Tire-road adhesion coefficient estimation method based on distributed driving electric vehicle

Abstract

The invention discloses a tire-road adhesion coefficient estimation method based on a distributed driving electric vehicle, and the method comprises the following steps: firstly, in order to improve the rotating speed control precision of a PMSM, combining SMC and ADRC for the rotating speed loop control of the PMSM, thereby improving the rotating speed control precision of the PMSM; secondly, the PMSM serves as a hub motor of the whole vehicle, and a whole vehicle model of the distributed driving electric vehicle is constructed; in order to reduce the use of a vehicle-mounted sensor, an MA-SR7thCKF algorithm is deduced, the algorithm can ensure the semi-positive qualification of an error covariance matrix and solve the problem that the filtering precision is reduced due to excessive use of historical data, and the algorithm is adopted to estimate the rotating speed and the rotor position of a PMSM and is used for estimating related vehicle state parameters. Finally, the estimated related vehicle state parameters serve as input, a Dugoff model is adopted to calculate normalized tire force, the normalized tire force serves as input, and an MA-SR7thCKF algorithm is adopted to estimate the tire-road adhesion coefficient.

Description

Technical Field

[0001] The present invention relates to the technical field of tire-road adhesion coefficient estimation methods, and specifically relates to a tire-road adhesion coefficient estimation method based on a distributed drive electric vehicle. Background Art

[0002] Tire-road adhesion coefficient estimation methods can be roughly divided into two recognition methods: Cause-Based and Effect-Based. Among them, the Cause-Based recognition method is to establish a mathematical model reflecting the relationship between various factors and the tire-road adhesion coefficient. For example, an optical sensor, a laser beam, an acoustic wave emitter, etc. are used to analyze the road surface type, so as to identify the tire-road adhesion coefficient. However, this method requires additional sensors, with high costs and is easily affected by external factors. The Effect-Based recognition method estimates the tire-road adhesion coefficient by measuring and analyzing the vehicle response caused by road surface changes. This method can be further divided into two types: the tire response method and the vehicle dynamics response method. Based on the tire response method, the tire-road adhesion coefficient can be identified by measuring tire noise, tire deformation, etc.; based on the tire response, the tire-road adhesion coefficient can be estimated by analyzing the adhesion conditions and vehicle states and using tire models and algorithms. This method generally does not require additional sensors and has low requirements for the environment, and is currently a research hotspot for tire-road adhesion coefficient estimation.

[0003] Most current estimation methods are based on traditional fuel vehicles, and there is little research on estimating the tire-road adhesion coefficient of distributed drive electric vehicles. The main tire-road adhesion coefficient estimation methods include improved algorithms such as EKF, UKF, and CKF. EKF expands the nonlinear function into a Taylor series and transforms the nonlinear system into a linear system by omitting high-order terms. However, the omission of high-order terms will introduce truncation errors, and the estimation accuracy may decrease when the nonlinearity increases; UKF samples near the estimation point to approximate the probability distribution of the nonlinear function, overcoming the defects brought by local linearization. However, when the probability density deviates greatly from the Gaussian distribution, it may cause the error covariance matrix to be non-positive definite; CKF optimizes the sampling method and weight ratio of Sigma points in UKF by using spherical integration and radial integration criteria, improving the performance of the filter, but still cannot ensure the positive definiteness of the error covariance matrix. And 5thCKF improves the filtering accuracy by improving the cubature points and weights, but still cannot meet the accuracy requirements under complex road conditions. Therefore, how to further improve the estimation accuracy of the tire-road adhesion coefficient is the problem to be solved currently. Summary of the Invention

[0004] The technical problem to be solved by the present invention is the problem of insufficient estimation accuracy of the tire-road adhesion coefficient in the prior art. To solve the above problem, a method for estimating the tire-road adhesion coefficient based on a distributed drive electric vehicle is provided.

[0005] The object of the present invention is achieved in the following manner:

[0006] A method for estimating the tire-road adhesion coefficient based on a distributed drive electric vehicle, the method comprising the following steps:

[0007] S1: According to the mathematical model of the permanent magnet synchronous motor (PMSM), the designed new sliding mode control-active disturbance rejection controller (SMC-ADRC) is used to control the speed of the permanent magnet synchronous motor (PMSM) to improve the speed control accuracy of the PMSM; and the designed multi-innovation square root cubature Kalman filter algorithm (MA-SR7thCKF) is used to estimate the speed and rotor position of the PMSM, so as to realize the sensorless control of the PMSM;

[0008] S2: The permanent magnet synchronous motor (PMSM) is used as the in-wheel motor of the whole vehicle to construct a distributed drive electric vehicle whole vehicle model;

[0009] Based on the existing vehicle-mounted sensors, the distributed drive electric vehicle whole vehicle model has the ability to collect the front wheel steering angle δ, wheel speed ω ij , longitudinal acceleration a x , lateral acceleration a y , driving torque T dij , braking torque T bij signals;

[0010] S3: The front wheel steering angle δ and longitudinal acceleration a x are used as the system input values, and the lateral acceleration a y is used as the system observation value. According to the vehicle dynamics model, the multi-innovation square root cubature Kalman filter algorithm (MA-SR7thCKF) is used to estimate the yaw rate r, center of mass side slip angle β, longitudinal speed v x ; thus, the estimated values of the vehicle state parameters used in the Dugoff model to calculate the normalized tire force are obtained;

