A vehicle and tire state observer design method based on distributed estimation

Abstract

The application discloses a vehicle and tire state observer design method based on distributed estimation, and relates to the technical field of vehicle state estimation. In consideration of the combined working conditions of tire slip and side slip, a combined working condition tire magic formula is established to realize the establishment of a vehicle-tire dynamics model; an observer form composed of four interconnected subsystems is designed based on a distributed estimation method; the stability of an error subsystem of the subsystem relative to an actual system is independently analyzed to obtain the value range of the gain of each subsystem; the stability of the error interconnection system is analyzed and the condition thereof is determined, and the condition is added to the gain of each subsystem to ensure the stability of the whole; and an observer interconnection system represented by the four subsystems is constructed to realize the state estimation of the vehicle and the tire. The observer design is simplified, the value range of the observer gain is determined based on the stability analysis, the calculation amount can be reduced, the accuracy is relatively high, and the real-time estimation demand can be met.

Description

Technical Field

[0001] This invention relates to the field of vehicle state estimation technology, specifically a design method for a vehicle and tire state observer based on distributed estimation. Background Technology

[0002] With the widespread and in-depth application of automotive electronics technology in the automotive industry, people have increasingly higher requirements for vehicle handling stability and active safety. Most automotive electronic control systems implement corresponding control logic based on the vehicle's driving state. Typically, the vehicle's driving state is directly measured by onboard sensors. However, due to the complexity of vehicle driving conditions and factors such as the measurement accuracy of onboard sensors and manufacturing processes, much vehicle driving state information cannot be directly measured by standard onboard sensors. Therefore, accurately and in real-time acquiring the vehicle's state information during driving is a key issue in automotive electronic control system research and a prerequisite and necessary condition for achieving closed-loop control.

[0003] Currently, there are two main categories of state estimation methods for high-order nonlinear vehicle-tire systems: centralized estimation and modular estimation. Centralized estimation typically employs filtering-based methods, preserving the nonlinear characteristics of the vehicle-tire model itself and directly targeting high-order nonlinear systems. Currently, unscented Kalman filtering and its derivatives are commonly used, achieving accurate estimation for most states. However, filtering methods involve numerous high-order matrix operations in handling high-order nonlinearities, and computational efficiency decreases significantly with increasing system order, making them unsuitable for hardware with high real-time requirements. Modular estimation decomposes the high-order nonlinear vehicle-tire system into multiple modular subsystems, using a cascaded modular structure. An independent observer is designed for each subsystem, sequentially estimating different state information. This significantly improves computational efficiency compared to centralized estimation. However, modular estimation neglects the coupling relationships of some state variables within each subsystem, resulting in incomplete consideration of the dynamic characteristics of the entire nonlinear system and consequently lower estimation accuracy.

[0004] Therefore, the core issue for current state estimation methods for high-order nonlinear vehicle-tire systems is how to consider the complete dynamic characteristics of the model as much as possible in the observer design while ensuring real-time computational efficiency, thus balancing estimation accuracy and computational efficiency. Summary of the Invention

[0005] To address the shortcomings of the prior art, this invention provides a design method for a vehicle and tire state observer based on distributed estimation. This method simplifies the observer design and determines the range of observer gain values ​​based on stability analysis, thereby reducing computational load, achieving higher accuracy, and meeting the requirements of real-time estimation.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a design method for a vehicle and tire state observer based on distributed estimation, comprising the following steps:

[0007] Step 1: Establishing the tire force formula and vehicle dynamics model

[0008] Considering the combined working conditions of tire slippage and lateral deviation, the following magic formula for tires under combined working conditions is established:

[0009]

