Commercial vehicle double-motor electric drive axle finite time cooperative control method

Abstract

The invention discloses a commercial vehicle double-motor electric drive axle finite time cooperative control method comprising the following steps that commercial vehicle double-motor electric drive axle system models are established, and the models comprise a drive motor electrical mechanical model, a drive motor dynamic model, a drive wheel model and a double-motor electric drive axle coupling model; based on the established model, the load torques of the two driving motors serve as input, an interval type-2 fuzzy observer is designed, and disturbance of the driving motors caused by coupling nonlinearity and gear shifting is observed in real time; and on the basis of the established commercial vehicle double-motor electric drive axle system model and the interval type-2 fuzzy observer, a finite time adaptive fuzzy cooperative controller is designed, and finite time cooperative control of the double-motor electric drive axle system is ensured. By means of the method, good cooperative control over the rotating speed and torque of the double-motor electric drive axle system is achieved, and meanwhile it is guaranteed that the state of the double-motor electric drive axle system can be stable within limited time.

Description

Technical Field

[0001] The present invention belongs to the field of automobile drive technology, and in particular relates to a limited-time collaborative control method for a dual-motor electric drive bridge of a commercial vehicle. Background Art

[0002] With the rapid development of new energy technologies for electric vehicles, the commercial vehicle sector is paying more and more attention to electric drive systems. In order to meet higher power output requirements and improve vehicle handling performance, dual-motor configurations have gradually become the development trend of commercial vehicle electric drive systems. Compared with single-motor systems, dual-motor configurations can not only provide stronger power support, but also achieve more sophisticated energy management and higher energy efficiency ratios under different driving conditions. However, dual-motor systems also face some new challenges, especially the coupling and nonlinear characteristics between motors, as well as torque disturbances caused by changes in operating conditions and mode switching during operation.

[0003] In the existing technical literature, there are research results on dual-motor drive axle systems. For example, Chinese patent CN118532469A introduces a dual-motor drive axle system and proposes a new lubrication method to improve drive efficiency. In addition, Chinese patent CN202410786934.6 designs a two-speed coaxial electric drive axle system that can achieve gear shifting without interrupting power output, thereby improving the vehicle's adaptability and driving experience under different driving conditions.

[0004] However, despite the breakthroughs in structural design of the above patents, the complex interactions within the dual-motor system have not been fully studied in actual applications. Specifically, the coupling and nonlinear characteristics between the two motors in the dual-motor system are inherent properties, which cause the structural parameters of the motors to change under different operating conditions. In addition, when the system needs to switch between different modes, such as switching from economy mode to sports mode, this switching may cause torque fluctuations, which in turn affect the synchronous operation between the two motors. This asynchrony problem may cause unstable power output, affecting the overall performance of the vehicle and user experience.

[0005] Therefore, developing an effective finite-time cooperative control method is of great significance for improving the performance of the dual-motor electric drive axle system of commercial vehicles. Finite-time cooperative control aims to ensure the synchronous operation of multiple subsystems within a predetermined time by designing a specific control algorithm. For the dual-motor electric drive axle system, this means that a control system that can monitor and adjust the torque difference between the two motors in real time needs to be developed to ensure that the two motors can work together in the most optimized way under any operating conditions. The control system should be able to take into account factors such as nonlinear interactions between motors and torque fluctuations caused by mode switching, and take corresponding compensation measures to maintain the synchronization of the system.

[0006] To achieve this goal, we first need to conduct an in-depth analysis of the dynamic model of the dual-motor system and build a mathematical model that can accurately describe the interaction between the motors. Secondly, a control algorithm suitable for the dual-motor system should be developed based on this model. The algorithm should not only be able to handle the coupling effect between the motors, but also be able to adjust the operating state of the motors in a short time to achieve the best synchronization effect. Finally, a large number of simulations and real vehicle tests are required to verify the effectiveness and practicality of the proposed control strategy.