[0011] S4: According to the front wheel steering angle δ, wheel speed ω ij , longitudinal acceleration a x , lateral acceleration a y , driving torque T dij , braking torque T bij collected by the whole vehicle model and the estimated yaw rate r, center of mass side slip angle β, longitudinal speed v x , the tire side slip angle α ij , slip ratio λ ij , vertical force F zij; On the premise that the tire-road adhesion coefficient is unknown, according to the known vehicle body parameters, the sideslip angle α ij , slip ratio λ ij and vertical force F zij are used as inputs, and the normalized tire force is calculated through the Dugoff model and

[0012] S5: The front wheel steering angle δ and the normalized tire force and are used as system input values, the longitudinal acceleration a x , lateral acceleration a y and yaw rate r are used as system observation values, and the MA-SR7thCKF algorithm is used to estimate the tire-road adhesion coefficient; in the time update, the sampling points and weights are redistributed according to the seventh-order-sphere radius criterion, and the state mean and covariance are predicted by using the numerical integration method; in the measurement update, the Kalman gain is calculated according to the observation values, and the predicted state and covariance are adjusted to obtain the corrected state estimation value; through recursive iteration, the input and observation data are effectively fused, the noise influence is suppressed, and the estimation accuracy of the road adhesion coefficient is further improved by introducing the decaying memory filter and QR decomposition, so as to improve the accuracy and stability of vehicle dynamic control.

[0013] The novel SMC-ADRC controller designed according to the PMSM mathematical model in S1:

[0014] The PMSM mathematical model is:

[0015]

[0016] Where: i α and i β are the current components of the stator winding in the stationary coordinate system; u α and u β are the voltage components of the stator winding in the stationary coordinate system; R s and L s are the resistance and inductance respectively; ψ f is the magnetic flux; ω m is the mechanical angular velocity of the rotor; θ e is the rotor position; p n is the number of pole pairs; J is the moment of inertia; B is the damping coefficient; T e is the electromagnetic torque; T L is the load torque;

[0017] The novel SMC-ADRC design method is:

[0018] To solve the difficulty in parameter tuning of the second-order ADRC and reduce the jitter of the system state, the SMC is combined with the NLESO in the ADRC, and a new reaching law is designed to improve the control performance of the ADRC. The designed new reaching law is as follows:

[0019]

[0020] where: s is the defined sliding surface; ε is the reaching coefficient; sign is the sign function; q is the exponential reaching coefficient; d is the parameter to be adjusted;

[0021] The new reaching law introduces the L(s) function, enabling the system to adaptively adjust the convergence speed. When the moving point is far from the sliding surface, it is in the convergence stage. At this time, |s| is large, L(s) tends to infinity, the convergence speed increases, and the convergence time is shortened. When the moving point is close to the sliding surface, it is in the motion stage. At this time, |s| is small, L(s) tends to d / (1 + d), the convergence speed decreases, and the jitter is weakened;

[0022] The NLESO improved by the SMC is as follows:

[0023]

[0024] where: b * is the control gain; k1 and k2 are the proportional and gain coefficients respectively, e, e1, e2, e3 are the error signals; c is the stability parameter; u is the system input; y is the system output; z1 is the tracking signal of y; z2 is the differential signal of y; z3 is the disturbance observation signal.

[0025] The vehicle dynamics model in S3 is as follows:

[0026] Longitudinal:

[0027]

[0028] Lateral:

[0029]

[0030] Yaw:

[0031]

[0032] The longitudinal and lateral accelerations are:

[0033]

[0034] The wheel dynamics equation is:

[0035]

[0036] where: m is the total vehicle mass, v x is the longitudinal speed; v y is the lateral speed; a x is the longitudinal acceleration; a y is the lateral acceleration; r is the yaw rate; I z is the moment of inertia about the z-axis; I ω is the moment of inertia of the tire; δ is the front wheel steering angle; t f is the front axle track width; t r is the rear axle track width; R ω is the wheel rolling radius; a and b represent the distances from the center of mass to the front axle and the rear axle respectively; T dij and T bij represent the tire driving torque and the braking torque respectively; F xij and F yij represent the longitudinal force and the lateral force acting on the tire respectively; ω ij is the wheel angular velocity; fl, fr, rl, rr represent the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel respectively;

[0037] Since the tire forces are unknown, a vehicle three-degree-of-freedom dynamic equation with tire cornering stiffness can be used to construct a vehicle state parameter estimation model:

[0038]

[0039] where: C yf is the front wheel cornering stiffness, C yr is the rear wheel cornering stiffness.

[0040] In step S4, the method for calculating the normalized tire force with the tire slip angle α ij , the slip ratio λ ij , and the vertical force F zij as inputs according to the Dugoff model is:

[0041] The calculation formulas for the tire slip angle α ij , the slip ratio λ ij , and the vertical force F ij are respectively:

[0042]

[0043] where, m is the total vehicle mass, v x is the longitudinal speed; v y is the lateral speed; a x is the longitudinal acceleration; a y is the lateral acceleration; r is the yaw rate; I z is the moment of inertia about the z-axis; I ω is the moment of inertia of the tire; δ is the front wheel steering angle; t fis the front axle track; t r is the rear axle track; R ω is the wheel turning radius; a and b respectively represent the distances from the center of mass to the front axle and the rear axle; ω ij is the wheel turning angular velocity; l is the distance between the front and rear axles; h g is the height of the center of mass; g is the acceleration due to gravity;

[0044] The formula for calculating the tire force using the Dugoff model is:

[0045] Where:

[0046]

[0047]

[0048] Where: C xij and C yij are respectively the longitudinal stiffness and the lateral stiffness of each tire; λ ij is the longitudinal slip ratio; ε v is the speed influence factor;

[0049] When estimating the tire-road adhesion coefficient, the formula for calculating the tire force can be transformed into:

[0050]

[0051] Where: F xij and F yij respectively represent the longitudinal force and the lateral force received by the tire; and are respectively the normalized longitudinal force and the lateral force, μ ij is the road adhesion coefficient of the wheel.

