A finite time collaborative control method for a double-motor electric drive axle of a commercial vehicle

Abstract

The application discloses a kind of commercial vehicle double-motor electric drive axle finite time collaborative control methods, comprising the following steps: establishing commercial vehicle double-motor electric drive axle system model, model includes: driving motor electromagnetism model and dynamics model, driving wheel model, double-motor electric drive axle coupling model.Based on the model established, the load torque of two driving motors is taken as input, interval two type fuzzy observer is designed, and the disturbance caused by coupling nonlinearity and gear shifting of driving motor is observed in real time;Based on the established commercial vehicle double-motor electric drive axle system model and interval two type fuzzy observer, design finite time adaptive fuzzy collaborative controller, ensure that double-motor electric drive axle system finite time collaborative control is realized.The method realizes the better collaborative control of double-motor electric drive axle system speed torque, while ensuring that the state of double-motor electric drive axle system can be stabilized in finite time.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of automobile driving, and particularly relates to a finite time collaborative control method for a double-motor electric drive axle of a commercial vehicle. BACKGROUND

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

[0003] In the prior art literature, there have been research results on double-motor drive axle systems. For example, Chinese patent CN118532469A introduces a double-motor drive axle system and proposes a new lubrication method to improve drive efficiency. In addition, Chinese patent CN202410786934.6 designs a two-gear coaxial electric drive axle system that can realize gear shifting without interrupting power output, thereby improving the adaptability and driving experience of the vehicle under different driving conditions.

[0004] However, although the above patents have made breakthroughs in structural design, the complex interactions within the double-motor system have not been fully studied in actual application. Specifically, the coupling and nonlinear characteristics between the two motors in the double-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 from an economic mode to a sporty mode, this switching may cause torque fluctuations, which in turn affect the synchronous operation between the two motors. This asynchronization problem may cause unstable power output, affecting the overall performance and user experience of the vehicle.

[0005] Therefore, developing an effective finite-time cooperative control method is of great significance to improve the performance of commercial vehicle dual-motor electric drive axle system. Finite-time cooperative control aims to ensure the synchronization of multiple subsystems within a predetermined time by designing specific control algorithms. For a dual-motor electric drive axle system, this means developing a control system that can monitor and adjust the torque difference between the two motors in real time to ensure that both motors work optimally in any working condition. The control system should be able to consider the nonlinear interaction between the motors and the torque fluctuations caused by mode switching, and take appropriate compensation measures to maintain the synchronization of the system.

[0006] To achieve this goal, first, the dynamics model of the dual-motor system needs to be analyzed in depth, and a mathematical model that can accurately describe the interaction between the motors needs to be constructed. Second, a control algorithm suitable for the dual-motor system should be developed based on this model. This 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 within a short time to achieve the best synchronization effect. Finally, a large number of simulations and real vehicle tests need to be conducted to verify the effectiveness and practicality of the proposed control strategy.

[0007] In summary, although some progress has been made in the design and application of dual-motor electric drive axle systems, more research and exploration are needed to effectively solve the coupling nonlinear problem and the different step problem caused by torque disturbance in the dual-motor system. Through continuous technological innovation and practical testing, it is expected to realize a more efficient and stable commercial vehicle dual-motor electric drive axle system in the future.

[0008] The information disclosed in this Background section is intended only to increase an understanding of the general context in which the present application can be practiced. It should not be taken as an acknowledgement or any form of suggestion that this information forms part of the prior art that is already known to a person of ordinary skill in the art. SUMMARY

[0009] The purpose of the present application is to provide a commercial vehicle dual-motor electric drive axle finite-time cooperative control method to overcome the synchronization problem caused by the coupling nonlinear and torque disturbance problem of the existing dual-motor electric drive axle.