[0007] In short, although some progress has been made in the design and application of dual-motor electric drive axle systems, more research and exploration is still needed to effectively solve the coupling nonlinearity problem and the asynchrony problem caused by torque disturbance in dual-motor systems. Through continuous technological innovation and practical testing, it is expected that a more efficient and stable dual-motor electric drive axle system for commercial vehicles will be realized in the future.

[0008] The information disclosed in this background technology section is only intended to enhance the understanding of the overall background of the invention and should not be regarded as an acknowledgment or any form of suggestion that the information constitutes the prior art already known to a person skilled in the art. Summary of the invention

[0009] The purpose of the present invention is to provide a finite-time cooperative control method for a dual-motor electric drive axle of a commercial vehicle, so as to overcome the asynchronous problem caused by the nonlinear coupling and torque disturbance problems of the dual-motor electric drive axle in the prior art.

[0010] To achieve the above object, the present invention provides a limited time cooperative control method for a dual-motor electric drive axle of a commercial vehicle, comprising the following steps:

[0011] Step 1: Establish a commercial vehicle dual-motor electric drive axle system model, which includes: drive motor electrical model and dynamic model, drive wheel model, and dual-motor electric drive axle coupling model.

[0012] Step 2: Based on the model established in step 1, the load torque of the two drive motors is used as input to design an interval type-II fuzzy observer to observe the disturbance caused by coupling nonlinearity and gear shifting of the drive motor in real time;

[0013] Step 3: Based on the commercial vehicle dual-motor electric drive axle system model established in step 1 and the interval type-II fuzzy observer established in step 2, a finite-time adaptive fuzzy collaborative controller is designed to ensure finite-time collaborative control of the dual-motor electric drive axle system.

[0014] Preferably, in the above technical solution, the system model of the dual-motor electric drive bridge in step 1 is specifically as follows:

[0015] The electrical model of the drive motor is established as:

[0016]

[0017] Where K j , R j are the armature inductance and stator winding resistance of motor j respectively; ψ j 、n p are the permanent magnet flux and rotor pole pair number of motor j respectively; U dj 、u qj 、i dj 、i qj are the d-axis and q-axis voltage and current of motor j respectively; ω j is the angular velocity of motor j.

[0018] The dynamic model of the driving motor is established as:

[0019]

[0020] Among them J mj , B mj is the moment of inertia and damping coefficient of motor j: T Lj is the load torque of the motor; T m is the sum of the electromagnetic torques of the dual motors; K is the stiffness coefficient; θ j is the rotation angle of motor j; N is the reduction ratio of the reducer; θ t is the driving wheel angle.

[0021] The driving wheel model is established as:

[0022]

[0023] Among them I t and ω t is the moment of inertia and angular velocity of the wheel; r is the effective rolling radius of the wheel; F x is the longitudinal force of the tire, and its expression is:

[0024]

[0025] Where, μ is the road adhesion coefficient; s is the slip rate; C x , C y are the longitudinal stiffness and lateral stiffness of the tire respectively; α is the wheel slip angle; σ is used to describe the nonlinear characteristic parameter of tire slip.

[0026] According to all the above formulas, we can get the dual-motor electric drive bridge coupling model:

[0027]

[0028] Let x 1 =θ t , x 2 =ω t , x 3j =θ j , x 4j =ω j , x 5j =i qj The spatial state equation is:

[0029]

[0030] It can be further simplified into the following form:

[0031]

[0032] in:

[0033] η 2j =1.5ψ j n p / J mj ; η 3j =K / J mj ; η j =B mj / J mj ; η 4j =1 / L j ; η 5j =R j / L j ; η 6j =ψ j n p / L j ;

[0034] η 0 =N / I t ; g(x) = -F x r / I t ; d(t)=-(d 0 +T f ) / It .