[0052] The steps of the MA-SR7thCKF algorithm are as follows:

[0053] For the discrete PMSM speed and rotor position estimation system, the three-degree-of-freedom vehicle state parameter estimation system, and the tire-road adhesion coefficient estimation system, it can be written as an n-order system with additive noise:

[0054]

[0055] Where: u k is the input value of the system at time k; x k is the state value at time k; z k is the observed value at time k; w k is the process noise; v k is the measurement noise; w k and v kis mutually independent Gaussian white noise with zero mean, i.e., w k ~N(0, Q k ), v k ~N(0, R k ); f and h are the nonlinear state space function and the measurement function respectively;

[0056] Approximate the standard Gaussian weighted integral as:

[0057]

[0058] The sampling points corresponding to the 7th CKF algorithm are:

[0059]

[0060] Among them: the sampling methods are h1, h2, and h3 sampling respectively;

[0061] The point set in h1 sampling is {e j} and {-e j}, e j represents the j-th column of the identity matrix, and there are 2n sampling points; the point sets in h2 sampling are {m1}, {m2}, {m3}, {m4}, which are respectively expressed as:

[0062]

[0063] There are 4n(n - 1) sampling points;

[0064] The point sets in h3 sampling are {m5}, {m6}, {m7}, {m8}, which are respectively expressed as:

[0065] {m5} = {e k + e g + e t , k < g < t, k, g, t = 1, 2,..., n} (25)

[0066] {m6} = {e k + e g - e t , k < g < t, k, g, t = 1, 2,..., n} (26)

[0067] {m7} = {e k - e g + e t , k < g < t, k, g, t = 1, 2,..., n} (27)

[0068] {m8} = {e k - e g - e t, k < g < t, k, g, t = 1, 2, …, n} There are 4n(n - 1)(n - 2) / 3 sampling points;

[0069] Among them: e k , e g , e t respectively represent the k-th, g-th, and t-th columns of the identity matrix;

[0070] The above is the method for allocating sampling points and weights according to the seventh-order - sphere radius criterion. The subsequent steps are as follows:

[0071] Determine the total number of sampling points:

[0072] γ = (8 / 3)n(n - 1)(n - 2) + 8n 2 -4n + 1 (29)

[0073] Calculate the sampling points:

[0074]

[0075] Calculate the sampling points propagated through the state equation:

[0076]

[0077] Calculate the predicted state value:

[0078]

[0079] Calculate the predicted square root error covariance matrix:

[0080]

[0081] Among them:

[0082]

[0083] Calculate the updated sampling points:

[0084]

[0085] Calculate the sampling points propagated through the measurement equation:

[0086] Z i,k|k-1 = h(X i,k|k-1 , u k ) (36)

[0087] Calculate the predicted measurement value:

[0088]

[0089] Calculate the cross-covariance matrix:

[0090]

[0091] Calculate the predicted square root measurement error covariance matrix:

[0092]

[0093] Where:

[0094]

[0095] Calculate the Kalman gain:

[0096]

[0097] Calculate the state estimate:

[0098]

[0099] Calculate the square root error covariance matrix:

[0100]

[0101] The above is the complete process of the MA-SR7thCKF algorithm. Formula section (next section)

[0102] Advantages of the present invention: The present invention can effectively improve the estimation accuracy of the tire-road adhesion coefficient of a distributed drive electric vehicle under sensorless control of PMSM. First, to improve the speed control accuracy of PMSM, a speed control method of PMSM based on a novel SMC-ADRC is designed; second, the 7thCKF algorithm is derived, and QR decomposition and fading memory filtering are introduced to design the MA-SR7thCKF algorithm, which can ensure the positive semi-definiteness of the error covariance matrix while solving the problem of the decrease in filtering accuracy caused by excessive use of historical data. The MA-SR7thCKF algorithm is used to estimate the speed and rotor position of PMSM and related vehicle state parameters, reducing the use and cost of on-vehicle sensors; finally, the estimated vehicle state parameters are used as the input of the Dugoff model to calculate the normalized tire force, and the MA-SR7thCKF algorithm is used to estimate the tire-road adhesion coefficient, and experimental verification shows that the proposed method has high estimation accuracy. Description of the Drawings

[0103] Figure 1 It is a structural diagram of a method for estimating the tire-road adhesion coefficient of a distributed drive electric vehicle in an embodiment of the present invention.

[0104] Figure 2 It is a structural diagram of a novel SMC-ADRC in an embodiment of the present invention.

[0105] Figure 3 This is the three - degree - of - freedom vehicle dynamics model diagram in the embodiment of the present invention.

