Where m is the vehicle mass (kg); v x is the longitudinal speed of the vehicle (m / s); v y is the lateral velocity (m / s); ω is the vehicle body yaw angular velocity (rad / s); F xf is the front wheel longitudinal tire force (N); F xr is the rear wheel longitudinal tire force (N); F yf is the front wheel lateral tire force (N); F yr is the rear wheel lateral tire force (N); I z is the moment of inertia of the vehicle around the z-axis (kg·m 2 );l f Front wheelbase (m); l r is the rear wheelbase (m);

[0017] Establish a wheel dynamics model that includes vehicle braking torque and driving torque input:

[0018]

[0019]

[0020] Among them, J z is the wheel moment of inertia; R e is the wheel rolling radius (m); ω f is the angular velocity of the vehicle's front wheels (rad / s); T df F is the front wheel driving torque of the vehicle (N·m); xf is the longitudinal tire force of the vehicle's front wheel (N); T bfis the front wheel braking torque of the vehicle (N·m); ω r is the angular velocity of the vehicle's rear wheels (rad / s); T dr is the rear wheel driving torque of the vehicle (N·m); F xr is the longitudinal tire force of the vehicle's rear wheel (N); T br is the vehicle rear wheel braking torque (N·m);

[0021] Building the Magic Formula Tire Model:

[0022] F=Dsin(Carctan(Bα-E(Bα-arctan(Bα))))

[0023] Where B is the stiffness factor, C is the shape factor, D is the peak factor, and E is the curvature factor; F is the tire longitudinal force or lateral force; α is the tire slip angle;

[0024] The front and rear wheel slip angles are:

[0025]

[0026]

[0027] Among them, α f , α r are the front and rear wheel slip angles, δ f is the front wheel turning angle, β is the sideslip angle of the center of mass;

[0028] Since there are many nonlinear terms and many influencing factors in the magic formula, it is necessary to simplify the tire force expression while retaining the nonlinear characteristics of the tire force; the simplified tire force expression F y as follows:

[0029] F y =k1α-k2α 3

[0030] Where: k1 = CBD, F y is the vehicle lateral tire force;

[0031] The tire force expressions for the front and rear tires are:

[0032]

[0033]

[0034] Preferably, the specific steps of step 2 are:

[0035] Select the state variables and bifurcation parameters required by the system:

[0036] The state variables are longitudinal velocity, lateral velocity, vehicle yaw angle, vehicle front wheel angular velocity, and vehicle rear wheel angular velocity; the bifurcation parameters are braking torque, front wheel angle, and road adhesion coefficient.

[0037] Based on the model in step 1, establish the vehicle dynamics system equations with five degrees of freedom coupled in the lateral and longitudinal directions. At the same time, the vehicle is front-wheel drive and the vertical load changes caused by the pitch and roll motion of the vehicle body are not considered;

[0038] The vehicle state space equations can be expressed as the following system of equations:

[0039]

[0040] Preferably, in order to facilitate the dimensionality reduction of nonlinear dynamic systems using central manifold theory, the equation in step 2 is reduced in dimension:

[0041]

[0042] Where f is the corresponding vector field, R is a set of real numbers, X is the system state variable, X = (x1, x2, x3, x4, x5) T Indicates (v x , v y ,ω,ω f ,ω r ) T ; θ is the system bifurcation parameter, θ=(δ f , T b , μ), μ is the road adhesion coefficient, T b is the wheel braking torque.

[0043] Preferably, the specific steps of step 3 are:

[0044] Assuming that there is a finite-dimensional central subspace in the system near the singular point, the central manifold principle is used to project the fast-changing state variables in the high-dimensional system state space into the low-dimensional space, and the obtained relationship is brought into the original nonlinear differential equation for dimensionality reduction, thereby obtaining a nonlinear differential equation equivalent to the differential equation.

[0045] Expand the vehicle dynamics system equation of the five degrees of freedom of the vehicle with lateral and longitudinal coupling established in step 2 into the linear part AX and the nonlinear part F(X) to express it as follows:

[0046]

[0047] Where A = D Xf(0) is the Jacobian matrix at the origin. The characteristic subspaces corresponding to the negative real part, zero real part, and positive real part characteristic roots of the matrix A are the local stable subspace E1, the local center subspace E2, and the local unstable subspace E3, respectively. The manifolds tangent to them are called the local stable manifold W1, the local center manifold W2, and the local unstable manifold W3, respectively. F(X) is a nonlinear function.