[0010] To achieve the above-mentioned purpose, the present application provides a commercial vehicle dual-motor electric drive axle finite-time cooperative control method, comprising the following steps:

[0011] Step 1: Establish a model of the commercial vehicle dual-motor electric drive axle system, which includes: a drive motor electromechanical model and a dynamics model, a drive wheel model, and a 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 taken as input to design an interval type-2 fuzzy observer to observe the disturbance of the drive motor caused by coupling nonlinearity and gear shifting in real time;

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

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

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

[0016]

[0017] wherein 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 linkage and rotor pole pair number of motor j respectively; U dj , u qj , i dj , i qj are the d, q axis voltage and current of motor j respectively; ω j is the angular velocity of motor j.

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

[0019]

[0020] wherein J mj , B mj are 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 electromagnetic torque of the double-motor; 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 drive wheel.

[0021] The drive wheel model is established as:

[0022]

[0023] wherein I t and ω t are 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 ratio; C x , C y are the longitudinal and lateral stiffness of the tire respectively; a is the wheel angle; s is the nonlinear parameter describing the tire slip.

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

[0027]

[0028] Let x1= θ t , x2= ω t , x 3j = θ j , x 4j = ω j , x 5j = i qj , we can get the space state equation as follows:

[0029]

[0030] It can be further simplified as follows:

[0031]

[0032] where:

[0033] η 2j = 1.5 ψ 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] η0= N / I t ; g(x) = -F x r / I t ; d(t) = -(d0+ T f ) / I t .

[0035] Preferably, in the technical scheme above, the interval type-2 fuzzy observer in step 2 is designed as follows:

[0036] Since the interval type-2 fuzzy set retains the processing ability of type-2 fuzzy set for high uncertainty, and has the advantages of less parameter design and simple calculation amount, we use the interval type-2 fuzzy logic system to approximate the double-motor electric drive bridge system model, and the fuzzy rule is expressed as follows:

[0037]

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

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

[0040]

[0041] wherein

[0042]

[0043] The interval values gl(x) and gr(x) are obtained by Karnik-Mendel (KM) algorithm; Φ = [Φ1, … Φ N ] T is an adaptive parameter.

[0044] For any continuous function g(x), there exists an optimal parameter Φ * of the interval type-2 fuzzy logic system and a positive constant such that

[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-2 fuzzy observer is designed:

[0047]

[0048] wherein and represent the input and output of the IT2FLS respectively; wherein U0 = T L1 + T L2 represents the input of the fuzzy system. is the estimated value of the time-varying disturbance d(t); 11 > 0, l2 > 0; χ1(·) and χ2(·) are defined as:

[0049] χ1(·) = μ1 1 / 2 + μ2

[0050] χ2(·) = μ1 2 / 2 1 / 2 + 3 μ1 μ2 / 2 1 / 2 + μ1 2 · Gain μ1, μ2 is designed as 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 finite-time adaptive fuzzy cooperative controller in step 3 is designed as follows:

[0054] 1) Define the first-order tracking error of the dual-motor electric drive axle system as and its derivative is:

[0055]

[0056] Where y d is the desired front wheel tracking angle. On this basis, define the second-order tracking error e2 as:

[0057]

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

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

[0060]

[0061] Consider the Lyapunov function as:

[0062] V1 = e1 z / 2 (17)

[0063] Taking the derivative of V1 gives:

[0064]

[0065] To improve the convergence speed and robustness of the system, a finite-time control algorithm is introduced, and the first-step virtual control signal X 2v is constructed as:

[0066]

[0067] where n1 is a positive number, q1 为 The first step finite time control coefficient and greater than 0, p is a finite time control index and between 0 ~ 1.

[0068] 2) According to formula (15) on the second order tracking error e2 derivative can be obtained:

[0069]

[0070] Define the third order tracking error e3 as:

[0071] e3 = η0Kx3-x 3v (21)

[0072] Where x3 = x 31 +x 32 , x 3v is the second step of the virtual control signal, as the expected value of η0Kx3. Consider the Lyapunov function as:

[0073] V2 = V1 + e2 2 / 2 (22)

[0074] The derivative of V2 can be obtained:

[0075]

[0076] Consider the finite time control design of the second step virtual control signal X 3v :

[0077]

[0078] Where n2 is a positive number, q2 is the second step finite time control coefficient and greater than 0.

