A hybrid model predictive control method for gear shifting process based on piecewise affine

Abstract

The present invention is applicable to the technical field of electric drive system control for new energy vehicles, and provides a hybrid model predictive control method for a shifting process based on piecewise affine, comprising the following steps: establishing a piecewise nonlinear dynamic model of the shifting process of the electric drive system; performing hybrid system modeling on the piecewise nonlinear dynamic model in the shifting process of the electric drive system based on the piecewise affine method; establishing a hybrid model predictive control problem model applied to the shifting process of the electric drive system, using a performance function with tracking error and control energy loss as control targets, converting the shifting process engagement control problem of the engagement sleeve and the engagement gear ring into a constrained finite time domain optimization control problem; converting the hybrid model predictive control problem into a quadratic programming problem for solution, thereby obtaining the hybrid model predictive control law in the shifting process of the electric drive system. The method effectively improves the control accuracy of the shifting process and reduces the shifting shock.

Description

Technical Field

[0001] The present invention belongs to the technical field of electric drive system control for new energy vehicles, and in particular relates to a hybrid model predictive control method for a gear shifting process based on piecewise affine. Background Art

[0002] At present, the electric drive system of new energy vehicles adopts the form of direct connection between the motor and the AMT gearbox, eliminating the clutch and synchronizer, improving the transmission efficiency and reducing the development cost. However, due to the absence of clutch and synchronizer, the control difficulty of the electric drive system shifting process is increased. The shifting process control of the electric drive system of new energy vehicles is divided into: drive motor torque reduction, gear shifting, synchronization, gear engagement and drive motor torque increase. In order to improve the control accuracy of the electric drive system shifting process and reduce the shifting shock, there are currently many control methods for drive motor control and speed synchronization control during the shifting process.

[0003] The Chinese invention patent "Shockless Shifting Control Method and System for an Electric Driven Mechanical Transmission without Synchronizer" with authorization announcement number CN106195249B adopts a system coordination controller to coordinate the working timing and working mode of the dual-target tracking controller and the rule-based controller, so that the drive motor and AMT coordinate to achieve gear shifting; and through precise control of the drive motor, the target engagement ring gear accurately tracks the rotation of the engagement sleeve during the engagement process.

[0004] The Chinese invention patent with application publication number CN118331036A, "Method for solving the shortest control law for speed synchronization angle alignment time during gear shifting", achieves precise control of the drive motor torque and synchronous speed difference during gear shifting by establishing optimization problems, solving the optimal control law through dynamic planning, controlling the speed difference and angle difference, and other steps.

[0005] The shifting process control of new energy electric drive system includes both the control of discrete events in the shifting process and the control of continuous variables such as the angle and angular velocity of the shifting element. Therefore, the shifting process control of new energy electric drive system is a hybrid system control in which discrete events and continuous state variables are coupled.

[0006] However, the current control methods for the shifting process of electric drive systems do not consider the hybrid characteristics of the piecewise nonlinear discrete events and continuous state variables of the shifting process dynamics, and do not propose a control method for the hybrid characteristics of the shifting process. Therefore, a hybrid model predictive control method for the shifting process based on piecewise affine is needed to improve the control accuracy of the shifting process and reduce the shifting shock. Summary of the invention

[0007] The purpose of the embodiments of the present invention is to provide a hybrid model predictive control method for a gear shift process based on piecewise affine, aiming to solve the problems raised in the above background technology.

[0008] The embodiment of the present invention is implemented as follows: a hybrid model predictive control method for a gear shift process based on piecewise affine, comprising the following steps:

[0009] Step 1: Establish a piecewise nonlinear dynamic model to describe the shifting process of the electric drive system. According to the different coupling relationships between the clutch sleeve and the clutch ring during the shifting process, the shifting process is divided into six states.

[0010] Step 2: Hybrid system modeling of the piecewise nonlinear dynamic model of the electric drive system during the gear shifting process is performed based on the piecewise affine method;

[0011] Step 3: Establish a hybrid model predictive control problem model applied to the electric drive system shifting process, adopt a performance function with tracking error and control energy loss as the control target, and transform the shifting process clutch and clutch ring engagement control problem into a constrained finite time domain optimization control problem;

[0012] Step 4: Convert the hybrid model predictive control problem into a quadratic programming problem and solve it to obtain the hybrid model predictive control law during the gear shifting process of the electric drive system.