[0048] Take the singular point as (0, 0), and for the singular point (X0, θ0) under different bifurcation parameters, it is necessary to pass Perform coordinate changes and transfer to the origin, that is,

[0049]

[0050] By making the left side of the system differential equation equal to zero, the singular point of the system can be obtained;

[0051] Given a non-singular transformation matrix T, the Jacobian matrix A of the system is transformed into a diagonal block form, that is,

[0052]

[0053] Where M and N are n2×n2 and n1×n1 matrices, respectively, whose eigenvalues ​​have zero real part and negative real part, n2 is the dimension of the local central subspace, and n1 is the dimension of the local stable subspace; let X = TY, where X C is the critical state variable, X s is a steady-state variable, then The differential equation is decomposed into the following form after transformation:

[0054]

[0055]

[0056] According to the central manifold theorem, there exists a diffeomorphism h such that X S =h(X c ), and satisfy h(0)=Dh(0)=0, and substituting into the first equation above, we can obtain the equation of the flow on the central manifold, that is, the local stability of the vehicle nonlinear dynamic system when the state variable X=0 is expressed as:

[0057]

[0058] In order to determine the differential homeomorphism h, substitute the first formula after non-singular transformation and the differential homeomorphism h into the second formula and transpose the terms to obtain:

[0059] DX C h(MX C +u(h,X C ))-Nh-v(h,XC )=0

[0060] Expand the differential homeomorphism h into a power series and substitute it into the above formula. After comparing the coefficients, h can be calculated, and then it is brought back into the above formula to complete the dimensionality reduction of the high-dimensional system to the dimension of the upper flow of the central manifold, thus completing the dimensionality reduction process.

[0061] Preferably, the specific steps of step 4 are:

[0062] Step 4.1: Simplify the nonlinear dynamic system model after dimensionality reduction in step 3;

[0063] Step 4.2: Based on the principle of isocline, use the multi-step recursive method to draw the phase trajectory of the vehicle system steering and braking integrated nonlinear dynamic system on the phase plane after dimensionality reduction, describing the system from the initial state to the unstable state;

[0064] Step 4.3: Obtain the vehicle's center of mass slip angle-center of mass slip velocity under no control Phase plane diagram, determine the instability critical line, as well as the degree of coupling between the changes in the three bifurcation parameters of braking torque, front wheel angle, and road adhesion coefficient, and determine the unstable area, stable area, and instability boundary in the steering and braking integration process of the vehicle system.

[0065] Preferably, the specific steps of step 4.1 are:

[0066] The nonlinear dynamic system model after dimensionality reduction in step 3 can be expressed as the following equation:

[0067]

[0068] Where F(x) is the nonlinear function of the system; a i (x)(i=1,2,…,n) is the state variable function with reduced dimension; x(t) is nth order differentiable, and the differential equations are all normalized; the initial condition is d i X0 / dt i , (i=1, 2,...,n), X0=x0.

[0069] Preferably, the specific steps of step 4.2 are:

[0070] First, through the initial point (d n-2 x0 / dt n-2 , d n-1 x0 / dt n-1 ) and the slope of the straight line from the origin (0,0) is k1=(d n-1 x0 / dt n-1 ) / (d n-2 x0 / dt n-2 ), determine the initial point (dn-2 x0 / dt n-2 , d n-1 x0 / dt n-1 )The tangent slope of the phase trajectory k2=(d n x0 / dt n ) / (d n-1 x0 / dt n-1 );

[0071] Then, the initial point (d n-2 x0 / dt n-2 , d n-1 x0 / dt n-1 ) and slope k2 to make a straight line, and according to the characteristic that the phase trajectory moves in the clockwise direction, any point on the straight line is selected as the second point of the phase trajectory, and the position coordinates of the second point of the phase trajectory (d n-2 x1 / dt n-2 , d n-1 x1 / dt n-1 );

[0072] Finally, according to the principle of isocline, the above steps are continued to recursively draw the phase trajectory on the phase plane of the steering and braking integrated nonlinear dynamic system after dimensionality reduction to describe the system from the initial state to the unstable state.