[0010] In the formula, F x and F y F represents the longitudinal force and lateral force of the tire, respectively. z F represents the current vertical load on the tire. z0 Indicates the tire's nominal load, σ X σ Y σ is an intermediate value in the calculation, κ is the slip ratio, α is the sideslip angle, μ represents the current road surface adhesion coefficient, μ0 = 1, B x and B y C represents the stiffness factor for longitudinal force and lateral force, respectively. x and C y The curve shape factors, D, represent the longitudinal and lateral forces, respectively. x and D y E represents the peak factor for longitudinal force and lateral force, respectively. x and E y These are the curvature factors of the curves for longitudinal force and lateral force, respectively;

[0011] The motion of a vehicle in the yaw plane consists of longitudinal, lateral, and yaw motions, as shown below:

[0012]

[0013] Wherein, longitudinal acceleration a x Lateral acceleration a y and yaw moment M z Calculated using the following formula:

[0014]

[0015] In the formula, v x and v y These represent the longitudinal and lateral velocities, respectively, where r is the yaw rate and I is the longitudinal and lateral velocities. z Let F be the vehicle's moment of inertia about the z-axis, m be the vehicle's mass, and F be the inertia of the vehicle about the z-axis. x1 ~F x4 and F y1 ~F y4These represent the longitudinal and lateral forces of the four tires as described by the composite tire magic formula, with δ1 to δ4 representing the four wheel rotation angles, and C... D Where A is the air resistance coefficient, ρ is the frontal area, and l is the air density. f and l r These are the distances from the vehicle's center of gravity to the centers of the front and rear axles, respectively, and w is the track width between the front and rear axles.

[0016] The differential equations for the four-wheel dynamics are established as follows:

[0017]

[0018] In the formula, J w Let ω be the moment of inertia of a single wheel. i T is the wheel speed. i R is the driving or braking torque acting on the wheels. e T is the effective radius of the wheel. ri T is the rolling resistance torque of the wheel. ri =F zi R e (R rc +R rv v x ), R rc and R rv It is a constant;

[0019] The vehicle's roll and pitch motions are simplified into two one-degree-of-freedom models as follows:

[0020]

[0021]

[0022] In the formula, I xx and I yy Let I be the roll and pitch moments of inertia of the vehicle body, respectively. xx +m s h R 2 For I x I yy +m s h P 2 For I y m s h is the sprung mass of the vehicle. R and h P Let φ and θ be the distances from the roll center and pitch center to the center of mass of the sprung mass, respectively; g be the acceleration due to gravity; φ and θ be the roll angle and pitch angle, respectively; and K be the distance from the roll center and pitch center, respectively. φ and K θ These are the roll and pitch stiffness, respectively, C φ and C θThese are the roll and pitch damping coefficients, respectively.

[0023] Step 2: Design the observer form for distributed estimation

[0024] The observer, consisting of four interconnected subsystems, is designed based on a distributed estimation method as follows:

[0025]

[0026]

[0027]

[0028]

[0029] In the formula, K x K y K r K roll K pitch and K ω1 ~K ω4 It is the gain to be designed for the observer, and the superscript ^ indicates the estimated value of the corresponding parameter;

[0030] Step 3: Stability Analysis of the Observer Subsystem

[0031] For the four subsystems (7) to (10), the stability of their error subsystems relative to the actual system is analyzed independently, and the range of values ​​of the gain of each subsystem is determined in the stability analysis.

[0032] Step 4: Stability analysis of the overall observer interconnection system

[0033] The four subsystems (7) to (10) form the observer interconnection system. The error subsystem between the actual system and the subsystems forms the error interconnection system. The stability of the error interconnection system is analyzed and its conditions are determined. The observer interconnection system adds this condition while determining the gain of each subsystem to ensure the overall stability of the observer interconnection system.

[0034] Step 5: Perform state estimation for the vehicle and tires.

[0035] An observer interconnection system is constructed, consisting of four subsystems (7) to (10). The observer interconnection system receives measurement information from the vehicle, including a x a y ,r, Taking ω1~ω4, δ1~δ4, and T1~T4 as inputs, the observer interconnect system directly outputs a series of state estimates of the vehicle, including longitudinal velocity. Lateral velocity yaw rate Wheel speed roll angle and roll rate and pitch angle and pitch angular velocity The tire's slip ratio κ, slip angle α, and longitudinal force F x and lateral force F y It is calculated as an intermediate quantity in each cycle of the observer interconnect system, and is also used by the observer interconnect system output for estimating the actual tire condition.