[0013] The embodiment of the present invention provides a hybrid model predictive control method for a gear shift process based on piecewise affine, and its beneficial effects are as follows:

[0014] (1) The hybrid system modeling of the electric drive system shifting process based on the piecewise affine method can solve the problem of difficulty in system modeling caused by the mutual coupling of discrete events and continuous state variables in the piecewise nonlinear dynamics of the shifting process;

[0015] (2) For the hybrid system model of the electric drive system shifting process, the model predictive control method is used to establish a performance function with tracking error and control energy loss as the control objectives, and the engagement control problem of the clutch and the engagement gear ring during the shifting process is transformed into a constrained finite time domain optimization control problem, which can improve the control accuracy of the clutch and the engagement gear ring during the shifting process and reduce the shifting shock;

[0016] (3) The hybrid model predictive control problem is transformed into a quadratic programming problem for solution, thereby obtaining the hybrid model predictive control law during the gear shifting process of the electric drive system. This can reduce the computational difficulty of the control algorithm and improve the real-time performance of online calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1A schematic diagram of the structure of a hybrid model predictive control method for a gear shift process based on piecewise affine provided by an embodiment of the present invention;

[0018] Figure 2 It is a schematic diagram of the mechanical structure of the electric drive system shifting process;

[0019] Figure 3 is the coupling relationship between the engagement sleeve and the engagement ring gear during the gear shifting process;

[0020] Figure 4 The six states between the engagement ring gear and the engagement sleeve during the gear shifting process;

[0021] Figure 5 It is a schematic diagram of the model predictive control method of the gear shift process based on piecewise affine;

[0022] Figure 6 Flowchart of the hybrid model predictive control method for the gear shifting process. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0024] The specific implementation of the present invention is described in detail below in conjunction with specific embodiments.

[0025] like Figure 1 As shown, a hybrid model predictive control method for a gear shift process based on piecewise affine is provided in one embodiment of the present invention, comprising the following steps:

[0026] Step 1: Establish a piecewise nonlinear dynamic model to describe the shifting process of the electric drive system. According to the different coupling relationships between the clutch sleeve and the clutch ring during the shifting process, the shifting process is divided into six states.

[0027] Step 2: Hybrid system modeling of the piecewise nonlinear dynamic model of the electric drive system during the gear shifting process is performed based on the piecewise affine method;

[0028] Step 3: Establish a hybrid model predictive control problem model applied to the electric drive system shifting process, adopt a performance function with tracking error and control energy loss as the control target, and transform the shifting process clutch and clutch ring engagement control problem into a constrained finite time domain optimization control problem;

[0029] Step 4: Convert the hybrid model predictive control problem into a quadratic programming problem and solve it to obtain the hybrid model predictive control law during the gear shifting process of the electric drive system.

[0030] As a preferred embodiment of the present invention, in step 1, the mechanical structure of the electric drive system shifting process is as follows: Figure 2 As shown, T m is the output torque of the driving motor, T a is the output torque of the shift motor, F w 、F i and F f They are air resistance, slope resistance and rolling resistance.

[0031] from Figure 2 It can be seen that the output torque of the drive motor is transmitted to the engagement rings Ⅰ and Ⅱ through the gears. The shift motor can engage with the engagement rings Ⅰ and Ⅱ by pushing the engagement sleeve to move axially, thereby transmitting the output torque of the drive motor to the vehicle. Let the engagement ring Ⅰ be the engagement ring of the current gear, and the engagement ring Ⅱ be the engagement ring of the target gear. During the shifting process, the engagement sleeve needs to be separated from the engagement ring Ⅰ, then move axially, and finally engage with the engagement ring Ⅱ. In this process, the coupling relationship between the engagement sleeve and the engagement ring is as follows: Figure 3 shown.

[0032] Figure 3 middle, and are the circumferential rotation angle and angular velocity of the target engagement ring gear, and are the circumferential rotation angle and angular velocity of the coupling sleeve, and are the axial displacement and axial velocity of the coupling sleeve, is the initial position of the clutch sleeve in the current gear position, b gr 、h gr and α gr are the tooth length, tooth width and chamfer of the engagement gear ring, b slv and h slv are the tooth length and tooth width of the clutch sleeve respectively, and l is the distance between the target gear and the current gear clutch ring.