[0035] Preferably, in the above technical solution, the design of the interval type-2 fuzzy observer in step 2 is specifically as follows:

[0036] Since interval type-2 fuzzy sets retain the ability of type-2 fuzzy sets to handle high uncertainty and have the advantages of less parameter design and simple calculation, we use interval type-2 fuzzy logic system to approximate the dual-motor electric drive axle system model, and the fuzzy rules are expressed as follows:

[0037]

[0038] Wherein, j=1, 2, ..., N is the number of fuzzy rules; is the antecedent of interval type-2 fuzzy set; Φ j is the output of fuzzy logic.

[0039] The defuzzified output of the computational fuzzy logic system is:

[0040]

[0041] in,

[0042]

[0043] The interval values ​​gl(x) and gr(x) are reduced by the Karnik-Mendel (KM) algorithm; Φ = [Φ 1 ,…Φ N ] T is an adaptive parameter.

[0044] For any continuous function g(x), there exists an interval type-2 fuzzy logic system with optimal parameters Φ * and a positive constant Make

[0045]

[0046] In order to simplify the complexity of the system, improve the reliability of the system, and eliminate the adverse effects of system nonlinearity and torque disturbance on the control input, the following interval type-II fuzzy observer is designed:

[0047]

[0048] in, and Respectively represent the input and output of IT2FLS; where U 0 =T L1 +T L2 Represents the input of the fuzzy system. is the estimated value of the time-varying disturbance d(t); 1 1 >0,l 2 >0; χ 1 (·) and χ 2 (·) is defined as:

[0049] χ 1 (·)=μ 1 「·」 1 / 2 +μ 2 「·」,

[0050] χ 2 (·)=μ 1 2 / 2「·」 1 / 2 +3μ 1 μ 2 / 2「·」 1 / 2 +μ 1 2 「·」Gain μ 1 , μ 2 Designed to be a positive constant,

[0051] Therefore, the state equation of the dual-motor electric drive axle system can be expressed as:

[0052]

[0053] Preferably, in the above technical solution, the design of the finite time adaptive fuzzy cooperative controller in step 3 is specifically as follows:

[0054] 1) Define the first-order tracking error of the dual-motor electric drive axle system as And taking its derivative we get:

[0055]

[0056] Among them, y d is the desired front wheel tracking angle. Based on this, the second-order tracking error e is defined 2 for:

[0057]

[0058] where x 2v is the virtual control signal of the first step, as expected value.

[0059] According to formula (15), formula (14) can be rewritten as:

[0060]

[0061] Consider the Lyapunov function as:

[0062] V 1 =e 1 z / 2 (17)

[0063] V 1 The derivative is:

[0064]

[0065] In order to improve the convergence speed and robustness of the system, a finite time control algorithm is introduced to construct the first step virtual control signal X 2v for:

[0066]

[0067] where n 1 is a positive number, q1 为 The first step is the finite time control coefficient and is greater than 0, p is the finite time control index and is between 0 and 1.

[0068] 2) According to formula (15), the second-order tracking error e 2 The derivative is:

[0069]

[0070] Define the third-order tracking error e 3 for:

[0071] e 3 =η 0 Kx 3 -x 3v (twenty one)

[0072] where x 3 =x 31 +x 32 , x 3v is the virtual control signal of the second step, as η 0 Kx 3 The expected value of . Consider the Lyapunov function as:

[0073] V 2 =V 1 +e 2 2 / 2 (22)

[0074] V 2 The derivative is:

[0075]

[0076] Considering finite time control design, the second step is to design the virtual control signal X 3v for:

[0077]

[0078] where n 2 is a positive number, q 2 is the finite time control coefficient of the second step and is greater than 0.

[0079] 3) According to formula (21), the third-order tracking error e 3 The derivative is:

[0080]

[0081]

[0082] Define the fourth-order tracking error e 4j for:

[0083] e 4j =η 0 Kx 4j -x 4v / 2 (26)

[0084] where x 4v is the virtual control signal of the third step. At the same time, in order to ensure the synchronization of the speeds of the two motors, η 0 K x4j The expected value of is defined as x 4v / 2.