[0073] Preferably, the specific steps of step 4.3 are:

[0074] The vehicle system's expressions for the center of mass sideslip angle and center of mass sideslip angular velocity are as follows:

[0075]

[0076]

[0077] in is the sideslip angular velocity of the center of mass;

[0078] Use the m function to set the simulation working condition, take the initial vehicle speed as a constant value, take the road adhesion coefficient, plan a fixed lane change trajectory, give the braking torque, and as the front wheel angle increases, obtain the center of mass slip angle-center of mass slip angle velocity under no control Phase plane diagram, which can more intuitively and accurately reflect the stability of the vehicle's lateral and longitudinal coupled five-degree-of-freedom nonlinear dynamic system, as well as the degree of coupling between the changes in bifurcation parameters such as braking torque and front wheel angle, and determine the unstable area, stable area and instability boundary during the vehicle system's rotation and braking integration process;

[0079] Vehicle stability region expression:

[0080]

[0081] Among them, B1 and B2 are the boundary parameters of the vehicle's stable working state;

[0082] When satisfied When the state point is In the phase plane stability region, the vehicle is in a stable state;

[0083] when The vehicle is in an unstable state.

[0084] Beneficial effects: The present invention establishes the connection between automobile braking and steering stability, reveals the nonlinear dynamic mechanism by which braking torque, front wheel angle and road adhesion coefficient affect handling stability; shortens the nonlinear dynamic stability analysis cycle, improves real-time performance, and increases analysis accuracy; can intuitively and accurately reflect the equilibrium state of the system, and can evaluate the impact of initial conditions and parameter changes on system motion. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0086] Figure 1 It is a structural principle diagram of the present invention;

[0087] Figure 2 is the vehicle dynamics model diagram;

[0088] Figure 3 This is the wheel dynamics model diagram. DETAILED DESCRIPTION

[0089] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0090] In the description of the present invention, it should be understood that the terms "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating directions or positional relationships, are based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore should not be understood as limiting the present invention.

[0091] In the present invention, unless otherwise expressly specified or limited, a first feature being "above" or "below" a second feature may include the first and second features being in direct contact, or may include the first and second features being in contact not directly but through another feature between them. Furthermore, a first feature being "above," "above," and "above" a second feature may include the first feature being directly above or obliquely above the second feature, or may simply mean that the first feature is higher in level than the second feature. A first feature being "below," "below," and "below" a second feature may include the first feature being directly below or obliquely below the second feature, or may simply mean that the first feature is lower in level than the second feature.

[0092] like Figure 1 、 Figure 2 and Figure 3 As shown, a vehicle stability analysis method based on central manifold dimensionality reduction includes the following steps:

[0093] Step 1: Establish vehicle dynamics model, wheel dynamics model and magic formula tire model;

[0094] Step 2: Based on the model in step 1, a nonlinear dynamic system model of the vehicle with five degrees of freedom coupled in the longitudinal and lateral directions is established;

[0095] Step 3: Based on the central manifold theory, the nonlinear dynamic system is subjected to dimensionality reduction processing to obtain a nonlinear dynamic system model after dimensionality reduction;

[0096] Step 4: Based on the dimensionality reduction model obtained in step 3, draw the phase plane trajectory diagram of the nonlinear dynamic system to determine the equilibrium state of the vehicle steering and braking integration;

[0097] Step 5: Control vehicle stability based on the unstable region, stable region, and instability boundary in step 4.

[0098] The specific steps of step 1 are:

[0099] Based on the fact that tires enter the nonlinear region under high-speed and large-angle conditions, the automobile tire force model adopts a nonlinear tire model. The influence of braking torque and steering angle is considered at the same time, and the influence of Ackerman steering structure is ignored. The dynamic equation of vehicle steering and braking integration including lateral motion, longitudinal motion and yaw motion is established:

[0100] The vehicle dynamics model is established based on the three-degree-of-freedom vehicle system dynamics model:

[0101]

[0102] Where m is the vehicle mass (kg); v x is the longitudinal speed of the vehicle (m / s); v y is the lateral velocity (m / s); ω is the vehicle body yaw angular velocity (rad / s); F xf is the front wheel longitudinal tire force (N); F xr is the rear wheel longitudinal tire force (N); F yf is the front wheel lateral tire force (N); F yr is the rear wheel lateral tire force (N); I z is the moment of inertia of the vehicle around the z-axis (kg·m 2 );l f Front wheelbase (m); l r is the rear wheelbase (m);