[0036] Compared with the prior art, the beneficial effects of the present invention are:

[0037] 1. This invention simplifies the design of observers for high-order nonlinear vehicle systems and determines the range of observer gain values ​​based on stability analysis.

[0038] 2. Compared with the overall estimation scheme for high-order nonlinear vehicle systems, the present invention greatly reduces the amount of computation and can achieve real-time estimation;

[0039] 3. This invention fully preserves the coupling relationship between state variables, and can reflect the dynamic characteristics of the vehicle-tire system itself more accurately;

[0040] 4. This invention can provide vehicle status information including longitudinal speed, lateral speed, wheel speed, roll, and pitch, as well as tire information including slip ratio, sideslip angle, longitudinal force, and lateral force, thus ensuring vehicle control and safe driving. Attached Figure Description

[0041] Figure 1 This is a flowchart of the present invention;

[0042] Figure 2 This is a structural diagram of the vehicle-tire dynamics model in this invention;

[0043] Figure 3 This is a structural diagram of the observer form of the distributed estimation in this invention;

[0044] Figure 4 This is a comparison chart of the estimated and actual values ​​of the vehicle state in the software simulation of the embodiment;

[0045] Figure 5 This is a comparison chart of the estimated and actual values ​​of tire information in the software simulation of the embodiment;

[0046] Figure 6 This is a comparison chart of the hardware-in-the-loop simulation and software simulation results in the embodiment. Detailed Implementation

[0047] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0048] like Figures 1-3 As shown in Figure 1, a design method for a vehicle and tire state observer based on distributed estimation includes the following steps:

[0049] Step 1: Establishing the tire force formula and vehicle dynamics model

[0050] The general tire force magic formula is only applicable to pure slip or pure sideslip conditions. However, considering that the tire operates under a combination of slip and sideslip conditions during actual vehicle operation, a combined tire force magic formula is established as follows:

[0051]

[0052] In the formula, F x and F y F represents the longitudinal force and lateral force of the tire, respectively. z F represents the current vertical load on the tire. z0 Indicates the tire's nominal load, σ X σ Y σ is an intermediate value in the calculation, κ is the slip ratio, α is the sideslip angle, μ represents the current road surface adhesion coefficient, μ0 = 1, B x and B y C represents the stiffness factor for longitudinal force and lateral force, respectively. x and C y The curve shape factors, D, represent the longitudinal and lateral forces, respectively. x and D y E represents the peak factor for longitudinal force and lateral force, respectively. x and E y These are the curvature factors of the curves for longitudinal force and lateral force, respectively.

[0053] The motion of a vehicle in the yaw plane consists of longitudinal, lateral, and yaw motions, as shown below:

[0054]

[0055] Wherein, longitudinal acceleration a x Lateral acceleration a y and yaw moment M z Calculated using the following formula:

[0056]

[0057] In the formula, v x and v y These represent the longitudinal and lateral velocities, respectively, where r is the yaw rate and I is the longitudinal and lateral velocities. z Let F be the vehicle's moment of inertia about the z-axis, m be the vehicle's mass, and F be the inertia of the vehicle about the z-axis. x1 ~F x4 and F y1 ~F y4 These represent the longitudinal and lateral forces of the four tires as described by the composite tire magic formula, with δ1 to δ4 representing the four wheel rotation angles, and C... D Where A is the air resistance coefficient, ρ is the frontal area, and l is the air density. f and l r These are the distances from the vehicle's center of gravity to the centers of the front and rear axles, respectively, and w is the track width between the front and rear axles.