[0033] from Figure 2 and Figure 3 It can be seen that during the gear shifting process, since the target gear and the current gear have different speed ratios, the gear rings of the target gear and the current gear rotate at different speeds. During the gear shifting process, the coupling sleeve first needs to be separated from the current gear ring. Then, the system adjusts the target gear ring speed by controlling the drive motor. When the target gear ring speed is consistent with the coupling sleeve, the coupling sleeve is controlled to engage with the target gear ring.

[0034] During the shifting process, according to the different positional relationships between the engagement ring and the engagement sleeve, the shifting process is divided into six states, such as Figure 4 shown.

[0035] The specific status descriptions are as follows:

[0036] State 1: The coupling sleeve is fully engaged with the current gear coupling ring gear, and the axial movement speed of the coupling sleeve is zero at this time, and the system gear is still in the current gear.

[0037] State 2: The engagement sleeve is in the separation stage from the engagement ring gear of the current gear. At this time, the engagement sleeve moves along the axial direction, and the engagement sleeve and the engagement ring gear of the current gear still rotate together.

[0038] State three: In the free travel stage of the clutch sleeve, the clutch sleeve and the current gear engagement ring gear no longer move synchronously in the rotation direction.

[0039] State 4: During the tooth collision stage, during the axial movement of the coupling sleeve, the chamfer of the coupling sleeve and the chamfer of the target gear gear ring will collide with each other.

[0040] State 5: The gear is engaged, the coupling sleeve enters the tooth groove of the target gear engagement ring and continues to move axially.

[0041] State six: The coupling sleeve is fully engaged with the target gear engagement ring gear, and at this time the axial movement speed of the coupling sleeve is zero, and the system gear is at the target gear.

[0042] The specific switching conditions and dynamic equations of each state are as follows:

[0043] State 1: Satisfaction s slv =s0,F a ≤F s_max . F a is the shift force acting on the clutch sleeve, F s_max is the maximum static friction force that the coupling sleeve needs to overcome for axial movement. The dynamic equation of the system is:

[0044] (1)

[0045] In the formula, and are the circumferential rotation angle and angular velocity of the target engagement ring gear respectively; and are the circumferential rotation angle and angular velocity of the coupling sleeve respectively; and are the axial displacement and axial velocity of the coupling sleeve respectively; i cur and i tar are the speed ratios of the current gear and the target gear respectively; J in 、c in and b in are the equivalent moment of inertia, damping and stiffness of all mechanical components connected to the transmission input shaft during the synchronization process; Jout 、c out and b out are the equivalent moment of inertia, damping and stiffness of all mechanical components connected to the transmission output shaft during the synchronization process; T m is the output torque of the driving motor; T fv is the vehicle resistance torque.

[0046] (2)

[0047] In the formula, F w 、F i and F f are air resistance, slope resistance and rolling resistance. is the tire rolling radius.

[0048] State 2: Satisfying s0<s slv ≤s0+h gr -b gr / tanα gr , F a ≥F k_max . F k_max is the maximum sliding friction force that the clutch sleeve needs to overcome in axial motion. The system dynamics equation in state 2 during the gear shift process is:

[0049] (3)

[0050] In the formula, is the mass of the joint sleeve, is the damping of the coupling sleeve, is the shift force, It is the friction force that the coupling sleeve is subjected to when it acts on the coupling ring gear and spline hub at the same time.

[0051] (4)

[0052] Where, T a is the output torque of the shift motor, r a The shift actuator converts the rotational motion of the shift motor into the axial motion of the clutch sleeve, using the equivalent radius r a Replace this conversion relationship.

[0053] State 3: Satisfies s0+h gr -b gr / tanα gr <s slv ≤s0+h gr +lb slv , F a ≥F k_max The system dynamics equation when the gear shift process is in state three is:

[0054] (5)

[0055] In the formula, It is the friction force that the coupling sleeve is subjected to when it acts on the spline hub at the same time.