[0079] 3) According to formula (21) on the third order tracking error e3 derivative can be obtained:

[0080]

[0081]

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

[0083] e 4j = η0Kx 4j -x 4v / 2 (26)

[0084] Where x 4v is the third step of the virtual control signal, and in order to ensure the synchronization of the two motor speed, the expected value of η0K x4j is defined as x4v / 2.

[0085] Consider the Lyapunov function as:

[0086] V3 = V2 + e3 2 / 2 (27)

[0087] The derivative of V3 is:

[0088]

[0089] where e4 = e 41 + e 42 . Consider the virtual control signal x 4v of the third step of finite time control design as:

[0090]

[0091] where n3 is a positive number, and q3 is a finite time control coefficient and greater than 0.

[0092] 4) The fourth-order tracking error e 4j is derived according to formula (26) as:

[0093]

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

[0095] e 5jj = η0Kη 2j x 5j - x 5jv (31)

[0096] x 5jv is the virtual control signal of the fourth step, which is the expected value of η0Kη 2j x 5j .

[0097] Consider the Lyapunov function as

[0098] V4 = V3 + e4 2 / 2 (32)

[0099] The derivative of V4 is:

[0100]

[0101] To strengthen the consistency of the dual-motor electric drive axle system, the speed error e s = e 42 - e 41 of the two motors is considered, and the virtual control signal x 5jv of the fourth step of finite time control design is:

[0102]

[0103] Where n4 is a positive number, q4 is the finite-time control coefficient for the fourth step and is greater than 0, and k s k s1 This represents the rotational speed error coefficient.

[0104] 5) According to equation (31), the fifth-order tracking error e 5j Differentiation yields:

[0105]

[0106] Consider the Lyapunov function as follows:

[0107] V5 = V4 + e5 2 / 2 (36)

[0108] Taking the derivative with respect to V5, we get:

[0109]

[0110] To further enhance the consistency of the dual motors and improve their service life, we designed a torque error e here. t =e 52 -e 51 Considering finite-time control, the virtual control signal u for the fifth step is obtained. qj .

[0111]

[0112] in n5 is a positive number, q5 is the finite-time control coefficient for the fifth step and is greater than 0. k c k s1 This 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 and finite-time cooperative control theory, finite-time adaptive backstepping control is introduced to achieve rapid convergence of the system under nonlinearity and disturbance, thereby realizing better cooperative control of speed and torque of the dual-motor electric drive bridge system, while ensuring that the state of the dual-motor electric drive bridge system can be stable within a finite time.

[0115] 2. Considering the torque disturbance of the dual-motor electric drive bridge and the nonlinearity of the system, an interval type II fuzzy observer was designed to estimate the state and load disturbance of the dual-motor electric drive bridge system to ensure the bounded state and accurate tracking of the system. Attached Figure Description

[0116] Figure 1Flow chart of the control step of the present application. DETAILED DESCRIPTION

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

[0118] Unless otherwise clearly indicated, throughout the specification and claims, the term "comprising" or variations such as "comprise" or "comprises" will be understood to imply the inclusion of a stated element or group of elements but not the exclusion of any other element or group of elements.

[0119] A finite time collaborative control method for a commercial vehicle double-motor electric drive axle, comprising the following steps:

[0120] Step 1: Establish a model of the commercial vehicle double-motor electric drive axle system, which includes: a drive motor electromechanical model and a dynamics model, a drive wheel model, and a double-motor electric drive axle coupling model.

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

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

[0123] Preferably, in the above technical solution, the system model of the double-motor electric drive axle in Step 1 is as follows:

[0124] The drive motor electromechanical model is established as:

[0125]

[0126] 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 linkage and rotor pole pair number of motor j respectively; u dj , u qj , i dj , i qj are the d, q axis voltage and current of motor j respectively; ω j is the angular velocity of motor j.

[0127] The drive motor dynamics model is established as:

[0128]

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

[0130] The model of driving wheel is established as:

[0131]

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

[0133]

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

[0135] According to all the above formulas, the coupling model of dual-motor electric drive axle can be obtained as:

[0136]

[0137] 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:

[0138]

[0139] which can be further simplified as:

[0140]

[0141] where:

[0142] η 2j = 1.5 ψ j n p / Jmj ; 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] η0= N / I t ; g(x) = -F x r / I t ; d(t) = -(d0+ T f ) / I t .