[0058] The differential equations for the four-wheel dynamics are established as follows:

[0059]

[0060] In the formula, J w Let ω be the moment of inertia of a single wheel. i T is the wheel speed. i R is the driving or braking torque acting on the wheels. e T is the effective radius of the wheel. ri T is the rolling resistance torque of the wheel. ri =F zi R e (R rc +R rv v x ), R rc and R rv It is a constant.

[0061] The vehicle's roll and pitch motions are simplified into two one-degree-of-freedom models as follows:

[0062]

[0063]

[0064] In the formula, I xx and I yy Let I be the roll and pitch moments of inertia of the vehicle body, respectively. xx +m s h R 2 For I x I yy +m s h P 2 For I y m sh is the sprung mass of the vehicle. R and h P Let φ and θ be the distances from the roll center and pitch center to the center of mass of the sprung mass, respectively; g be the acceleration due to gravity; φ and θ be the roll angle and pitch angle, respectively; and K be the distance from the roll center and pitch center, respectively. φ and K θ These are the roll and pitch stiffness, respectively, C φ and C θ These are the roll and pitch damping coefficients, respectively. In summary, this allows for the establishment of a vehicle-tire dynamics model, combined with... Figure 2 As shown.

[0065] Step 2: Design the observer form for distributed estimation

[0066] Combination Figure 3 As shown, the observer form, consisting of four interconnected subsystems, is designed based on the distributed estimation method as follows:

[0067]

[0068]

[0069]

[0070]

[0071] In the formula, K x K y K r K roll K pitch and K ω1 ~K ω4 It represents the gain to be designed for the observer, and the superscript ^ indicates the estimated value of the corresponding parameter.

[0072] Step 3: Stability Analysis of the Observer Subsystem

[0073] For the four subsystems (7) to (10), the stability of their error subsystems relative to the actual system is analyzed independently, and the range of values ​​of the gain of each subsystem is obtained in the stability analysis, as follows:

[0074] 3.1 Stability of the first error subsystem

[0075] For the first subsystem represented by formula (7), the error subsystem between the actual system and this subsystem is as follows:

[0076]

[0077] In the formula, and These represent the estimation errors for the corresponding parameters. and These are functions represented by the actual and estimated values ​​of the corresponding parameters, respectively. They are merely intermediate variables introduced during stability analysis and their values ​​do not need to be calculated. u1 to u3 are considered as input terms separated from this error subsystem, and have the following forms:

[0078]

[0079] When analyzing the stability of the error subsystem here, u1 to u3 are ignored.

[0080] definition The Lyapunov function is constructed as follows:

[0081]

[0082] Its derivative is as follows:

[0083]

[0084] Among them and After scaling, we get:

[0085]

[0086] In the formula, c1 to c9 are all positive constants.

[0087]

[0088] The necessary and sufficient condition for the derivative of this Lyapunov function to be negative definite is that P1 is a positive definite matrix. Solving for the conditions under which its principal minors are positive, we obtain the following range of values ​​for the gain in the first subsystem:

[0089]

[0090] 3.2 Stability of the second error subsystem

[0091] For the second subsystem represented by formula (8), the wheel rolling resistance torque T ri The error term is relatively small and can be ignored. The error subsystem of the actual system and this subsystem is as follows:

[0092]

[0093] In the formula, This represents the estimation error of the corresponding parameters. It is a function represented by the actual and estimated values ​​of the corresponding parameters. The intermediate variables introduced during stability analysis do not need to be calculated. u4 to u7 are the input terms separated from this error subsystem, and have the following forms:

[0094]

[0095] Similarly, u4 to u6 are ignored when analyzing the stability of the error subsystem here.

[0096] definition The Lyapunov function is constructed and its derivative is calculated as follows:

[0097]

[0098] After scaling, we get:

[0099]

[0100] In the formula, c 12 It is a positive number.

[0101] Therefore, only the gain value K in the second subsystem is needed. ωi >-c 12 .