[0056] State 4: Satisfying s0+h gr +lb slv <s slv ≤s0+h gr +lb slv +b gr / tanα gr , F a ≥F k_max When the gear shift process is in state 4, the system dynamics equation is:

[0057] (6)

[0058] In the formula, F cos is the extrusion force when the coupling sleeve collides with the chamfer of the coupling gear ring, r gr is the pitch circle radius of the target engagement gear ring.

[0059] State 5: Satisfying s0+h gr +lb slv +b gr / tanα gr <s slv <s0+2h gr +lb slv , F a ≥F k_max The system dynamics equation when the gear shift process is in state five is:

[0060] (7)

[0061] State 6: Satisfied slv =s0+2h gr +lb slv , F a = 0. The system dynamics equation when the shift process is in state six is:

[0062] (8)

[0063] As a preferred embodiment of the present invention, in step 2, during the gear shifting process of the electric drive system, the state variable is x and the control variable is u.

[0064] State variable: x=[s slv ,v slv ,θ slv ,ωslv , θ gr ,ω gr ];

[0065] Control variable: u=[T m , F a ];

[0066] According to the dynamic description of the six states in the electric drive shifting process, the discrete time state space expression of the shifting process based on piecewise affine can be obtained as follows:

[0067] (9)

[0068] In the formula, x(t+1) is the state variable value at time t+1, x(t) and u(t) are the state variable value and control variable value at time t, respectively. The system matrix A is i and Bi, and the bias term f i (where i=1,2,3,4,5,6) is as follows:

[0069] ;

[0070] ;

[0071] ;

[0072] ;

[0073] ;

[0074] ;

[0075] ;

[0076] ;

[0077] The general form of the discrete-time piecewise affine system of the gear shifting process and its constraints are:

[0078] (10)

[0079] The constraints are:

[0080] (11)

[0081] In the formula, for A non-empty compact set in Representation Domain The polyhedron area inside, n x and n u Represent the dimensions of state variables and control variables respectively.

[0082] As a preferred embodiment of the present invention, in step 3, during the gear shifting process of the electric drive system, the target value of the state variable is x ref , the error is e.

[0083] Target reference value: x ref =[s slv_ref ,v slv_ref ,θ slv_ref ,ω slv_ref , θ gr_ref ,ω gr_ref ];

[0084] Error: e=[e s_slv ,e v_slv ,e θ_slv ,e ω_slv , e θ _ gr ,e ω _ gr ];

[0085] Axial displacement error of the coupling sleeve: e s_slv =s slv− s slv_ref ;

[0086] Axial speed error of the coupling sleeve: e v_slv =v slv − v slv_ref ;

[0087] Circumferential angle error of the coupling sleeve: e θ_slv =θ slv− θ slv_ref ;

[0088] Angular velocity error of the coupling sleeve: e ω_slv =ω slv − ω slv_ref ;

[0089] Circumferential angle error of the engagement ring gear: e θ _ gr =θ gr − θ gr_ref ;

[0090] Angular velocity error of the meshing gear ring: e ω _ gr =ω gr − ω gr_ref ;

[0091] Among them, s slv_ref and v slv_ref are the target values ​​of the axial displacement and speed of the coupling sleeve, θ slv_ref and ωslv_ref are the target values ​​of the coupling sleeve circumferential angle and acceleration, θ gr_ref and ω gr_ref are the target values ​​of the target combined gear ring circular angle and angular velocity respectively.

[0092] At time t, the prediction interval is N p , the hybrid model predictive control performance function of the electric drive system shifting process:

[0093] (12)

[0094] In the formula, S, Q, and R are weight coefficient matrices. Indicates that at time t, p The error prediction value at time, represents the error prediction value at time t for time t+k, It represents the predicted value of the control variable at time t+k.

[0095] Constraints:

[0096] (13)

[0097] Where x(t+1|t) represents the predicted value of the state variable at time t+1, x(t|t) and u(t|t) represent the predicted value of the state variable and the predicted value of the control variable at time t, respectively.

[0098] The shift process model predictive control method based on piecewise affine is shown as follows: Figure 5 As shown in Figure 1, first, the prediction model based on the piecewise affine model predicts the future dynamics of the system x(t+k|t); second, given the target reference value x ref (t), and calculate the error e ( t+k|t ); then, solve the optimization problem according to the performance function; finally, the first control quantity of the solution Acts on the electric drive shift system.