[0103] Establish a wheel dynamics model that includes vehicle braking torque and driving torque input:

[0104]

[0105]

[0106] Among them, J z is the wheel moment of inertia; R e is the wheel rolling radius (m); ω f is the angular velocity of the vehicle's front wheels (rad / s); T df F is the front wheel driving torque of the vehicle (N·m); xf is the longitudinal tire force of the vehicle's front wheel (N); T bf is the front wheel braking torque of the vehicle (N·m); ω r is the angular velocity of the vehicle's rear wheels (rad / s); T dr is the rear wheel driving torque of the vehicle (N·m); F xr is the longitudinal tire force of the vehicle's rear wheel (N); T br is the vehicle rear wheel braking torque (N·m);

[0107] Building the Magic Formula Tire Model:

[0108] F=Dsin(Carctan(Bα-E(Bα-arctan(Bα))))

[0109] Where B is the stiffness factor, C is the shape factor, D is the peak factor, and E is the curvature factor; F is the tire longitudinal force or lateral force; α is the tire slip angle;

[0110] The front and rear wheel slip angles are:

[0111]

[0112]

[0113] Among them, α f , α r are the front and rear wheel slip angles, δ f is the front wheel turning angle, β is the sideslip angle of the center of mass;

[0114] Since there are many nonlinear terms and many influencing factors in the magic formula, it is necessary to simplify the tire force expression while retaining the nonlinear characteristics of the tire force; the simplified tire force expression F y as follows:

[0115] F y =k1α-k2α 3

[0116] Where: k1 = CBD, F y is the vehicle lateral tire force;

[0117] The tire force expressions for the front and rear tires are:

[0118]

[0119]

[0120] The specific steps of step 2 are:

[0121] Select the state variables and bifurcation parameters required by the system:

[0122] The state variables are longitudinal velocity, lateral velocity, vehicle yaw angle, vehicle front wheel angular velocity, and vehicle rear wheel angular velocity; the bifurcation parameters are braking torque, front wheel angle, and road adhesion coefficient.

[0123] Based on the model in step 1, establish the vehicle dynamics system equations with five degrees of freedom coupled in the lateral and longitudinal directions. At the same time, the vehicle is front-wheel drive and the vertical load changes caused by the pitch and roll motion of the vehicle body are not considered;

[0124] The vehicle state space equations can be expressed as the following system of equations:

[0125]

[0126] In order to facilitate the dimensionality reduction of nonlinear dynamic systems using central manifold theory, the equation in step 2 is reduced in dimension:

[0127]

[0128] Where f is the corresponding vector field, R is a set of real numbers, X is the system state variable, X = (x1, x2, x3, x4, x5) T Indicates (v x , v y ,ω,ω f ,ω r ) T ; θ is the system bifurcation parameter, θ=(δ f , T b , μ), μ is the road adhesion coefficient, T b is the wheel braking torque.

[0129] The specific steps of step 3 are:

[0130] Assuming that there is a finite-dimensional central subspace in the system near the singular point, the central manifold principle is used to project the fast-changing state variables in the high-dimensional system state space into the low-dimensional space, and the obtained relationship is brought into the original nonlinear differential equation for dimensionality reduction, thereby obtaining a nonlinear differential equation equivalent to the differential equation.

[0131] Expand the vehicle dynamics system equation of the five degrees of freedom of the vehicle with lateral and longitudinal coupling established in step 2 into the linear part AX and the nonlinear part F(X) to express it as follows:

[0132]

[0133] Where A = D X f(0) is the Jacobian matrix at the origin. The characteristic subspaces corresponding to the negative real part, zero real part, and positive real part characteristic roots of the matrix A are the local stable subspace E1, the local center subspace E2, and the local unstable subspace E3, respectively. The manifolds tangent to them are called the local stable manifold W1, the local center manifold W2, and the local unstable manifold W3, respectively. F(X) is a nonlinear function.