[0102] 3.3 Stability of the last two error subsystems

[0103] For the third subsystem represented by formula (9) and the fourth subsystem represented by formula (10), the error subsystems of the actual system and these two subsystems are as follows:

[0104]

[0105] It can be written in state-space form as follows:

[0106]

[0107] The Lyapunov function is constructed and its derivative is calculated as follows:

[0108]

[0109] In the formula, P3 and P4 are obtained by solving the Lyapunov equation A3. T P3 + P3A3 = -Q and A4 T P4 + P4A4 = -Q yields the following: The necessary and sufficient condition for the Lyapunov equation to have a solution for any positive definite matrix Q is that matrices A3 and A4 are Hurwitz matrices, which is equivalent to the following three conditions holding true:

[0110] K φ -m s gh R >0, Kθ -m s gh P >0 (25)

[0111]

[0112]

[0113] Formula (25) is a constant expression that always holds true, while formula (26) determines the gain K in the third subsystem. roll The range of values ​​for K is determined by formula (27), which in turn determines the gain K in the fourth subsystem. pitch The range of values ​​for .

[0114] Step 4: Stability analysis of the overall observer interconnection system

[0115] In step three, the input terms u1 to u7 in error subsystems (11) and (18) are ignored, and the range of gain values ​​that stabilize each error subsystem is initially determined. Further considering the observer form, the four subsystems (7) to (10) actually form an observer interconnected system. The subsystems are coupled through the transfer of state variables, and the error subsystems between the actual system and the subsystems form an error interconnected system. Therefore, it is necessary to analyze the stability of the error interconnected system, and the four error subsystems are denoted as follows:

[0116]

[0117] In the formula, f i (x i To separate the remaining components of the input, g i Let g1(x) be the input term, and g1(x) = [u1, u2, u3] T g2(x) = [u4, u5, u6, u7] T g3(x) and g4(x) are 0.

[0118] Construct the Lyapunov function and take its derivative as follows:

[0119]

[0120]

[0121] In the formula, V i (x i ) represents the Lyapunov function corresponding to each error subsystem in step three, and d i For the positive constants to be designed.

[0122] Since step three ensures the stability of the subsystem with no input error, the following scaling applies.

[0123]

[0124] In the formula, α1~α4 are positive numbers related to the gain, and φ i Let x be the error state quantity. i The square root of the sum of the squares of the elements.

[0125] For the second term in formula (30), the two product terms have the following scaling:

[0126]

[0127] In the formula, γ 12 γ 13 γ 14 and γ 21 γ 23 γ 24 It is a positive constant related to gain.

[0128] Combining formulas (31) and (32), scaling down formula (30) and writing it in matrix form, we get:

[0129]

[0130] A sufficient condition for the existence of the Lyapunov function and the negative definite derivative of equation (29) is that there exists a positive diagonal matrix D such that DS+S T D is a positive definite matrix. For a special form of matrix S, where the diagonal elements are positive and all off-diagonal elements are negative, if the principal minors of S are positive, then the aforementioned matrix D must exist. Since α1 to α4 are all positive, it is only necessary to satisfy α1α2 > γ. 12 γ 21 The condition is that the principal minors of S are positive. The specific forms of these parameters are given below:

[0131] α1 is the smallest eigenvalue of the positive definite matrix P1 in formula (16), i.e., α1 = λ min (P1);

[0132] Take K ω1 ~K ω4 For the same value K ω Combining formulas (21) and (31), we can obtain α2 = c 12 +K ω .

[0133] γ 12 It has the following forms:

[0134]

[0135] γ 21 It has the following forms:

[0136]

[0137] Finally, the condition α1α2>γ 12 γ 21 Transformed into a gain K ω The restrictions are as follows:

[0138]

[0139] Under the condition that the subsystems are stable and gain is achieved, the stability of the observer interconnection system can be guaranteed by adding the condition of formula (36).

[0140] Step 5: Perform state estimation for the vehicle and tires.