[0099] exist Figure 5 In the above example, x(t+k|t) represents the predicted value of the state variable at time t for time t+k, and x ref (t) is the target value of the state variable at time t, e(t+k|t) represents the error prediction value at time t for time t+k, It represents the optimal predicted value of the control variable at time t, and x(t+1) is the value of the state variable at time t+1.

[0100] As a preferred embodiment of the present invention, in step 4, the hybrid model predictive control method flow of the gear shift process is as follows: Figure 6As shown. First determine the system matrix A i , B i and weight coefficient matrices Q, R, S, and according to the target reference value x ref Determine the target transfer matrix A ref_i . Secondly, construct the augmented state variable x e (t), and determine the augmented transfer matrix A e , B e , Q e , S e Then, the performance function about the error e(t) and the control variable u(t) is transformed into the performance function about the augmented state variable x e (t), the performance function of the control variable u(t), and calculate the transition matrix Φ, F e , Γ, Ω, Ψ. Optimally, the optimization problem is transformed into a quadratic programming problem to obtain the optimal control sequence , take the first term u(t|t) to act on the gear shifting system.

[0101] For the target reference variable x ref , its dynamic equation can be expressed as:

[0102] (14)

[0103] In the formula, x ref (t) and x ref (t+1) are the target values ​​at time t and time t+1 respectively, A ref_i is the transition matrix of the target state.

[0104] Define the augmented state variable x e (t), construct a state space representation containing augmented state variables:

[0105] (15)

[0106] make:

[0107] ;

[0108] In the formula, x e (t) is the augmented state variable, A e is the augmented transfer matrix of state variables and errors, B e is the augmented transfer matrix of the control variables, f e is the augmented bias term.

[0109] Therefore, the state space expression including the augmented state variables is:

[0110] (16)

[0111] In the formula, xe (t+1|t) represents the predicted value of the augmented state variable at time t for time t+1, x e u(t|t) and u(t|t) represent the predicted value of the augmented state variable at time t and the predicted value of the augmented control variable at time t, respectively.

[0112] Therefore, the state error is:

[0113] (17)

[0114] In the formula, the augmented error coefficient matrix .

[0115] Therefore, the performance function including the augmented state variables is:

[0116] (18)

[0117] In the formula, x e (t+N p |t) represents the time t for t+N p The predicted value of the augmented state variable at time t, x e (t+k|t) represents the predicted value of the augmented state variable at time t for time t+k, and u(t+k|t) represents the predicted value of the augmented control variable at time t for time t+k.

[0118] make , we can get:

[0119] (19)

[0120] For the model , at time t, backward prediction N p step length, we can get:

[0121] (20)

[0122] make:

[0123] ;

[0124] Among them, the X(t) vector contains the augmented state variables in all prediction intervals predicted at time k, the U(t) vector contains the augmented control variables in all prediction intervals predicted at time k, and Φ, F e , Γ is the augmented transformation matrix.

[0125] Therefore, the model prediction state space expression in compact form is:

[0126] ;

[0127] Then, the performance function expressed by X(t) and U(t) is:

[0128] (twenty one)

[0129] Define the augmented transformation matrix Ω, Ψ:

[0130] ;

[0131] Then, the performance function in compact form is:

[0132] (twenty two)

[0133] Next, by transforming, we can express X(t) with U(t) and convert Substituting into the performance function J to get the second term:

[0134] (twenty three)

[0135] In the formula, the first term From the initial state The second item is decided From the initial state and Determined, uncontrolled amount Therefore, it can be ignored during the optimization calculation and a new performance index is obtained:

[0136] (twenty four)

[0137] Solve the performance function and let J be the derivative of U(t):

[0138] (25)

[0139] Obtain the optimal control law:

[0140] (26)

[0141] The first term of the optimal control sequence is :

[0142] (27)

[0143] In practical applications, according to the requirements of rolling optimization, it is only necessary to calculate and extract The first item in Just act on the system.