[0106] Figure 4 This is the comparison curve diagram of the PMSM speed and rotor position control effect in the embodiment of the present invention.

[0107] Figure 5 This is the comparison curve diagram of the PMSM speed and rotor position estimation in the embodiment of the present invention.

[0108] Figure 6 This is the comparison curve diagram of the vehicle state parameter estimation in the embodiment of the present invention.

[0109] Figure 7 This is the comparison curve diagram of the tire - road adhesion coefficient estimation in the embodiment of the present invention. Detailed implementation manners

[0110] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0111] It should be noted that the following detailed description is exemplary and is intended to provide further illustration of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same technical meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0112] The present invention aims to provide a method for estimating the tire - road adhesion coefficient of a distributed - drive electric vehicle based on PMSM sensorless control, so as to improve the control and estimation accuracy of the PMSM speed and rotor position, and estimate the tire - road adhesion coefficient of the distributed - drive electric vehicle under the condition of reducing the cost of on - vehicle sensors.

[0113] As Figure 1 shown, a method for estimating the tire - road adhesion coefficient of a distributed - drive electric vehicle based on PMSM sensorless control includes a PMSM sensorless control module, a distributed - drive electric vehicle vehicle model, a vehicle state parameter estimation module, and a tire - road adhesion coefficient estimation module. The steps are as follows:

[0114] S1: The process of designing a new SMC - ADRC controller according to the PMSM mathematical model is as follows:

[0115] The PMSM mathematical model is:

[0116]

[0117] Where: i α and i β are the current components of the stator winding in the stationary coordinate system; u α and u βis the voltage component of the stator winding in the stationary coordinate system; R s and L s are the resistance and inductance respectively; ψ f is the magnetic flux; ω m is the mechanical angular velocity of the rotor; θ e is the rotor position; p n is the number of pole pairs; J is the moment of inertia; B is the damping coefficient; T e is the electromagnetic torque; T L is the load torque.

[0118] As Figure 2 shown, the novel SMC-ADRC designed by the present invention can be regarded as the combination of TD, improved NLESO, and NLSEF. The improved controller can not only solve the difficulty of ADRC in parameter tuning, but also weaken the jitter of the system state.

[0119] Among them, TD can track the reference signal and its differential signal as soon as possible; the improved NLESO can integrate the sliding mode variable structure and design a novel reaching law to observe the disturbance; NLSEF can tune the error signal into the form of non-linear PID control.

[0120] For the following form of non-linear second-order system:

[0121]

[0122] The mechanical motion equation of PMSM is:

[0123]

[0124] From the above formula, it can be obtained that:

[0125]

[0126] Adopt the control strategy of i d = 0, and substitute θ e = p n ∫ω m dt into it, and thus it can be obtained that:

[0127]

[0128] Converting the mechanical motion equation of PMSM into the above form of non-linear second-order system, it can be obtained that:

[0129]

[0130] According to the above derivation, the process of designing the novel SMC-ADRC is as follows:

[0131] The expression of TD is as follows:

[0132]

[0133] Where: y* is the target output; v1 and v2 are the tracking signal and the differential signal of the target signal respectively; h is the discrete integration step; fhan is the maximum speed control synthesis function.

[0134] The NLSEF expression is as follows:

[0135]

[0136] The expression of the fal function is as follows:

[0137]

[0138] Where: e, e1, and e2 are error signals; α1 and α2 are tracking factors; δ* is a filtering factor; β1 and β2 are gain adjustment factors.

[0139] The design process of the improved NLESO is as follows:

[0140] The NLESO expression is as follows:

[0141]

[0142] Where: y is the system output; z1 is the tracking signal of y; z2 is the differential signal of y; z3 is the disturbance observation signal; β nl1 , β nl2 and β nl3 are error correction factors.

[0143] According to the SMC principle, equation (10) can be rewritten as:

[0144]

[0145] Where: g is the optimal control function, and g(e) is used to replace the nonlinear function fal(e, α, δ), thereby reducing the number of adjustment parameters; k1 and k2 are the proportional and gain coefficients respectively.

[0146] The error equation is constructed as follows:

[0147]

[0148] Taking the derivative of equation (12) gives:

[0149]

[0150] Where: f can be obtained through equation (6). The designed sliding mode surface is:

[0152] s = ce1 + e2 (14)

[0153] Taking the derivative of Equation (14) gives:

[0154]

[0155] where c is the stability parameter and c > 0. When the state variable is in sliding, it is required to quickly converge to the linear sliding mode surface. To meet the above characteristics, the designed new reaching law is as follows:

[0156]

[0157] where: s is the defined sliding mode surface; ε is the reaching coefficient; sign is the sign function; q is the exponential reaching coefficient; d is the parameter to be adjusted.

[0158] The new reaching law introduces the L(s) function, enabling the system to adaptively adjust the convergence speed. When the moving point is far from the sliding mode surface, it is in the convergence stage. At this time, |s| is large, L(s) tends to infinity, the convergence speed increases, and the convergence time is accelerated. When the moving point is close to the sliding mode surface, it is in the motion stage. At this time, |s| is small, L(s) tends to d / (1 + d), the convergence speed decreases, and the jitter weakens.