[0134] Take the singular point as (0, 0), and for the singular point (X0, θ0) under different bifurcation parameters, it is necessary to pass Perform coordinate changes and transfer to the origin, that is,

[0135]

[0136] By making the left side of the system differential equation equal to zero, the singular point of the system can be obtained;

[0137] Given a non-singular transformation matrix T, the Jacobian matrix A of the system is transformed into a diagonal block form, that is,

[0138]

[0139] Where M and N are n2×n2 and n1×n1 matrices, respectively, whose eigenvalues ​​have zero real part and negative real part, n2 is the dimension of the local central subspace, and n1 is the dimension of the local stable subspace; let X = TY, where X C is the critical state variable, X S is a steady-state variable, then The differential equation is decomposed into the following form after transformation:

[0140]

[0141]

[0142] According to the central manifold theorem, there exists a diffeomorphism h such that X S =h(X c ), and satisfy h(0)=Dh(0)=0, and substituting into the first equation above, we can obtain the equation of the flow on the central manifold, that is, the local stability of the vehicle nonlinear dynamic system when the state variable X=0 is expressed as:

[0143]

[0144] In order to determine the differential homeomorphism h, substitute the first formula after non-singular transformation and the differential homeomorphism h into the second formula and transpose the terms to obtain:

[0145] DX C h(MX C +u(h,X C ))-Nh-v(h,X C )=0

[0146] Expand the differential homeomorphism h into a power series and substitute it into the above formula. After comparing the coefficients, h can be calculated, and then it is brought back into the above formula to complete the dimensionality reduction of the high-dimensional system to the dimension of the upper flow of the central manifold, thus completing the dimensionality reduction process.

[0147] The specific steps of step 4 are:

[0148] Step 4.1: Simplify the nonlinear dynamic system model after dimensionality reduction in step 3;

[0149] Step 4.2: Based on the principle of isocline, use the multi-step recursive method to draw the phase trajectory of the vehicle system steering and braking integrated nonlinear dynamic system on the phase plane after dimensionality reduction, describing the system from the initial state to the unstable state;

[0150] Step 4.3: Obtain the vehicle's center of mass slip angle-center of mass slip velocity under no control Phase plane diagram, determine the instability critical line, as well as the degree of coupling between the changes in the three bifurcation parameters of braking torque, front wheel angle, and road adhesion coefficient, and determine the unstable area, stable area, and instability boundary in the steering and braking integration process of the vehicle system.

[0151] The specific steps of step 4.1 are:

[0152] The nonlinear dynamic system model after dimensionality reduction in step 3 can be expressed as the following equation:

[0153]

[0154] Where F(x) is the nonlinear function of the system; a i (x)(i=1,2,…,n) is the state variable function with reduced dimension; x(t) is nth order differentiable, and the differential equations are all normalized; the initial condition is d i X0 / dt i , (i=1, 2,...,n), X0=x0.

[0155] The specific steps of step 4.2 are:

[0156] First, through the initial point (d n-2 x0 / dt n-2 , d n-1 x0 / dt n-1 ) and the slope of the straight line from the origin (0,0) is k1=(d n-1 x0 / dt n-1 ) / (d n-2 x0 / dt n-2 ), determine the initial point (d n-2 x0 / dt n-2 , d n-1 x0 / dt n-1 )The tangent slope of the phase trajectory k2=(d n x0 / dt n ) / (d n-1 x0 / dt n-1 );

[0157] Then, the initial point (d n-2 x0 / dt n-2 , d n-1 x0 / dt n-1 ) and slope k2 to make a straight line, and according to the characteristic that the phase trajectory moves in the clockwise direction, any point on the straight line is selected as the second point of the phase trajectory, and the position coordinates of the second point of the phase trajectory (d n-2 x1 / dt n-2 , d n-1 x1 / dt n-1 );

[0158] Finally, according to the principle of isocline, the above steps are continued to recursively draw the phase trajectory on the phase plane of the steering and braking integrated nonlinear dynamic system after dimensionality reduction to describe the system from the initial state to the unstable state.