[0141] By determining the gain range and selecting an appropriate gain through the stability proof above, formula (17) gives K. x K y and K r The range of values ​​for K is given by formulas (26) and (27). roll and K pitch The range of values ​​for K is determined by formula (36). ω The range, take K ω1 ~K ω4 =K ω .

[0142] After determining the gain, an observer interconnection system represented by four subsystems (7) to (10) is constructed, combined with Figure 3 As shown, the observer interconnection system receives measurement information from the vehicle, including a x a y ,r, ω1~ω4, δ1~δ4 and T1~T4 are used as inputs. The four subsystems operate independently while outputting their own state variables and receiving the state variable values ​​of the other subsystems. This preserves the coupling relationship between the state variables and makes the four subsystems form an overall observer interconnected system.

[0143] Ultimately, the observer interconnect system can directly output a series of state estimates for the vehicle, including longitudinal speed. Lateral velocity yaw rate Wheel speed roll angle and roll rate and pitch angle and pitch angular velocity The tire's slip ratio κ, slip angle α, and longitudinal force F x and lateral force F y It is calculated as an intermediate quantity in each cycle of the observer interconnect system, and is also used by the observer interconnect system output for estimating the actual tire condition.

[0144] Example

[0145] The superiority of the method of this invention was verified by simulation. The relevant vehicle parameters in the simulation are as follows: m = 1613 kg, m s =1370kg, l f =1.11m, l r =1.756m, I xx = 671.3 kg·m 2 I yy =1972.8 kg·m 2 I z = 2966.5 kg·m 2 w = 1.55m, h R =0.576m, h P =0.59m, K φ =129580 N·m / rad, C φ = 9473 N·m / rad·s, K θ = 459706 N·m / rad, C θ = 39780 N·m / rad·s, J w = 9473 kg·m 2 R e =0.325m, C D =0.3, A=2.4m 2 R rc =0.0038, R rv =2.6×10 -5 h / km.

[0146] The parameters for the tire magic formula are as follows:

[0147] B x =21.58, B y =12.38, C x =1.397, C y =1.41, D x =4654, D y =4466, E x =0.507, E y = -0.284, F z0 =4769N.

[0148] The designed observer gain is as follows:

[0149] K x =0.5, K y =0.4, K r =20, K ω1 ~K ω4 =50, K roll =10, K pitch =5.

[0150] In the software simulation test, the vehicle dynamics simulation software VeDYNA provided a high-precision vehicle model, set up the road environment, and controlled the vehicle's motion. A relatively small road surface adhesion coefficient of 0.4 was set to simulate a low-adhesion road surface. To test the observer's estimation effect under the combined lateral and longitudinal motion of the vehicle, the vehicle was set to accelerate from 10 km / h to 80 km / h within 10 seconds, with a sinusoidal steering wheel angle of 90° and a period of 4 seconds applied continuously.

[0151] Combination Figure 4 As shown, the results of the distributed estimation method for vehicle state information are presented and compared with the true values ​​provided by the vehicle dynamics simulation software VeDYNA. The results show that the estimated values ​​of each state variable of the vehicle are very close to their true values.

[0152] Combination Figure 5 As shown, the distributed estimation method is used to estimate the tire slip ratio, sideslip angle, and lateral and longitudinal tire forces, and the results are compared with the actual values. The results show that the distributed estimation method combined with the magic formula for composite driving conditions can accurately reflect tire information.

[0153] In hardware-in-the-loop simulation, the observer is deployed on the hardware platform and communicates with the computer via the CAN bus. The hardware platform receives vehicle information output by VeDYNA via the CAN bus, estimates it in the observer model, and then transmits the estimated information back to the computer.

[0154] Combination Figure 6 As shown, the estimation results in the hardware-in-the-loop simulation are very close to those in the pure simulation, indicating that the influence of CAN bus signal transmission on state estimation can be ignored, and the observer algorithm has high computational efficiency on conventional hardware platforms.