[0085] Consider the Lyapunov function as:

[0086] V 3 =V 2 +e 3 2 / 2 (27)

[0087] V 3 The derivative is:

[0088]

[0089] where e 4 =e 41 +e 42 . Considering finite time control design, the third step is to design the virtual control signal x 4v for:

[0090]

[0091] where n 3 is a positive number, q 3 is the finite time control coefficient and is greater than 0.

[0092] 4) According to formula (26), the fourth-order tracking error e 4jThe derivative is:

[0093]

[0094] Define the fifth-order tracking error e 5j for:

[0095] e 5jj =η 0 Kη 2j x 5j -x 5jv (31)

[0096] x 5jv is the virtual control signal of the fourth step, as η 0 Kη 2j x 5j expected value.

[0097] Consider the Lyapunov function as

[0098] V 4 =V 3 +e 4 2 / 2 (32)

[0099] V 4 The derivative is:

[0100]

[0101] In order to enhance the consistency of the dual-motor electric drive axle system, the speed error e of the two motors is designed. s =e 42 -e 41 , considering the virtual control signal x in the fourth step of finite time control design 5jv for:

[0102]

[0103] where n 4 is a positive number, q 4 is the finite time control coefficient of the fourth step and is greater than 0, k s , k s1 is the speed error coefficient.

[0104] 5) According to formula (31), the fifth-order tracking error e 5j The derivative is:

[0105]

[0106] Consider the Lyapunov function as:

[0107] V 5 =V 4 +e5 2 / 2 (36)

[0108] V 5 The derivative is:

[0109]

[0110] In order to further enhance the consistency of the dual motors and increase their service life, we designed the torque error e t =e 52 -e 51 , considering finite time control, we get the fifth step virtual control signal u qj .

[0111]

[0112] in n 5 is a positive number, q 5 is the finite time control coefficient of the fifth step and is greater than 0. k c , k s1 is the torque error coefficient.

[0113] Compared with the prior art, the present invention has the following beneficial effects:

[0114] 1. By effectively combining fuzzy control theory with finite-time cooperative control theory, finite-time adaptive backstepping control is introduced to achieve rapid convergence under system nonlinearity and disturbance, and to achieve better coordinated control of the speed and torque of the dual-motor electric drive axle system, while ensuring that the state of the dual-motor electric drive axle system can be stable within a limited time.

[0115] 2. Considering the torque disturbance and system nonlinearity of the dual-motor electric drive axle, an interval type-II fuzzy observer is designed to estimate the state and load disturbance of the dual-motor electric drive axle system to ensure the bounded state and accurate tracking of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] Figure 1 It is a flow chart of the control steps of the present invention. DETAILED DESCRIPTION

[0117] The specific embodiments of the present invention are described in detail below, but it should be understood that the protection scope of the present invention is not limited by the specific embodiments.

[0118] Unless explicitly stated otherwise, throughout the specification and claims, the term “comprise” or variations such as “include” or “comprising”, etc., will be understood to include the stated elements or components but not to exclude other elements or components.

[0119] A limited time cooperative control method for a dual-motor electric drive axle of a commercial vehicle comprises the following steps:

[0120] Step 1: Establish a commercial vehicle dual-motor electric drive axle system model, which includes: drive motor electrical model and dynamic model, drive wheel model, and dual-motor electric drive axle coupling model.

[0121] Step 2: Based on the model established in step 1, the load torque of the two drive motors is used as input to design an interval type-II fuzzy observer to observe the disturbance caused by coupling nonlinearity and gear shifting of the drive motor in real time;

[0122] Step 3: Based on the commercial vehicle dual-motor electric drive axle system model established in step 1 and the interval type-II fuzzy observer established in step 2, a finite-time adaptive fuzzy collaborative controller is designed to ensure finite-time collaborative control of the dual-motor electric drive axle system.