[0159] The specific steps of step 4.3 are:

[0160] The vehicle system's expressions for the center of mass sideslip angle and center of mass sideslip angular velocity are as follows:

[0161]

[0162]

[0163] in is the sideslip angular velocity of the center of mass;

[0164] Use the m function to set the simulation working condition, take the initial vehicle speed as a constant value, take the road adhesion coefficient, plan a fixed lane change trajectory, give the braking torque, and as the front wheel angle increases, obtain the center of mass slip angle-center of mass slip angle velocity under no control Phase plane diagram, which can more intuitively and accurately reflect the stability of the vehicle's lateral and longitudinal coupled five-degree-of-freedom nonlinear dynamic system, as well as the degree of coupling between the changes in bifurcation parameters such as braking torque and front wheel angle, and determine the unstable area, stable area and instability boundary during the vehicle system's rotation and braking integration process;

[0165] Vehicle stability region expression:

[0166]

[0167] Among them, B1 and B2 are the boundary parameters of the vehicle's stable working state;

[0168] When satisfied When the state point is In the phase plane stability region, the vehicle is in a stable state;

[0169] when The vehicle is in an unstable state.

[0170] Step 5: Control vehicle stability based on the unstable region, stable region, and instability boundary in step 4:

[0171] The vehicle's handling stability is analyzed through the phase plane. Given the braking torque and road adhesion coefficient, as the front wheel angle increases, the system will become unstable. If active stability control is not taken on the wheels, the vehicle will eventually lose control.

[0172] Considering that the vehicle is traveling at high speed, in order to ensure the stability of the vehicle, the ideal center of mass sideslip angle amplitude constraint β is taken max =tan -1 (0.02μg); At the same time, considering the influence of road adhesion on vehicle lateral acceleration, the yaw rate amplitude constraint is taken The ideal center of mass sideslip angle β d and the ideal yaw rate ω d The calculation formula is:

[0173] β d =min(β,β max )sgn(β)

[0174] ω d =min(ω,ω max )sgn(δ f )

[0175] Where g is the acceleration due to gravity (m / s 2 );β max is the maximum value of the ideal center of mass sideslip angle constraint; ω max is the maximum value of the yaw rate constraint; β d is the ideal center of mass sideslip angle; ω d is the ideal yaw rate.

[0176] The vehicle's center of mass slip angle-center of mass slip velocity in the uncontrolled state obtained by step 4 The phase plane diagram determines the instability critical line and controls the output front wheel angle and braking torque;

[0177] The current state of the vehicle's center of mass slip angle is obtained and estimated through Kalman filtering. When the vehicle is operating in the area inside the parallel line, in order to maintain normal driving under time-varying driving conditions, an active front wheel steering control strategy based on SMC is established. The sliding membrane switching function S is defined as the difference between the actual value and the ideal value of the vehicle's yaw angular velocity. Taking the derivative of both sides, we can get:

[0178]

[0179] The designed sliding mode reaching law is K1 and K2 are positive constants and satisfy is much smaller than 0, and the saturation function sat(S) is used to replace the sign function sgn(S) to eliminate the chattering, then:

[0180]

[0181] The additional front wheel turning angle can be obtained from the above

[0182] When the vehicle is outside the parallel line, the longitudinal force of the tire is less affected by the nonlinear characteristics of the tire. The control effect is achieved by adding the optimal yaw moment. Specifically, the yaw moment is calculated by calculating the shortest distance from the unstable phase point to the stable boundary and using the PID control method. The specific steps are as follows:

[0183]

[0184]

[0185] e=d1-d0 / 2

[0186] Where e is the distance from the unstable phase point to the stable boundary, and e≥0; d1 is the perpendicular distance from the unstable phase point to the midline of the boundary; and d0 is the distance between parallel lines.

[0187] The yaw moment M is obtained by using the PID control method:

[0188]

[0189] Where K p yes Phase plane scale parameter, K i is the parameter of integration, K d is the parameter of differentiation.