[0159] According to the above derivation, the optimal control function g(e) is:

[0160]

[0161] The improved NLESO expression is as follows:

[0162]

[0163] where: b * is the control gain; k1 and k2 are the proportional and gain coefficients respectively; e, e1, e2, e3 are the error signals; c is the stability parameter; u is the system input; y is the system output; z1 is the tracking signal of y; z2 is the differential signal of y; z3 is the disturbance observation signal;

[0164] Define the Lyapunov function as:

[0165] V = s 2 / 2 (19)

[0166] Taking the derivative of Equation (19) gives:

[0167]

[0168] Since q > 0, s * sign(s) > 0, L(s) > 0, so V < 0 is satisfied.

[0169] S2: The Carsim software can simulate the dynamic responses of a vehicle under different working conditions, and conduct simulations and verifications on the power performance, braking performance, handling stability, etc. of the vehicle during driving. However, the vehicle models provided in the Carsim software are mainly traditional internal combustion engine vehicle models. Therefore, when studying distributed drive electric vehicles, the power system built-in in Carsim needs to be changed to an external interface for access and connected to the PMSM model built in the Matlab / Simulink software, so that the wheel speed output by the vehicle model is the target speed of the in-wheel motor, and the in-wheel motor provides the driving torque for the whole vehicle model. The error between the target speed and the actual speed is used to obtain the load torque of the in-wheel motor through PID control, thereby building a whole vehicle model of a distributed drive electric vehicle. And collect signals including the front wheel steering angle δ, wheel speed ω ij , longitudinal acceleration a x , lateral acceleration a y , driving torque T dij , braking torque T bij .

[0170] S3: As Figure 3 shown, the three-degree-of-freedom dynamic equation of a vehicle with tire cornering stiffness is:

[0171]

[0172] Where: C yf is the front wheel cornering stiffness; C yr is the rear wheel cornering stiffness; a and b respectively represent the distances from the center of mass to the front axle and the rear axle; m is the total mass of the vehicle; δ is the front wheel steering angle; v x is the longitudinal speed; v y is the lateral speed; a x is the longitudinal acceleration; r is the yaw angular velocity; β is the center of mass side slip angle; I z is the moment of inertia about the z-axis; I ω is the moment of inertia of the tire;

[0173] S4: According to the collected sensing information and the estimated values of vehicle state parameters, with the wheel side slip angle α ij , slip ratio λ ij , vertical force F ij as inputs, the process of calculating the normalized tire force according to the Dugoff model is:

[0174] The calculation formulas for the wheel side slip angle α ij , slip ratio λ ij , vertical force F ij are respectively:

[0175]

[0176] Where: αfl 、 α fr 、 α rl 、 α rr are the sideslip angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively.

[0177]

[0178] Where: ij = fl represents the left front wheel, ij = fr represents the right front wheel, ij = rl represents the left rear wheel, ij = rr represents the right rear wheel, λ fl 、 λ fr 、 λ rl 、 λ rr are the slip ratios of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively.

[0179]

[0180] Where: F zfl 、 F zfr 、 F zrl 、 F zrr are the vertical forces of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively; l is the distance between the front and rear axles; h g is the height of the center of mass; g is the acceleration due to gravity.

[0181] The formula for calculating the tire force using the Dugoff model is:

[0182]

[0183] Where: μ ij is the tire-road adhesion coefficient.

[0184] Where:

[0185]

[0186] Where: C xij and C yij are the longitudinal stiffness and lateral stiffness of each tire, respectively; α ij is the tire sideslip angle; λ ij is the longitudinal slip ratio; ε v is the speed influence factor.

[0187] When estimating the tire-road adhesion coefficient, the formula for calculating the tire force can be transformed into:

[0188]

[0189] Among S1, S3, and S5: When using the MA-SR7thCKF algorithm for estimation, the system needs to be discretized. The systems to be discretized include: the PMSM speed and rotor position estimation system, the three-degree-of-freedom vehicle state parameter estimation system, and the tire-road adhesion coefficient estimation system.

[0190] For the following non-linear system:

[0191]

[0192] where: u k is the system input value at time k; x k is the state value at time k; z k is the observation value at time k; f and h are the non-linear state space function and measurement function respectively.

[0193] If the sampling time is T s， The discretized PMSM speed and rotor position estimation system is:

[0194] State equation:

[0195]

[0196] Measurement equation:

[0197]

[0198] where: i α,k and i β,k are the current components of the stator winding in the stationary coordinate system at time k; u α,k and u β,k are the voltage components of the stator winding in the stationary coordinate system at time k; R s and L s are the resistance and inductance respectively; ψ f is the magnetic flux; ω m,k is the mechanical angular velocity of the rotor at time k; θ e,k is the rotor position at time k; p n is the number of pole pairs; J is the moment of inertia; B is the damping coefficient; T e,k is the electromagnetic torque at time k; T L,k is the load torque at time k.

[0199] where: x 1,k =[i α,k i β,k ω α,k θ α,k T , u 1,k =[u α,k u β,k T e,k θ​α,k T , z 1,k = [i α,k i β,k T 。

[0200] The discrete vehicle state parameter estimation system is as follows:

[0201] State equation:

[0202]

[0203] Measurement equation:

[0204]

[0205] Where: C yf is the front wheel cornering stiffness; C yr is the rear wheel cornering stiffness; a and b respectively represent the distances from the center of mass to the front axle and the rear axle; m is the total vehicle mass; δ k is the front wheel steering angle at time k; v x,k is the longitudinal speed at time k; v y,k is the lateral speed at time k; a x,k is the longitudinal acceleration at time k; a y,k is the lateral acceleration at time k; r k is the yaw rate at time k; β k is the center of mass side slip angle at time k; I z is the moment of inertia about the z-axis; I ω is the moment of inertia of the tire.