[0155] The above results show that the distributed estimation method of the present invention has good estimation accuracy in both software simulation and hardware-in-the-loop simulation, and can achieve accurate estimation of vehicle and tire state information.

[0156] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0157] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A design method for a vehicle and tire state observer based on distributed estimation, characterized in that: Includes the following steps: Step 1: Establishing the tire force formula and vehicle dynamics model Considering the combined working conditions of tire slippage and lateral deviation, the following magic formula for tires under combined working conditions is established: In the formula, F x and F y F represents the longitudinal force and lateral force of the tire, respectively. z F represents the current vertical load on the tire. z0 Indicates the tire's nominal load, σ X σ Y σ is an intermediate value in the calculation, κ is the slip ratio, α is the sideslip angle, μ represents the current road surface adhesion coefficient, μ0 = 1, B x and B y C represents the stiffness factor for longitudinal force and lateral force, respectively. x and C y The curve shape factors, D, represent the longitudinal and lateral forces, respectively. x and D y E represents the peak factor for longitudinal force and lateral force, respectively. x and E y These are the curvature factors of the curves for longitudinal force and lateral force, respectively; The motion of a vehicle in the yaw plane consists of longitudinal, lateral, and yaw motions, as shown below: Wherein, longitudinal acceleration a x Lateral acceleration a y and yaw moment M z Calculated using the following formula: In the formula, v x and v y These represent the longitudinal and lateral velocities, respectively, where r is the yaw rate and I is the longitudinal and lateral velocities. z Let F be the vehicle's moment of inertia about the z-axis, m be the vehicle's mass, and F be the inertia of the vehicle about the z-axis. x1 ~F x4 and F y1 ~F y4 These represent the longitudinal and lateral forces of the four tires as described by the composite tire magic formula, with δ1 to δ4 representing the four wheel rotation angles, and C... D Where A is the air resistance coefficient, ρ is the frontal area, and l is the air density. f and l r These are the distances from the vehicle's center of gravity to the centers of the front and rear axles, respectively, and w is the track width between the front and rear axles. The differential equations for the four-wheel dynamics are established as follows: In the formula, J w Let ω be the moment of inertia of a single wheel. i T is the wheel speed. i R is the driving or braking torque acting on the wheels. e T is the effective radius of the wheel. ri T is the rolling resistance torque of the wheel. ri =F zi R e (R rc +R rv v x ), R rc and R rv It is a constant; The vehicle's roll and pitch motions are simplified into two one-degree-of-freedom models as follows: In the formula, I xx and I yy Let I be the roll and pitch moments of inertia of the vehicle body, respectively. xx +m s h R 2 For I x I yy +m s h P 2 For I y m s h is the sprung mass of the vehicle. R and h P Let φ and θ be the distances from the roll center and pitch center to the center of mass of the sprung mass, respectively; g be the acceleration due to gravity; φ and θ be the roll angle and pitch angle, respectively; and K be the distance from the roll center and pitch center, respectively. φ and K θ These are the roll and pitch stiffness, respectively, C φ and C θ These are the roll and pitch damping coefficients, respectively. Step 2: Design the observer form for distributed estimation The observer, consisting of four interconnected subsystems, is designed based on a distributed estimation method as follows: In the formula, K x K y K r K roll K pitch and K ω1 ~K ω4 It is the gain to be designed for the observer, and the superscript ^ indicates the estimated value of the corresponding parameter; Step 3: Stability Analysis of the Observer Subsystem For the four subsystems (7) to (10), the stability of their error subsystems relative to the actual system is analyzed independently, and the range of values ​​of the gain of each subsystem is determined in the stability analysis. Step 4: Stability analysis of the overall observer interconnection system The four subsystems (7) to (10) form the observer interconnection system. The error subsystem between the actual system and the subsystems forms the error interconnection system. The stability of the error interconnection system is analyzed and its conditions are determined. The observer interconnection system adds this condition while determining the gain of each subsystem to ensure the overall stability of the observer interconnection system. Step 5: Perform state estimation for the vehicle and tires. An observer interconnection system is constructed, consisting of four subsystems (7) to (10). The observer interconnection system receives measurement information from the vehicle, including a x a y ,r, Taking ω1~ω4, δ1~δ4, and T1~T4 as inputs, the observer interconnect system directly outputs a series of state estimates of the vehicle, including longitudinal velocity. Lateral velocity yaw rate Wheel speed roll angle and roll rate and pitch angle and pitch angular velocity The tire's slip ratio κ, slip angle α, and longitudinal force F x and lateral force F y It is calculated as an intermediate quantity in each cycle of the observer interconnect system, and is also used by the observer interconnect system output for estimating the actual tire condition.