[0144] Preferably, in the above technical solutions, the interval type-2 fuzzy observer in step 2 is designed as follows:

[0145] Since the interval type-2 fuzzy set retains the processing ability of type-2 fuzzy set for high uncertainty, and has the advantages of fewer parameter designs and simple calculation amount, we use the interval type-2 fuzzy logic system to approximate the double-motor electric drive bridge system model, and the fuzzy rules are expressed as follows:

[0146]

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

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

[0149]

[0150] where

[0151]

[0152] The interval values gl(x) and gr(x) are obtained by Karnik-Mendel (KM) algorithm; Φ = [φ1, … Φ N ] T is an adaptive parameter.

[0153] For any continuous function g(x), there exists an optimal parameter Φ *and normal number such that

[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 control input, the following interval type-2 fuzzy observer is designed:

[0156]

[0157] wherein, and respectively represent the input and output of the IT2FLS; wherein U0=T L1 +T L2 represent 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:

[0158] χ1(·)=μ1 1 / 1 +μ2 2 χ2(·)=μ1 1 / 2 / 2 1 / 2 +3μ1μ2 / 2 2 +μ1 d , the gains μ1, μ2 are designed as positive constants,

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

[0160]

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

[0162] 1) Define the first-order tracking error of the dual-motor electric drive bridge system as and its derivative can be obtained as:

[0163]

[0164] wherein y d is the desired front wheel tracking angle. On this basis, define the second-order tracking error e2 as:

[0165]

[0166] wherein x 2v is the virtual control signal of the first step, which is the desired value of .

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

[0168]

[0169] Consider the Lyapunov function as:

[0170] V1 = e1 2 / 2 (55)

[0171] The derivative of V1 can be obtained as:

[0172]

[0173] To improve the convergence speed and robustness of the system, a finite-time control algorithm is introduced, and the first step virtual control signal x 2v is constructed as:

[0174]

[0175] 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 exponent and is between 0 and 1.

[0176] 2) According to formula (15), the derivative of the second-order tracking error e2 can be obtained as:

[0177]

[0178]

[0179] Define the third-order tracking error e3 as:

[0180] e3 = η0Kx3 - x 3v (59)

[0181] Where X3 = X 31 +x 32 , X 3v is the second step virtual control signal, which is the expected value of η0Kx3. Consider the Lyapunov function as:

[0182] V2 = V1 + e2 2 / 2 (60)

[0183] The derivative of V2 can be obtained as:

[0184]

[0185] Consider the finite-time control design of the second step virtual control signal x 3v as:

[0186]

[0187] where n2 is a positive number, q2 is the second step finite time control coefficient and greater than 0.

[0188] 3) Derivation of the third order tracking error e3 according to formula (21) can be obtained:

[0189]

[0190] Define the fourth order tracking error e4 as: 4j

[0191] e 4j = η0Kx 4j - x 4v / 2 (64)

[0192] where x 4v is the third step virtual control signal, and in order to ensure the synchronization of the two motor speeds, the expected value of η0Kx 4j is defined as x 4v / 2.

[0193] Consider the Lyapunov function as:

[0194] V3 = V2 + e3 2 / 2 (65)

[0195] Derivation of V3 can be obtained:

[0196]

[0197] where e4 = e 41 + e 42 . Consider the third step virtual control signal x 4v of the finite time control design as:

[0198]

[0199] where n3 is a positive number, q3 is the finite time control coefficient and greater than 0.

[0200] 4) Derivation of the fourth order tracking error e4 according to formula (26) can be obtained: 4j

[0201]

[0202] Define the fifth order tracking error e5 as: 5j

[0203] e 5j = η0Kη 2j x 5j - x 5jv (69)

[0204] X 5jv ​​​For the fourth step of the virtual control signal, as η0Kη 2j x 5j the expected value.