[0206] Where: x 2,k = [r k β ,k v x,k T , u 2,k = [δ k-1 a x,k-1 T , z 2,k = [a y,k-1 T 。

[0207] The discrete tire-road adhesion coefficient estimation system is as follows:

[0208] State equation:

[0209]

[0210] Measurement equation:

[0211] ​​​​​

[0212] where: μ fl,k , μ fr,k , μ rl,k , μ rr,k are respectively the tire-road adhesion coefficients of the left front wheel, right front wheel, left rear wheel, and right rear wheel at time k.

[0213] where: x 3,k = [μ fl,k μ fr,k μ rl,k μ rr,k T ,

[0214] where:

[0215]

[0216] are the normalized longitudinal tire forces; is the normalized lateral tire force; a and b respectively represent the distances from the center of mass to the front axle and the rear axle; m is the total vehicle mass; δ is the front wheel steering angle; I z is the moment of inertia about the z-axis; t f is the front axle track width; t r is the rear axle track width.

[0217] For the above system, it can be written as an nth-order system with additive noise:

[0218]

[0219] where: u k is the input value of the system; x k is the state value; z k is the observed value; w k is the process noise; v k is the measurement noise; w k and v k are independent of each other and Gaussian white noise with zero mean, i.e., w k ~N(0, Q k ), v k ~N(0, R k ).

[0220] Approximate the standard Gaussian weighted integral as:

[0221]

[0222] The sampling points corresponding to the 7th CKF algorithm are:

[0223]

[0224] ​

[0225] Among them: the sampling methods are h1, h2, and h3 sampling respectively.

[0226] The point set in h1 sampling is {e j} and {-e j}, where e j represents the j-th column of the identity matrix, and there are 2n sampling points.

[0227] The point sets in h2 sampling are {m1}, {m2}, {m3}, {m4}, which are respectively represented as:

[0228]

[0229] There are 4n(n - 1) sampling points.

[0230] The point sets in h3 sampling are {m5}, {m6}, {m7}, {m8}, which are respectively represented as:

[0231] {m5} = {e k + e g + e t , k < g < t, k, g, t = 1, 2, …, n} (45)

[0232] {m6} = {e k + e g - e t , k < g < t, k, g, t = 1, 2, …, n} (46)

[0233] {m7} = {e k - e g + e t , k < g < t, k, g, t = 1, 2, …, n…, n} (47)

[0234] {m8} = {e k - e g - e t , k < g < t, k, g, t = 1, 2, …, n…, n} (48)

[0235] There are 4n(n - 1)(n - 2) / 3 sampling points.

[0236] Among them: e k , e g , e t respectively represent the k-th, g-th, and t-th columns of the identity matrix.

[0237] The above is the result of allocating sampling points and weights according to the seventh-order - sphere radius criterion. The subsequent steps are as follows:

[0238] Determine the total number of sampling points:

[0239] γ = (8 / 3)n(n - 1)(n - 2) + 8n 2 -4n + 1 (49)

[0240] Calculate the sampling points:

[0241]

[0242] Calculate the sampling points propagated through the state equation:

[0243]

[0244] Calculate the predicted state value:

[0245]

[0246] Calculate the predicted square root error covariance matrix:

[0247]

[0248] Where:

[0249]

[0250] Calculate the updated sampling points:

[0251]

[0252] Calculate the sampling points propagated through the measurement equation:

[0253] Z i,k|k-1 = h(X i,k|k-1 , u k ) (56)

[0254] Calculate the predicted measurement value:

[0255]

[0256] Calculate the cross - covariance matrix:

[0257]

[0258] Calculate the predicted square root measurement error covariance matrix:

[0259]

[0260] Where:

[0261]

[0262] Calculate the Kalman gain:

[0263]

[0264] Calculate the state estimation value:

[0265]

[0266] Calculate the square root error covariance matrix:

[0267]

[0268] The above is the complete process of the MA-SR7thCKF algorithm.

[0269] In summary, a method for estimating the tire-road adhesion coefficient based on a distributed drive electric vehicle designed by the present invention. To achieve sensorless control of the PMSM, a new speed control method of SMC-ADRC is designed. As Figure 4 shown, by comparing with the SMC-ADRC method, the results show that the new SMC-ADRC can effectively reduce the overshoot and chattering of speed control; the designed MA-SR7thCKF algorithm is used to estimate the speed and rotor position of the PMSM. As Figure 5 shown, by comparing with SRCKF and SR5thCKF, the results show that the MA-SR7thCKF algorithm can effectively improve the estimation accuracy of the PMSM speed and rotor position; as Figure 6 shown, by comparing with SRCKF and SR5thCKF, the yaw rate r, lateral velocity vy, sideslip angle β, and longitudinal velocity vx are estimated using the MA-SR7thCKF algorithm. The results show that the MA-SR7thCKF algorithm has the highest estimation accuracy. As Figure 7 shown, the MA-SR7thCKF algorithm is used to estimate the tire-road adhesion coefficient. By comparing with SRCKF and SR5thCKF, the results show that the MA-SR7thCKF algorithm has the best convergence and can effectively improve the estimation accuracy of the tire-road adhesion coefficient.