2. The method for designing a vehicle and tire state observer based on distributed estimation according to claim 1, characterized in that: The stability analysis of the observer subsystem in step three specifically includes: 3.1 Stability of the first error subsystem For the first subsystem represented by formula (7), the error subsystem between the actual system and this subsystem is as follows: In the formula, and These represent the estimation errors for the corresponding parameters. and These are functions represented by the actual and estimated values ​​of the corresponding parameters, respectively. They are intermediate variables and their values ​​do not need to be calculated. u1 to u3 are regarded as input terms separated from the error subsystem. When analyzing the stability of the error subsystem, u1 to u3 are ignored. definition The Lyapunov function is constructed as follows: Its derivative is as follows: Among them and After scaling, we get: In the formula, c1 to c9 are all positive constants; The final range of gain values ​​in the first subsystem is as follows: 3.2 Stability of the second error subsystem For the second subsystem represented by formula (8), the wheel rolling resistance torque T is ignored. ri The error subsystem between the actual system and this subsystem is as follows: In the formula, This represents the estimation error of the corresponding parameters. The function is represented by the actual and estimated values ​​of the corresponding parameters. The intermediate variables do not need to be calculated. u4 to u7 are the input terms separated from the error subsystem. u4 to u6 are ignored when analyzing the stability of the error subsystem. definition The Lyapunov function is constructed and its derivative is calculated as follows: After scaling, we get: In the formula, c 12 It is a positive number; Finally, the gain value K in the second subsystem is obtained. ωi >-c 12 ; 3.3 Stability of the last two error subsystems For the third subsystem represented by formula (9) and the fourth subsystem represented by formula (10), the error subsystems of the actual system and these two subsystems are as follows: It can be written in state-space form as follows: The Lyapunov function is constructed and its derivative is calculated as follows: The final gain ranges for the third and fourth subsystems are as follows:

3. The method for designing a vehicle and tire state observer based on distributed estimation according to claim 2, characterized in that: The stability analysis of the overall observer interconnection system in step four specifically includes: The four error subsystems are represented in the following form: In the formula, f i (x i To separate the remaining components of the input, g i Let g1(x) be the input term, and g1(x) = [u1, u2, u3] T g2(x) = [u4, u5, u6, u7] T g3(x) and g4(x) are 0; Construct the Lyapunov function and take its derivative as follows: In the formula, V i (x i ) represents the Lyapunov function corresponding to each error subsystem in step three, and d i For the positive constants to be designed; Scaling up and rewriting formula (30) in matrix form, we get: In the formula, α1~α4 are positive numbers related to the gain, and φ i Let x be the error state quantity. i The square root of the sum of squares of the elements, γ 12 γ 13 γ 14 and γ 21 γ 23 γ 24 It is a positive constant related to gain; Since α1 to α4 are all positive, α1α2 > γ 12 γ 21 The condition is that the principal minors of S are positive, and the specific form of the parameter is as follows: α1=λ min (P1); Take K ω1 ~K ω4 For the same value K ω α2=c 12 +K ω ; γ 12 It has the following forms: γ 21 It has the following forms: Finally, the condition α1α2>γ 12 γ 21 Transformed into a gain K ω The restrictions are as follows:

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