[0123] Preferably, in the above technical solution, the system model of the dual-motor electric drive bridge in step 1 is specifically as follows:

[0124] The electrical model of the drive motor is established as:

[0125]

[0126] Where L j , R j They are the armature inductance and stator winding resistance of motor j: ψ j 、n p are the permanent magnet flux and rotor pole pair number of motor j respectively; u dj 、u qj 、i dj 、i qj are the d-axis and q-axis voltage and current of motor j respectively; ω j is the angular velocity of motor j.

[0127] The dynamic model of the driving motor is established as:

[0128]

[0129] Among them J mj , B mj is the moment of inertia and damping coefficient of motor j; T Lj is the load torque of the motor; T m is the sum of the electromagnetic torques of the dual motors; K is the stiffness coefficient; θ j is the rotation angle of motor j; N is the reduction ratio of the reducer; θ t is the driving wheel angle.

[0130] The driving wheel model is established as:

[0131]

[0132] Among them I t and ω t is the moment of inertia and angular velocity of the wheel; r is the effective rolling radius of the wheel; F x is the longitudinal force of the tire, and its expression is:

[0133]

[0134] Where, μ is the road adhesion coefficient; s is the slip rate; C x , C y are the longitudinal stiffness and lateral stiffness of the tire respectively; α is the wheel slip angle; σ is used to describe the nonlinear characteristic parameter of tire slip.

[0135] According to all the above formulas, we can get the dual-motor electric drive bridge coupling model:

[0136]

[0137] Let x 1 =θ t , x 2 =ω t , x 3j =θ j , x 4j =ω j , x 5j =i qj The spatial state equation is:

[0138]

[0139] It can be further simplified into the following form:

[0140]

[0141] in:

[0142] η 2j =1.5ψ j n p / J mj ; η 3j =K / J mj ; η j =B mj / J mj ; η 4j =1 / L j ; η 5j =R j / L j ; η 6j =ψ j n p / L j ;

[0143] η 0 =N / I t ; g(x) = -F x r / I t ; d(t)=-(d 0 +T f ) / I t .

[0144] Preferably, in the above technical solution, the design of the interval type-2 fuzzy observer in step 2 is specifically as follows:

[0145] Since interval type-2 fuzzy sets retain the ability of type-2 fuzzy sets to handle high uncertainty and have the advantages of less parameter design and simple calculation, we use interval type-2 fuzzy logic system to approximate the dual-motor electric drive axle system model, and the fuzzy rules are expressed as follows:

[0146]

[0147] Wherein, j=1, 2, ..., N is the number of fuzzy rules; is the antecedent of interval type-2 fuzzy set; Φ j is the output of fuzzy logic.

[0148] The defuzzified output of the computational fuzzy logic system is:

[0149]

[0150] in,

[0151]

[0152] The interval values ​​gl(x) and gr(x) are reduced by the Karnik-Mendel (KM) algorithm; Φ = [φ 1 ,…Φ N ] T is an adaptive parameter.

[0153] For any continuous function g(x), there exists an interval type-2 fuzzy logic system with optimal parameters Φ * and a positive constant Make

[0154]

[0155] In order to simplify the complexity of the system, improve the reliability of the system, and eliminate the adverse effects of system nonlinearity and torque disturbance on the control input, the following interval type-II fuzzy observer is designed:

[0156]

[0157] in, and Respectively represent the input and output of IT2FLS; where U 0 =T L1 +T L2 Represents the input of the fuzzy system. is the estimated value of the time-varying disturbance d(t); 1 1 >0,l 2 >0; χ 1 (·) and χ 2 (·) is defined as:

[0158] χ 1 (·)=μ 1 「·」 1 / 1 +μ 2 「·」,χ 2 (·)=μ 1 2 / 2「·」 1 / 2 +3μ 1 μ 2 / 2「·」 1 / 2 +μ 1 2 "·", gain μ 1 , μ 2 Designed to be a positive constant,

[0159] Therefore, the state equation of the dual-motor electric drive axle system can be expressed as:

[0160]

[0161] Preferably, in the above technical solution, the design of the finite time adaptive fuzzy cooperative controller in step 3 is specifically as follows:

[0162] 1) Define the first-order tracking error of the dual-motor electric drive axle system as And taking its derivative we get:

[0163]

[0164] Among them, y d is the desired front wheel tracking angle. Based on this, the second-order tracking error e is defined 2 for:

[0165]

[0166] where x 2v is the virtual control signal of the first step, as expected value.