[0144] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A hybrid model predictive control method for gear shifting process based on piecewise affine, characterized in that: The following steps are involved: Step 1: Establish a piecewise nonlinear dynamic model to describe the shifting process of the electric drive system. According to the different coupling relationships between the clutch sleeve and the clutch ring during the shifting process, the shifting process is divided into six states. Step 2: Hybrid system modeling of the piecewise nonlinear dynamic model of the electric drive system during the gear shifting process is performed based on the piecewise affine method; Step 3: Establish a hybrid model predictive control problem model applied to the electric drive system shifting process, adopt a performance function with tracking error and control energy loss as the control target, and transform the shifting process clutch and clutch ring engagement control problem into a constrained finite time domain optimization control problem; Step 4: Convert the hybrid model predictive control problem into a quadratic programming problem and solve it, so as to obtain the hybrid model predictive control law in the gear shifting process of the electric drive system; In step 4, the hybrid model predictive control method process of the gear shift process is as follows: First determine the system matrix A i , B i and weight coefficient matrices Q, R, S, and according to the target reference value x ref Determine the target transfer matrix A ref_i ; Secondly, construct the augmented state variable x e (t), and determine the augmented transfer matrix A e , B e , Q e , S e ; Then, the performance function about the error e(t) and the control variable u(t) is converted into the performance function about the augmented state variable x e (t), the performance function of the control variable u(t), and calculate the transition matrix Φ, F e , Γ, Ω, Ψ; optimal, transform the optimization problem into a quadratic programming problem, and obtain the optimal control sequence U(t) * , take the first term u(t|t) to act on the shifting system; For the target reference variable x ref , its dynamic equation can be expressed as: x ref (t+1)=A ref_i x ref (t) (14) In the formula, x ref (t) and x ref (t+1) are the target values ​​at time t and time t+1 respectively, A ref_i is the transfer matrix of the target state; Define the augmented state variable x e (t), construct a state space representation containing augmented state variables: make: In the formula, x e (t) is the augmented state variable, A e is the augmented transfer matrix of state variables and errors, B e is the augmented transfer matrix of the control variables, f e is the augmented bias term; Therefore, the state space expression including the augmented state variables is: x e (t+1|t)=A e x e (t|t)+B e u(t|t)+f e (16) In the formula, x e (t+1|t) represents the predicted value of the augmented state variable at time t for time t+1, x e (t|t) and u(t|t) represent the predicted value of the augmented state variable at time t and the predicted value of the augmented control variable at time t, respectively; Therefore, the state error is: In the formula, the augmented error coefficient matrix C e =[-I,I]; Therefore, the performance function including the augmented state variables is: In the formula, x e (t+N p |t) represents the time t for t+N p The predicted value of the augmented state variable at time t, x e (t+k|t) represents the predicted value of the augmented state variable at time t for time t+k, and u(t+k|t) represents the predicted value of the augmented control variable at time t for time t+k; make We can get: For model x e (t+1|t)=A e x(t|t)+B e u(t|t)+f e , at time t, backward prediction N p step length, we can get: make: Among them, the X(t) vector contains the augmented state variables in all prediction intervals predicted at time k, the U(t) vector contains the augmented control variables in all prediction intervals predicted at time k, and Φ, F e , Γ is the augmented transformation matrix; Therefore, the model prediction state space expression in compact form is: X(t)=Φx e (t|t)+ΓU(t)+F e f e Then, the performance function expressed by X(t) and U(t) is: Define the augmented transformation matrix Ω, Ψ: Then, the performance function in compact form is: Next, by transformation, we can express X(t) with U(t) and convert X(t)=Φx e (t|t)+ΓU(t)+F e f e Substituting into the performance function J to get the second term: In the formula, the first term The initial state x e (t|t)], the second term The initial state x e (t|t)] and F e f e It is determined by and is not affected by the control quantity U(t); therefore, it can be ignored during the optimization calculation and a new performance index is obtained: Solve the performance function and let J be the derivative of U(t): Obtain the optimal control law: [U(t)] * =-(Γ T OG+ψ)G T Ω[Φx e (t|t)+F e f e ] (26) The first term of the optimal control sequence is u(t|t) * : In practical applications, according to the requirements of rolling optimization, it is only necessary to calculate and extract [U(t)] * The first term in [u(t|t)] * Just act on the system.