[0190] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0191] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A vehicle stability analysis method based on central manifold dimensionality reduction, characterized by: The following steps are involved: Step 1: Establish vehicle dynamics model, wheel dynamics model and magic formula tire model; Based on the fact that tires enter the nonlinear region under high-speed and large-angle conditions, the vehicle tire force model adopts a nonlinear tire model, taking into account the effects of braking torque and steering angle, while ignoring the influence of the Ackerman steering structure. The dynamic equation of vehicle steering and braking integration including lateral motion, longitudinal motion and yaw motion is established; Step 2: Based on the model in step 1, a nonlinear dynamic system model of the vehicle with five degrees of freedom coupled in the longitudinal and lateral directions is established; Select the state variables and bifurcation parameters required by the system: The state variables are longitudinal velocity, lateral velocity, vehicle yaw angle, vehicle front wheel angular velocity, and vehicle rear wheel angular velocity; the bifurcation parameters are braking torque, front wheel angle, and road adhesion coefficient. Based on the model in step 1, establish the vehicle dynamics system equations with five degrees of freedom coupled in the lateral and longitudinal directions. At the same time, the vehicle is front-wheel drive and the vertical load changes caused by the pitch and roll motion of the vehicle body are not considered; Step 3: Based on the central manifold theory, the nonlinear dynamic system is subjected to dimensionality reduction processing to obtain a nonlinear dynamic system model after dimensionality reduction; Assuming that there is a finite-dimensional central subspace in the system near the singular point, the central manifold principle is used to project the fast-changing state variables in the high-dimensional system state space into the low-dimensional space, and the obtained relationship is brought into the original nonlinear differential equation for dimensionality reduction, thereby obtaining a nonlinear differential equation equivalent to the differential equation. Step 4: Based on the dimensionality reduction model obtained in step 3, draw the phase plane trajectory diagram of the nonlinear dynamic system to determine the equilibrium state of the vehicle steering and braking integration; Step 4.1: Simplify the nonlinear dynamic system model after dimensionality reduction in step 3; Step 4.2: Based on the principle of isocline, use the multi-step recursive method to draw the phase trajectory of the vehicle system steering and braking integrated nonlinear dynamic system on the phase plane after dimensionality reduction, describing the system from the initial state to the unstable state; Step 4.3: Obtain the vehicle's center of mass slip angle and center of mass slip velocity under no control - Phase plane diagram, determine the instability critical line, as well as the coupling degree between the changes of the three bifurcation parameters of braking torque, front wheel angle, and road adhesion coefficient, and determine the unstable region, stable region, and instability boundary during the steering and braking integration process of the vehicle system; Step 5: Control vehicle stability based on the unstable region, stable region, and instability boundary in step 4.

2. The vehicle stability analysis method based on central manifold dimensionality reduction according to claim 1, characterized in that: The specific steps of step 1 also include: The vehicle dynamics model is established based on the three-degree-of-freedom vehicle system dynamics model: ； in is the vehicle mass in kg; is the vehicle longitudinal speed m / s; is the lateral velocity m / s; is the vehicle body yaw angular velocity rad / s; is the front wheel longitudinal tire force N; is the rear wheel longitudinal tire force N; is the front wheel lateral tire force N; is the rear wheel lateral tire force N; For vehicles to go around Shaft moment of inertia kg·m 2 ; Front wheelbase m; is the rear wheelbase m; Establish a wheel dynamics model that includes vehicle braking torque and driving torque input: ； ； in, is the wheel moment of inertia kg·m 2 ; is the wheel rolling radius m; is the angular velocity of the vehicle's front wheel rad / s; is the vehicle front wheel driving torque N·m; is the longitudinal tire force of the vehicle’s front wheel in N; is the vehicle front wheel braking torque N·m; is the angular velocity of the vehicle's rear wheels rad / s; is the vehicle rear wheel driving torque N·m; is the longitudinal tire force of the vehicle's rear wheel in N; is the vehicle rear wheel braking torque N·m; Building the Magic Formula Tire Model: ； in is the stiffness factor, is the shape factor, is the peak factor, is the curvature factor; is the tire longitudinal force or lateral force; is the tire slip angle; The front and rear wheel slip angles are: ； ； in, , are the front and rear wheel slip angles, is the front wheel turning angle, is the sideslip angle of the center of mass; Since there are many nonlinear terms and many influencing factors in the magic formula, it is necessary to simplify the tire force expression while retaining the nonlinear characteristics of the tire force; the simplified tire force expression is as follows: ； in: , , is the vehicle lateral tire force; The tire force expressions for the front and rear tires are: ； 。 3. The vehicle stability analysis method based on central manifold dimensionality reduction according to claim 2, characterized in that: The specific steps of step 2 also include: The vehicle state space equations are expressed as the following system of equations: 。 4. The vehicle stability analysis method based on central manifold dimensionality reduction according to claim 3, characterized in that: In order to facilitate the dimensionality reduction of nonlinear dynamic systems using central manifold theory, the equation in step 2 is reduced in dimension: ； in is the corresponding vector field, is the set of real numbers, is the system state variable, express ; is the system bifurcation parameter, , is the road adhesion coefficient, is the wheel braking torque.