[0205] Consider the Lyapunov function as

[0206] V4 = V3 + e4 2 / 2 (70)

[0207] The derivative of V4 is:

[0208]

[0209] To strengthen the consistency of the dual-motor electric drive axle system, the speed error e s = e 42 -e 41 of the two motors is considered, and the virtual control signal x 5jv of the fourth step of the finite time control is designed as:

[0210]

[0211] Where n4 is a positive number, q4 is the fourth step of the finite time control coefficient and greater than 0, k s , k s1 is the speed error coefficient.

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

[0213]

[0214] Consider the Lyapunov function as:

[0215] V5 = V4 + e5 2 / 2 (74)

[0216] The derivative of V5 is:

[0217]

[0218] To further enhance the consistency of the dual-motor and improve its service life, we designed the torque error e t = e 52 -e 51 , and the virtual control signal u q，j of the fifth step of the finite time control is obtained.

[0219]

[0220] Where n5 is a positive number, q5 is the fifth step of the finite time control coefficient and greater than 0. k c, k c1 is a torque error coefficient.

[0221] The foregoing description of specific exemplary embodiments of the application has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the application to the precise form disclosed, and various modifications and variations are possible in light of the above teachings. It is intended that the application embrace all alternatives, modifications, and variations as can come within the scope of the description and claims. It is intended that the scope of the application be limited not with the specific embodiments described above, but rather by the claims below and their equivalents.

Claims

1. A finite time collaborative control method for a commercial vehicle dual-motor electric drive axle, comprising the following steps: Step 1: establishing a model of the commercial vehicle dual-motor electric drive axle system, the model comprising: a driving motor electromechanical model and a driving motor dynamics model, a driving wheel model, and a dual-motor electric drive axle coupling model; Step 2: based on the model established in Step 1, taking the load torque of the two driving motors as input, designing an interval type-2 fuzzy observer to observe the disturbance of the driving motor caused by coupling nonlinearity and gear shifting in real time; Step 3: based on the model of the commercial vehicle dual-motor electric drive axle system established in Step 1 and the interval type-2 fuzzy observer established in Step 2, designing a finite time adaptive fuzzy collaborative controller; The system model of the dual-motor electric drive axle in Step 1 is as follows: The driving motor electromechanical model 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 linkage and rotor pole pair number of motor j respectively; u dj , u qj , i dj , i qj are the d, q axis voltage and current of motor j respectively; ω j is the angular speed of motor j; The driving motor dynamics model is established as: where 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 torque of the dual motor; 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 drive wheel; The driving wheel model is established as: where I t and ω t are the moment of inertia and the angular velocity of the wheel; r is the effective rolling radius of the wheel; F x is the longitudinal force of the tyre, whose expression is: wherein μ is the road adhesion coefficient; s is the slip ratio; C x , C y are the longitudinal and lateral stiffness of the tire, respectively; a is the wheel slip angle; σ is a parameter describing the non-linear behavior of the tire slip. According to all the above formulas, the dual-motor electric drive axle coupling model can be obtained as: Let x1 = θ t , x2 = ω t , x 3j = θ j , x 4j = ω j , x 5j = i qj The spatial state equation of the system is obtained as follows: It can be further simplified as follows: where: η 2j = 1.5ψ j n p / J mj ; η 3j = K / Jm j ; 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 ; η0= N / I t ; g(x) = -F x r / I t ; d(t) = -(d0+ T f ) / I t .