[0167] According to formula (15), formula (14) can be rewritten as:

[0168]

[0169] Consider the Lyapunov function as:

[0170] V 1 =e 1 2 / 2 (55)

[0171] V 1 The derivative is:

[0172]

[0173] In order to improve the convergence speed and robustness of the system, a finite time control algorithm is introduced to construct the first step virtual control signal x 2v for:

[0174]

[0175] where n 1 is a positive number, q 1 is the first step finite time control coefficient and is greater than 0, p is the finite time control index and is between 0 and 1.

[0176] 2) According to formula (15), the second-order tracking error e 2 The derivative is:

[0177]

[0178]

[0179] Define the third-order tracking error e 3 for:

[0180] e 3 =η 0 Kx 3 -x 3v (59)

[0181] Where X 3 =X 31 +x 32 , X 3v is the virtual control signal of the second step, as η 0 Kx 3 The expected value of . Consider the Lyapunov function as:

[0182] V 2 =V 1 +e 2 2 / 2 (60)

[0183] V 2 The derivative is:

[0184]

[0185] Considering finite time control design, the second step is to design the virtual control signal x 3v for:

[0186]

[0187] where n 2 is a positive number, q 2 is the finite time control coefficient of the second step and is greater than 0.

[0188] 3) According to formula (21), the third-order tracking error e 3 The derivative is:

[0189]

[0190] Define the fourth-order tracking error e 4j for:

[0191] e 4j =η 0 Kx 4j -x 4v / 2 (64)

[0192] where x 4v is the virtual control signal of the third step. At the same time, in order to ensure the synchronization of the speeds of the two motors, η 0 Kx 4j The expected value of is defined as x 4v / 2.

[0193] Consider the Lyapunov function as:

[0194] V 3 =V 2 +e 3 2 / 2 (65)

[0195] V 3 The derivative is:

[0196]

[0197] where e 4 =e 41 +e 42 . Considering finite time control design, the third step is to design the virtual control signal x 4v for:

[0198]

[0199] where n 3 is a positive number, q 3 is the finite time control coefficient and is greater than 0.

[0200] 4) According to formula (26), the fourth-order tracking error e 4j The derivative is:

[0201]

[0202] Define the fifth-order tracking error e 5j for:

[0203] e 5j =η 0 Kη 2j x 5j -x 5jv (69)

[0204] X 5jv is the virtual control signal of the fourth step, as η 0 Kη 2j x 5j expected value.

[0205] Consider the Lyapunov function as

[0206] V 4 =V 3 +e 4 2 / 2 (70)

[0207] V 4 The derivative is:

[0208]

[0209] In order to enhance the consistency of the dual-motor electric drive axle system, the speed error e of the two motors is designed. s =e 42 -e 41 , considering the virtual control signal x in the fourth step of finite time control design 5jv for:

[0210]

[0211] where n 4 is a positive number, q 4 is the finite time control coefficient of the fourth step and is greater than 0, k s , k s1 is the speed error coefficient.

[0212] 5) According to formula (31), the fifth-order tracking error e 5j The derivative is:

[0213]

[0214] Consider the Lyapunov function as:

[0215] V 5 =V 4 +e 5 2 / 2 (74)

[0216] V 5 The derivative is:

[0217]

[0218] In order to further enhance the consistency of the dual motors and increase their service life, we designed the torque error e t =e 52 -e 51 , considering finite time control, we get the fifth step virtual control signal u q，j .