5. The vehicle stability analysis method based on central manifold dimensionality reduction according to claim 4, characterized in that: The specific steps of step 3 also include: Expand the vehicle dynamics system equations of the five degrees of freedom of the vehicle with lateral and longitudinal coupling established in step 2 into the linear part and nonlinear part express: ； in, is the Jacobian matrix at the origin, the matrix The characteristic subspaces corresponding to the negative real part, zero real part and positive real part characteristic roots are the local stable subspaces , local central subspace and locally unstable subspaces , and the manifolds tangent to them are called locally stable manifolds , local center manifold and locally unstable manifolds , is a nonlinear function; Take the singular point as , for the singular points existing under different bifurcation parameters , you need to pass , Perform coordinate changes and transfer to the origin, that is, ； By making the left side of the system differential equation equal to zero, the singular point of the system can be obtained; Given a nonsingular transformation matrix The Jacobian matrix of the system Transformed into diagonal blocks, ； in and They are and matrices whose eigenvalues ​​have zero and negative real parts, is the local center subspace dimension, is the dimension of the local stable subspace; let ,in , is the critical state variable, is a steady-state variable, then The differential equation is decomposed into the following form after transformation: First Form Second form According to the central manifold theorem, there exists a diffeomorphism , making , and satisfies , put it into the first equation above, and we can get the equation of the flow on the central manifold, that is, the vehicle nonlinear dynamic system in the state variable The local stability of is expressed as: ； To determine diffeomorphism , the first formula after non-singular transformation and the differential homeomorphism Substituting into the second formula and shifting the terms, we can get: ； Diffeomorphism Expand it into a power series and substitute it into the above formula. After comparing the coefficients, we can find , and then bring back the above formula to complete the dimensionality reduction process of reducing the dimensionality of the high-dimensional system to the dimensionality of the upper flow of the central manifold.

6. The vehicle stability analysis method based on central manifold dimensionality reduction according to claim 5, characterized in that: The specific steps of step 4.1 are: The nonlinear dynamic system model after dimensionality reduction in step 3 is expressed as the following equation: ； in is a nonlinear function of the system; is the state variable function of dimensionality reduction; for The order is differentiable, and the differential equations are all normalized; the initial conditions are .

7. The vehicle stability analysis method based on central manifold dimensionality reduction according to claim 6, characterized in that: The specific steps of step 4.2 are: First, through the initial point on the phase plane and origin The slope of a straight line , determine the initial point Tangent slope of the phase locus ; Then, the initial point and slope Make a straight line, and according to the characteristic that the phase trajectory moves in a clockwise direction, select any point on the straight line as the second point of the phase trajectory, and the position coordinates of the second point of the phase trajectory are obtained. ; Finally, according to the principle of isocline, the above steps are continued to recursively draw the phase trajectory on the phase plane of the steering and braking integrated nonlinear dynamic system after dimensionality reduction to describe the system from the initial state to the unstable state.

8. The vehicle stability analysis method based on central manifold dimensionality reduction according to claim 7, characterized in that: The specific steps of step 4.3 are: The vehicle system's expressions for the center of mass sideslip angle and center of mass sideslip angular velocity are as follows: ； ； in is the sideslip angular velocity of the center of mass; use The function sets the simulation working condition, takes the initial vehicle speed as a constant value, takes the road adhesion coefficient, plans a fixed lane change trajectory, gives the braking torque, and as the front wheel angle increases, obtains the center of mass slip angle under no control - the center of mass slip angle velocity - Phase plane diagram, which can more intuitively and accurately reflect the stability of the vehicle's lateral and longitudinal coupled five-degree-of-freedom nonlinear dynamic system, as well as the degree of coupling between the braking torque and the front wheel angle bifurcation parameter changes, and determine the unstable area, stable area and instability boundary of the vehicle system during the rotation and braking integration process; Vehicle stability region expression: ； in , is the boundary parameter of the vehicle's stable working state; When satisfied When the state point is - In the phase plane stability region, the vehicle is in a stable state; when The vehicle is in an unstable state.

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