[0270] The present invention uses the MA-SR7thCKF algorithm to estimate the PMSM speed and rotor position and uses them to estimate relevant vehicle state parameters. Finally, the estimated relevant vehicle state parameters are used as inputs, and the Dugoff model is used to calculate the normalized tire force. The normalized tire force is used as an input, and the MA-SR7thCKF algorithm is used to estimate the tire-road adhesion coefficient.

[0271] The above are only the preferred embodiments of the present invention. It should be noted that for those skilled in the art, without departing from the overall concept of the present invention, several changes and improvements can still be made, and these should also be regarded as the protection scope of the present invention.

Claims

1. A method for estimating the tire-road adhesion coefficient based on a distributed drive electric vehicle, characterized in that: The method includes the following steps: S1: According to the permanent magnet synchronous motor (PMSM) mathematical model, the designed new sliding mode control - active disturbance rejection control (SMC - ADRC) controller is used to control the speed of the PMSM to improve the speed control accuracy of the PMSM; and the designed multi - scale - square - root - seventh - order cubature Kalman filter (MA - SR7thCKF) algorithm is used to estimate the speed and rotor position of the PMSM, thereby realizing sensorless control of the PMSM. S2: The PMSM is used as the in - wheel motor of the whole vehicle to construct a distributed - drive electric vehicle whole - vehicle model. Based on existing vehicle-mounted sensors, the vehicle model of distributed drive electric vehicles has the ability to collect the signals of front wheel steering angle δ, wheel speed ω ij , longitudinal acceleration a x , lateral acceleration a y , driving torque T dij , braking torque T bij ; S3: Take the front wheel steering angle δ and the longitudinal acceleration a x as the system input values, and take the lateral acceleration a y as the system observation values. According to the vehicle dynamics model, use the MA-SR7thCKF algorithm to estimate the yaw rate r, the sideslip angle β of the center of mass, and the longitudinal velocity v x ; thereby obtaining the estimated values of the vehicle state parameters used in the Dugoff model to calculate the normalized tire force; S4: Front wheel steering angle δ, wheel speed ω collected according to the vehicle model ij , longitudinal acceleration a x , lateral acceleration a y , driving torque T dij , braking torque T bij and the estimated yaw rate r, center of mass sideslip angle β, longitudinal speed v x , the tire sideslip angle α can be calculated according to the formula ij , slip ratio λ ij , vertical force F zij ; On the premise that the tire-road adhesion coefficient is unknown, according to the known vehicle body parameters, the sideslip angle α ij , slip ratio λ ij and vertical force F zij are used as inputs, and the normalized tire force is calculated through the Dugoff model and S5: Take the front wheel steering angle δ and the normalized tire force and as the system input values, take the longitudinal acceleration a x , the lateral acceleration a y and the yaw rate r as the system observation values, and use the MA-SR7thCKF algorithm to estimate the tire-road adhesion coefficient; in the time update, reallocate the sampling points and weights according to the seventh-order-sphere radius criterion, and use the numerical integration method to predict the state mean and covariance; in the measurement update, calculate the Kalman gain according to the observation values, and adjust the predicted state and covariance to obtain the corrected state estimate value; through recursive iteration, effectively fuse the input and observation data, suppress the influence of noise, and further improve the estimation accuracy of the road adhesion coefficient by introducing the fading memory filter and QR decomposition, so as to improve the accuracy and stability of vehicle dynamic control.

2. The tire-road adhesion coefficient estimation method based on a distributed drive electric vehicle according to claim 1, wherein: The new SMC - ADRC controller designed according to the PMSM mathematical model in S1: The PMSM mathematical model is: where: i α and i β are the current components of the stator winding in the stationary coordinate system; u α and u β are the voltage components of the stator winding in the stationary coordinate system; R s and L s are the resistance and inductance respectively; ψ f is the magnetic flux linkage; ω m is the mechanical angular velocity of the rotor; θ e is the rotor position; p n is the number of pole pairs; J is the moment of inertia; B is the damping coefficient; T e is the electromagnetic torque; T L is the load torque; The new SMC - ADRC design method is: To solve the difficulty in parameter tuning of the second - order ADRC and reduce the jitter of the system state, SMC is combined with the non - linear extended state observer (NLESO) in ADRC, and a new reaching law is designed to improve the control performance of ADRC; the designed new reaching law is as follows: Where: s is the defined sliding mode surface; ε is the reaching coefficient; sign is the sign function; q is the exponential reaching coefficient; d is the parameter to be adjusted. The new reaching law introduces the L(s) function, enabling the system to adaptively adjust the convergence speed; when the moving point is far from the sliding mode surface, it is in the convergence stage, at this time |s| is larger, L(s) tends to infinity, the convergence speed increases, and the convergence time is shortened; when the moving point is close to the sliding mode surface, it is in the motion stage, at this time |s| is smaller, L(s) tends to d / (1 + d), the convergence speed decreases, and the jitter weakens. The NLESO improved by SMC is as follows: where: b * is the control gain; k1 and k2 are the proportional and gain coefficients respectively, e, e1, e2, e3 are error signals; c is the stability parameter; u is the system input; y is the system output; z1 is the tracking signal of y; z2 is the differential signal of y; z3 is the disturbance observation signal.