[0219]

[0220] in n 5 is a positive number, q 5 is the finite time control coefficient of the fifth step and is greater than 0. k c , k c1 is the torque error coefficient.

[0221] The foregoing description of specific exemplary embodiments of the present invention is for the purpose of illustration and demonstration. These descriptions are not intended to limit the present invention to the precise form disclosed, and it is clear that many changes and variations can be made based on the above teachings. The purpose of selecting and describing the exemplary embodiments is to explain the specific principles of the present invention and its practical application, so that those skilled in the art can realize and utilize various different exemplary embodiments of the present invention and various different selections and changes. The scope of the present invention is intended to be limited by the claims and their equivalents.

Claims

1. A limited time cooperative control method for a dual-motor electric drive axle of a commercial vehicle, comprising the following steps: Step 1: Establish a dual-motor electric drive axle system model for commercial vehicles, which includes: drive motor electrical model and drive motor dynamics model, drive wheel model, and dual-motor electric drive axle coupling model; Step 2: Based on the model established in step 1, the load torque of the two drive motors is used as input to design an interval type-II fuzzy observer to observe the disturbance caused by coupling nonlinearity and gear shifting of the drive motor in real time; Step 3: Based on the commercial vehicle dual-motor electric drive axle system model established in step 1 and the interval type-2 fuzzy observer established in step 2, a finite-time adaptive fuzzy cooperative controller is designed; The system model of the dual-motor electric drive bridge in step 1 is as follows: The electrical model of the drive motor is established as: Where L j , R j are the armature inductance and stator winding resistance of motor j respectively; ψ j 、n p are the permanent magnet flux and rotor pole pair number of motor j respectively; u dj 、u qj 、i di 、i qj are the d-axis and q-axis voltage and current of motor j respectively; ω j is the angular velocity of motor j; The dynamic model of the driving motor is established as: Among them J mj , B mj is the moment of inertia and damping coefficient of motor j; T Lj is the load torque of the motor; T m is the sum of the electromagnetic torques of the dual motors; K is the stiffness coefficient; θ j is the rotation angle of motor j; N is the reduction ratio of the reducer; θ t is the rotation angle of the driving wheel; The driving wheel model is established as: Among them I t and ω t is the moment of inertia and angular velocity of the wheel; r is the effective rolling radius of the wheel; F x is the longitudinal force of the tire, and its expression is: Where, μ is the road adhesion coefficient; s is the slip rate; C x , C y are the longitudinal stiffness and lateral stiffness of the tire respectively; α is the wheel slip angle; σ is used to describe the nonlinear characteristic parameter of tire slip; According to all the above formulas, we can get the dual-motor electric drive bridge coupling model: Let x1 = θ t , x2=ω t , x 3j =θ j , x 4j =ω j , x 5j =i qj The spatial state equation can be obtained as: It can be further simplified into the following form: Among them: h 2j =1.5ψ j n p / J mj ;or 3j =K / J mj ;or j =B m，j / J mj ;or 4j =1 / L j ;or 5j =R j / L j ;or 6j =ψ j n p / L j ; η0=N / I t ;g(x)=-F x r / I t ;d(t)=-(d0+T f ) / I t 。 2. The commercial vehicle dual-motor electric drive axle finite time cooperative control method according to claim 1 is characterized in that: The design of the interval type-2 fuzzy observer in step 2 is as follows: The dual-motor electric drive axle system model is approximated by the interval type-2 fuzzy logic system, and the fuzzy rules are expressed as follows: R (j) :if x1 is x2 is Then is Φ j j=1,2,...,N. Wherein, jj=1, 2, ..., N is the number of fuzzy rules; is the antecedent of interval type-2 fuzzy set; Φ j is the output of fuzzy logic; The defuzzified output of the computational fuzzy logic system is: in, The interval values ​​gl(x) and gr(x) are reduced by the Karnik-Mendel (KM) algorithm; Φ = [φ1, …Φ N ] T is the adaptive parameter For any continuous function g(x), there exists an interval type-2 fuzzy logic system with optimal parameters Φ * and a positive constant Make The following interval type-2 fuzzy observer is designed: in, and Respectively represent the input and output of IT2FLS; where u0=T L1 +T L2 represents the input of the fuzzy system; is the estimated value of the time-varying disturbance d(t); l1>0, l2>0; χ1(·) and χ2(·) are defined as: Gains μ1 and μ2 are designed to be positive constants. Therefore, the state equation of the dual-motor electric drive axle system can be expressed as:

3. The commercial vehicle dual-motor electric drive axle finite time cooperative control method according to claim 1 is characterized in that: The design of the finite time adaptive fuzzy cooperative controller in step 3 is as follows: 1) Define the first-order tracking error of the dual-motor electric drive axle system as And taking its derivative we get: Among them, y d is the desired front wheel tracking angle. On this basis, the second-order tracking error e2 is defined as: where x 2v is the virtual control signal of the first step, as expected value. According to formula (15), formula (14) can be rewritten as: Consider the Lyapunov function: V1 = e1 2 / 2 (17) Taking the derivative of V1, we get: In order to improve the convergence speed and robustness of the system, a finite time control algorithm is introduced to construct the first step virtual control signal x 2v for: Where n1 is a positive number, q1 is the first step finite time control coefficient and is greater than 0, and p is the finite time control index and is between 0 and 1; 2) According to formula (15), the derivative of the second-order tracking error e2 can be obtained: The third-order tracking error e3 is defined as: e3=η0Kx3-x 3v (21) where x3 = x 31 +x 32 , x 3v is the virtual control signal of the second step, which is the expected value of η0Kx3. Consider the Lyapunov function as: <h2 style=";text-align:left;direction:ltr">V2 = V1 + e2<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> / 2 (22) Taking the derivative of V2, we get: Considering finite time control design, the second step is to design the virtual control signal x 3v for: Where n2 is a positive number, q2 is the second step finite time control coefficient and is greater than 0; 3) According to formula (21), the derivative of the third-order tracking error e3 can be obtained: Define the fourth-order tracking error e 4j for: e 4j =η0Kx 4j -x 4v / 2 (26) where x 4v is the virtual control signal of the third step. At the same time, in order to ensure the synchronization of the speeds of the two motors, η0Kx 4j The expected value of is defined as x 4v / 2. Consider the Lyapunov function as: <h2 style=";text-align:left;direction:ltr">V3 = V2 + e3<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> / 2 (27) Taking the derivative of V3, we get: where e4 = e 41 +e 42 . Considering finite time control design, the third step is to design the virtual control signal x 4v for: Where n3 is a positive number, q3 is a finite time control coefficient and is greater than 0; 4) According to formula (26), the fourth-order tracking error e 4j The derivative is: Define the fifth-order tracking error e 5j for: e 5j =η0Kη 2j x 5j -x 5jv (31) x 5jv is the virtual control signal of the fourth step, as η0Kη 2j x 5j Expected value; Consider the Lyapunov function as V4=V3+e4 2 / 2 (32) Taking the derivative of V4, we get: In order to enhance the consistency of the dual-motor electric drive axle system, the speed error e of the two motors is designed. s =e 42 -e 41 , considering the virtual control signal x in the fourth step of finite time control design 5jv for: Where n4 is a positive number, q4 is the finite time control coefficient of the fourth step and is greater than 0, k s , k s1 is the speed error coefficient; 5) According to formula (31), the fifth-order tracking error e 5j The derivative is: Consider the Lyapunov function as: V5=V4+e5 2 / 2 (36) Taking the derivative of V5, we get: In order to further enhance the consistency of the dual motors and increase their service life, the torque error e is designed here. t =e 52 -e 51 , considering finite time control, we get the fifth step virtual control signal u qj . in n5 is a positive number, q5 is the fifth step finite time control coefficient and is greater than 0; k c , k c1 is the torque error coefficient.

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