2. The finite time cooperative control method of commercial vehicle double-motor electric drive axle according to claim 1, characterized in that, The interval type-2 fuzzy observer design in Step 2 is as follows: The dual-motor electric drive axle system model is approximated by an interval type-2 fuzzy logic system, and the fuzzy rules are represented as follows: where j = 1, 2,..., N is the number of fuzzy rules; is the antecedent of the interval-valued intuitionistic fuzzy set; Φ j is the output of the fuzzy logic. The defuzzified output of the fuzzy logic system is calculated as: wherein Interval value g l (x) and g r (x) is obtained by Karnik-Mendel (KM) algorithm reduction; Φ = [Φ1, … Φ N ] T is an adaptive parameter For any continuous function g(x), there exists an interval-valued two-tuple fuzzy logic system optimal parameter Φ * and a positive constant such that The following interval type-2 fuzzy observer is designed: wherein, and denote the input and output of the IT2 FLS, respectively; wherein u0= T L1 + T L2 denote the input of the fuzzy system; is an estimate of the time-varying disturbance d(t); li > 0, l2 > 0; xi(·) and x2(·) are defined as: xi(·) = mi · 1 / 2 + m2 ·, x2(·) = mi 2 / 2 · 1 / 2 + 3mi m2 / 2 · 1 / 2 + mi 2 ·, the gains mi, m2 are designed as positive constants, Therefore, the state equation of the dual-motor electric drive axle system can be represented as:

3. The finite time cooperative control method of commercial vehicle double-motor electric drive axle according to claim 1, characterized in that, The finite time adaptive fuzzy collaborative controller design in Step 3 is as follows: 1) Define the first order tracking error of the dual-motor electric drive axle system as Taking the derivative of this gives where y d is the desired front wheel tracking angle, on the basis of which a second order tracking error e2 is defined as: where x 2v is the virtual control signal of the first step, as the desired value, According to formula (15), formula (14) can be rewritten as: Consider the Lyapunov function as: V1 = e1 2 / 2 (17) Taking the derivative of V1 gives: To improve the convergence speed and robustness of the system, a finite time control algorithm is introduced, and the first step virtual control signal x 2v is constructed as where n1 is a positive number, q1 is the first step finite time control coefficient and greater than 0, and p is the finite time control exponent and located between 0 and 1; 2) Taking the derivative of the second-order tracking error e2 according to formula (15) gives: Define the third-order tracking error e3 as: e3 = η0Kx3-x 3v (21) where x3= x 31 + x 32 , x 3v is the virtual control signal of the second step, as the desired value of η0Kx3, Consider the Lyapunov function as: V2 = V1 + e2 2 / 2 (22) Taking the derivative of V2 gives: Consider the second step of finite time control design virtual control signal x 3v is: where n2 is a positive number, and q2 is the second step finite time control coefficient and greater than 0; 3) Taking the derivative of the third-order tracking error e3 according to formula (21) gives: Defining the fourth order tracking error e 4j is: e 4j = η0Kx 4j - x 4v / 2 (26) where x 4v is the virtual control signal of the third step, and in order to ensure the synchronization of the two motor speeds, the expected value of η0Kx 4j is defined as x 4v / 2, Consider the Lyapunov function as: V3 = V2 + e3 2 / 2 (27) Taking the derivative of V3 gives: where e4= e 41 +e 42 . Consider the third step of finite-time control design virtual control signal x 4v is: where n3 is a positive number, and q3 is the finite time control coefficient and greater than 0; 4) Fourth order tracking error e is calculated according to equation (26) 4j Taking derivative, we have: Define the fifth order tracking error e 5j is: e 5j = η0Kη 2j x 5j -x 5jv (31) x 5jv is the virtual control signal for the fourth step, as η0Kη 2j x 5j is the desired value; Consider the Lyapunov function as V4 = V3 + e4 2 / 2 (32) Taking the derivative of V4 gives: To strengthen the consistency of the dual-motor electric drive axle system, the rotational speed error e of the two motors is designed s = e 42 - e 41 , the virtual control signal x of the fourth step of the finite time control design is considered 5jv : where n4 is a positive number, q4 is a fourth step finite time control coefficient and is greater than 0, k s , k s1 is a rotational speed error coefficient; 5) The fifth order tracking error e is according to formula (31) 5j The derivation can be obtained: Consider the Lyapunov function as: V5 = V4 + e5 2 / 2 (36) Taking the derivative of V5 gives: To further enhance the consistency of the dual-motor and improve its service life, the torque error e t = e 52 - e 51 , considering the finite time control, the virtual control signal u qj of the fifth step is obtained. wherein n5 is a positive number, q5 is a fifth step finite time control coefficient and is greater than 0; k c , k c1 is a torque error coefficient.

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