3. According to the tire - road adhesion coefficient estimation method for distributed - drive electric vehicles described in claim 1, it is characterized in that: The vehicle dynamics model in S3 is as follows: Longitudinal: Lateral: Yaw: The longitudinal and lateral accelerations are: The wheel dynamics equation is: where: m is the total vehicle mass, v x is the longitudinal speed; v y is the lateral speed; a x is the longitudinal acceleration; a y is the lateral acceleration; r is the yaw angular velocity; I z is the moment of inertia about the z-axis; I ω is the moment of inertia of the tire; δ is the front wheel steering angle; t f is the front axle track; t r is the rear axle track; R ω is the wheel rolling radius; a and b respectively represent the distances from the center of mass to the front axle and the rear axle; T dij and T bij respectively represent the tire driving torque and the braking torque; F xij and F yij respectively represent the longitudinal force and the lateral force acting on the tire; ω ij is the wheel rotational angular velocity; fl, fr, rl, rr respectively represent the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel; Since the tire force is unknown, a vehicle three - degree - of - freedom dynamics equation with tire cornering stiffness can be used to construct a vehicle state parameter estimation model. Where: C yf is the cornering stiffness of the front wheels, and C yr is the cornering stiffness of the rear wheels.

4. According to the tire - road adhesion coefficient estimation method for distributed - drive electric vehicles described in claim 1, it is characterized in that: In the above S4, using the tire sideslip angle α ij , slip ratio λ ij , and vertical force F zij as inputs, the method for calculating the normalized tire force according to the Dugoff model is as follows: Tire sideslip angle α ij , Slip ratio λ ij , Vertical force F ij The calculation formulas are as follows: where m is the total vehicle mass, v x is the longitudinal speed; v y is the lateral speed; a x is the longitudinal acceleration; a y is the lateral acceleration; r is the yaw angular velocity; I z is the moment of inertia about the z-axis; I ω is the moment of inertia of the tire; δ is the front wheel steering angle; t f is the front axle track width; t r is the rear axle track width; R ω is the wheel rolling radius; a and b respectively represent the distances from the center of mass to the front axle and the rear axle; ω ij is the wheel angular velocity; l is the distance between the front and rear axles; h g is the center of mass height; g is the acceleration due to gravity; The formula for calculating the tire force by the Dugoff model is: Where: Where: C xij and C yij are the longitudinal stiffness and lateral stiffness of each tire respectively; λ ij is the longitudinal slip ratio; ε v is the speed influence factor; When estimating the tire - road adhesion coefficient, the formula for calculating the tire force can be transformed into: Where: F xij and F yij respectively represent the longitudinal force and the lateral force acting on the tire; and are the normalized longitudinal force and lateral force respectively, and μ ij is the road adhesion coefficient of the wheel.

5. The tire-road adhesion coefficient estimation method based on a distributed drive electric vehicle according to claim 1, characterized in that: The steps of the MA - SR7thCKF algorithm are as follows: For the discrete PMSM speed and rotor position estimation system, three - degree - of - freedom vehicle state parameter estimation system, and tire - road adhesion coefficient estimation system, they can be written as an n - order system with additive noise: where: u k is the input value of the system at time k; x k is the state value at time k; z k is the observed value at time k; w k is the process noise; v k is the measurement noise; w k and v k are independent and Gaussian white noise with zero mean, i.e., w k ~N(0, Q k ), v k ~N(0, R k );; f and h are the nonlinear state space function and the measurement function respectively; The standard Gaussian weighted integral is approximated as: The sampling points corresponding to the 7thCKF algorithm are: Where: the sampling methods are h1, h2, and h3 sampling respectively. The point sets in h1 sampling are {e j} and {-e j}, where e j represents the j-th column of the identity matrix, and there are 2n sampling points; The point sets in h2 sampling are {m1}, {m2}, {m3}, {m4}, which are respectively expressed as: There are 4n(n - 1) sampling points. The point sets in h3 sampling are {m5}, {m6}, {m7}, {m8}, which are respectively expressed as: {m5} = {e k + e g + e t , k < g < t, k, g, t = 1, 2, …, n} (25) {m6} = {e k + e g - e t , where k < g < t, k, g, t = 1, 2, …, n} (26) {m7} = {e k -e g +e t , where k < g < t, k, g, t = 1, 2, …, n} (27) {m8} = {e k -e g -e t , where k < g < t, k, g, t = 1, 2, …, n} (28) There are 4n(n - 1)(n - 2) / 3 sampling points; where: e k , e g , e t respectively represent the k-th, g-th, and t-th columns of the identity matrix; The above is the way to distribute sampling points and weights according to the seventh-order spherical radius criterion. The subsequent steps are as follows: Determine the total number of sampling points: γ = (8 / 3)n(n - 1)(n - 2) + 8n 2 -4n + 1 (29) Calculate the sampling points: Calculate the sampling points propagated through the state equation: Calculate the predicted state value: Calculate the predicted square root error covariance matrix: Where: Calculate the updated sampling points: Calculate the sampling points propagated through the measurement equation: Z i,k|k-1 = h(X i,k|k-1 , u k ) (36) Calculate the predicted measurement value: Calculate the cross-covariance matrix: Calculate the predicted square root measurement error covariance matrix: Where: Calculate the Kalman gain: Calculate the state estimate value: Calculate the square root error covariance matrix: The above is the complete process of the MA-SR7thCKF algorithm.

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