2. The hybrid model predictive control method for gear shifting process based on piecewise affine according to claim 1, characterized in that: In step 1, the output torque of the driving motor is transmitted to the engagement ring gears I and II through the gears, and the shift motor can engage with the engagement ring gears I and II by pushing the engagement sleeve to move axially, thereby transmitting the output torque of the driving motor to the vehicle; the engagement ring gear I is the engagement ring gear at the current gear position, and the engagement ring gear II is the engagement ring gear at the target gear position; During the gear shifting process, the clutch sleeve needs to separate from the clutch gear ring I, then move axially, and finally engage with the clutch gear ring II; During the gear shifting process, since the target gear and the current gear have different speed ratios, the engagement ring gears of the target gear and the current gear rotate at different speeds. During the gear shifting process, the engagement sleeve first needs to be separated from the current engagement ring gear. Then, the system adjusts the target engagement ring gear speed by controlling the driving motor, and when the target engagement ring gear speed is consistent with the engagement sleeve, the engagement sleeve is controlled to engage with the target engagement ring gear; During the shifting process, according to the different positional relationships between the engagement ring gear and the engagement sleeve, the shifting process is divided into six states. The specific descriptions of each state are as follows: State 1: The engagement sleeve is fully engaged with the engagement ring gear of the current gear, and the axial movement speed of the engagement sleeve is zero at this time, and the system gear is still in the current gear; State 2: The engagement sleeve is separated from the engagement ring gear of the current gear. At this time, the engagement sleeve moves along the axial direction, and the engagement sleeve and the engagement ring gear of the current gear still rotate together; State 3: The free travel stage of the clutch sleeve, the clutch sleeve and the current gear engagement ring gear no longer move synchronously in the rotation direction; State 4: The tooth collision stage, during the axial movement of the coupling sleeve, the chamfer of the coupling sleeve and the chamfer of the target gear engagement ring will collide with each other; State 5: The gear is engaged, the engagement sleeve enters the tooth groove of the target gear engagement ring and continues to move axially; State six: The coupling sleeve is fully engaged with the target gear engagement ring gear, and at this time the axial movement speed of the coupling sleeve is zero, and the system gear is at the target gear.

3. The hybrid model predictive control method for gear shifting process based on piecewise affine according to claim 2, characterized in that: The specific switching conditions and dynamic equations of each state are as follows: State 1: Satisfaction s slv =s0,F a ≤F s_max ; F a is the shift force acting on the clutch sleeve, F s_max is the maximum static friction force that the coupling sleeve needs to overcome for axial movement; the dynamic equation of the system is: In the formula, θ gr and ω gr are the circumferential rotation angle and angular velocity of the target engagement ring gear respectively; θ slv and ω slv are the circumferential rotation angle and angular velocity of the coupling sleeve respectively; s slv and v slv are the axial displacement and axial velocity of the coupling sleeve respectively; i cur and i tar are the speed ratios of the current gear and the target gear respectively; J in 、c in and b in are the equivalent moment of inertia, damping and stiffness of all mechanical components connected to the transmission input shaft during the synchronization process; J out 、c out and b out are the equivalent moment of inertia, damping and stiffness of all mechanical components connected to the transmission output shaft during the synchronization process; T m is the output torque of the driving motor; T fv is the vehicle resistance torque; In the formula, F w 、F i and F f are air resistance, slope resistance and rolling resistance, r wheel is the tire rolling radius; State 2: Satisfying s0<s slv ≤s0+h gr -b gr / tanα gr , F a ≥F k_max ; F k_max is the maximum sliding friction force that the clutch sleeve needs to overcome in axial motion; the system dynamics equation in state 2 during the shifting process is: In the formula, m slv is the mass of the joint sleeve, c slv is the damping of the coupling sleeve, F a is the shift force, F n1 It is the friction force that the coupling sleeve is subjected to when it acts on the coupling gear ring and spline hub at the same time; Where, T a is the output torque of the shift motor, r a is the equivalent radius; the shift actuator converts the rotational motion of the shift motor into the axial motion of the engagement sleeve, using the equivalent radius r a Instead of this conversion relationship; State 3: Satisfies s0+h gr -b gr / tanα gr <s slv ≤s0+h gr +lb slv , F a ≥F k_max , the system dynamics equation when the shift process is in state three is: In the formula, F n2 It is the friction force that the coupling sleeve is subjected to when it acts on the spline hub at the same time; State 4: Satisfying s0+h gr +lb slv <s slv ≤s0+h gr +lb slv +b gr / tanα gr , F a ≥F k_max When the gear shift process is in state 4, the system dynamics equation is: In the formula, F cos is the extrusion force when the coupling sleeve collides with the chamfer of the coupling gear ring, r gr is the pitch circle radius of the target engagement gear ring; State 5: Satisfying s0+h gr +lb slv +b gr / tanα gr <s slv <s0+2h gr +lb slv , F a ≥F k_max When the gear shift process is in state five, the system dynamics equation is: State 6: Satisfied slv =s0+2h gr +lb slv , F a = 0; the system dynamics equation when the shift process is in state six is:

4. The hybrid model predictive control method for gear shifting process based on piecewise affine according to claim 3, characterized in that: In step 2, during the gear shifting process of the electric drive system, the state variable is x and the control variable is u; State variable: x = [s slv ,v slv ,θ slv ,ω slv ,θ gr ,ω gr ]; Control variable: u=[T m ,F a ]; According to the dynamic description of the six states in the electric drive shifting process, the discrete time state space expression of the shifting process based on piecewise affine can be obtained as follows: In the formula, x(t+1) is the state variable value at time t+1, x(t) and u(t) are the state variable value and control variable value at time t, respectively. The system matrix A is i and Bi, and the bias term f i (where i = 1, 2, 3, 4, 5, 6) as follows: The general form of the discrete-time piecewise affine system of the gear shifting process and its constraints are: x(t + 1) = A i x(t) + B i u(t) + f i where i = 1, 2,..., 6 (10) The constraints are: In the formula, for A non-empty compact set in Representation domain ξ i The polyhedron area inside, n x and n u Represent the dimensions of state variables and control variables respectively.

5. The hybrid model predictive control method for gear shifting process based on piecewise affine according to claim 4, characterized in that: In step 3, during the gear shifting process of the electric drive system, the target value of the state variable is x ref , the error is e; Target reference value: x ref =[s slv_ref ,v slv_ref ,θ slv_ref ,ω slv_ref ,θ gr_ref ,ω gr_ref ]; Difference: e=[e s_slv ,e v_slv ,e θ_slv ,e ω_slv ,e θ _ gr ,e ω _ gr ]; Axial displacement error of the coupling sleeve: e s_slv =s slv -s slv_ref ; Axial speed error of the coupling sleeve: e v_slv =v slv -v slv_ref ; Circumferential rotation angle error of the coupling sleeve: e θ_slv =θ slv -θ slv_ref ; Angular velocity error of the coupling sleeve: e ω_slv =ω slv -ω slv_ref ; Circumferential angle error of the engagement ring gear: e θ_gr =θ gr -θ gr_ref ; Angular velocity error of the meshing gear ring: e ω_gr =ω gr -ω gr_ref ; Among them, s slv_ref and v slv_ref are the target values ​​of the axial displacement and speed of the coupling sleeve, θ slv_ref and ω slv_ref are the target values ​​of the coupling sleeve circumferential angle and acceleration, θ gr_ref and ω gr_ref are the target values ​​of the target combined gear ring circular angle and angular velocity respectively; At time t, the prediction interval is N p , the hybrid model predictive control performance function of the electric drive system shifting process: In the formula, S, Q, and R are weight coefficient matrices, e(t+N p |t) represents the time t for t+N p The error prediction value at time t, e(t+k|t) represents the error prediction value at time t for time t+k, and u(t+k|t) represents the control variable prediction value at time t for time t+k; Constraints: x(t + 1|t) = A i x(t|t) + B i u(t|t) + f i where i = 1, 2, ..., 6 (13) In the formula, x(t+1|t) represents the predicted value of the state variable at time t+1, x(t|t) and u(t|t) represent the predicted value of the state variable and the predicted value of the control variable at time t, respectively. The process of the gear shift process model predictive control method based on piecewise affine is as follows: first, the prediction model based on the piecewise affine model predicts the future dynamics of the system x(t+k|t); second, given the target reference value x ref (t), and calculate the error e(t+k|t); then, solve the optimization problem according to the performance function; finally, convert the first control variable u(t|t) * Acts on the electric drive shift system.

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