Active steering and differential braking integrated rollover control method

Abstract

The present application belongs to the technical field of vehicle engineering, and relates to a kind of active steering and differential brake integrated rollover control method, comprising: constructing tractor steering and differential brake integrated dynamics model;Adopt model prediction method to establish controller;Based on road adhesion coefficient setting steering angle and brake torque constraint, the optimal control output is obtained by using quadratic programming to solve constraint optimization problem.The present application introduces the dynamic estimation of road adhesion coefficient in the constraint of front wheel steering angle and trailer yaw moment, which can effectively reduce the tire slip phenomenon caused by insufficient adhesion on low adhesion road and solve the problem that static value cannot adapt to any working condition in real time, at the same time, the model prediction method is used to set the controller, the future state of the vehicle is predicted in advance, and the driving safety is improved, the present application can effectively improve the adaptability of articulated vehicle in low adhesion coefficient road under rollover control, and the integrated method can effectively strengthen the rollover control effect.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of vehicle engineering and relates to a method for active steering and differential braking integrated rollover control. BACKGROUND

[0002] The rapid development of e-commerce and the logistics demand have strengthened the market demand for heavy-duty tractor safety, and heavy-duty semitrailers play an important role in improving logistics efficiency and comprehensive economic benefits. However, due to the large tonnage and high gravity center of the semitrailer, and the change of road conditions caused by weather, the semitrailer is prone to rollover, folding and other accidents. The existing research on the rollover control of the articulated vehicle train mostly focuses on separate steering or differential braking control, and lacks the adaptability and effectiveness of the rollover control method under low adhesion road conditions.

[0003] Therefore, the active steering and differential braking integrated control is adopted, the model prediction control method with a prediction stage is used, and the lateral moment constraint based on the road adhesion coefficient is added to the prediction model to prevent braking from slipping, which becomes the key to improving the active safety of the semitrailer. SUMMARY

[0004] In order to overcome the problems existing in the prior art, the application provides a method for active steering and differential braking integrated rollover control, which adopts active steering and differential braking integrated control, uses a model prediction control method with a prediction stage, and improves the control effect of the rollover control. The constraints of the turning angle and the braking torque are set by the road adhesion coefficient to prevent the vehicle from slipping and improve the active safety of the semitrailer on the low adhesion road.

[0005] The technical scheme for solving the above problems is that the method for active steering and differential braking integrated rollover control comprises the following steps:

[0006] S1, a tractor-trailer steering and braking rollover model is constructed, including a tractor and a trailer dynamics model;

[0007] S2, a model prediction method is used to establish a rollover controller, and the future state of the semitrailer is predicted in the prediction stage;

[0008] S3, the turning angle and the lateral moment constraint are set based on the road adhesion coefficient, and a quadratic programming algorithm is used to solve the constraint optimization problem to obtain the optimal control output.

[0009] Further, in the step S1, the tractor steering and differential braking dynamics model is established.

[0010] The tractor steering and differential braking integrated dynamics equation is:

[0011]

[0012]

[0013]

[0014] In the formula: m1 is the mass of the tractor, u1 is the instantaneous velocity of the tractor's center of gravity, β1 is the sideslip angle of the tractor's center of gravity, ψ1 is the yaw angle of the tractor, and m 1s Let f be the sprung mass of the tractor, h1 be the distance from the center of gravity of the tractor to the roll axis, φ1 be the roll angle of the tractor, F1 be the lateral force on the front axle, δ be the steering angle of the front wheels of the tractor, F2 be the lateral force on the rear axle of the tractor, F4 be the force at the articulation point, and I be the lateral force on the rear axle of the tractor. 1zz Let I be the moment of inertia of the tractor unit about the Z-axis. 1xz Let I be the product of yaw and roll inertia of the sprung mass of the tractor unit, a be the distance from the center of gravity of the tractor unit to the front axle, b be the distance from the center of gravity of the tractor unit to the rear axle, c be the distance from the center of gravity of the tractor unit to the articulation point, and I be the distance from the sprung mass of the tractor unit to the articulation point. xx Let g be the moment of inertia of the tractor about the X-axis, g be the acceleration due to gravity, and k be the moment of inertia of the tractor about the X-axis. r1 Let c1 be the lateral stiffness of the tractor unit, c1 be the lateral roll damping of the tractor unit, and k be the lateral stiffness of the tractor unit. 12 φ2 is the lateral stiffness at the articulation point, h is the trailer roll angle, and h is the lateral stiffness at the articulation point. 1c This is the distance from the articulation point to the tilt axis of the tractor.

[0015] Integrated dynamic model of trailer steering and differential braking:

[0016]

[0017]

[0018]

[0019] In the formula: m2 is the trailer mass, β2 is the trailer's sideslip angle, ψ2 is the trailer's yaw angle, u2 is the instantaneous velocity of the trailer's center of gravity, and m 2x h1 is the sprung mass of the trailer, h2 is the distance from the trailer's center of gravity to the trailer axle, F3 is the lateral force on the trailer's rear axle, Γ is the hinge angle, and I is the lateral force on the trailer's rear axle. 2zz Let I be the moment of inertia of the trailer about the Z-axis. 2xz Let d be the product of yaw and tilt inertia of the trailer sprung mass, d be the distance between the trailer center of gravity and the trailer axle, e be the distance between the trailer center of gravity and the articulation point, and I be the distance between the trailer center of gravity and the articulation point. 2xx Let k be the moment of inertia of the trailer about the X-axis. r2 c1 is the trailer roll stiffness, c2 is the trailer roll damping, and h is the trailer roll resistance. 2c This is the distance from the articulation point to the trailer's tilt axis;

[0020] Kinematic constraints of tractor and trailer:

[0021]

[0022] Using a linear tire model, the tire slip angle does not exceed 5°; therefore, the lateral force on each axle of the trailer is equal to the product of the lateral stiffness and the slip angle.

[0023]

[0024] Furthermore, step S2 above uses a model predictive method to design the controller, specifically including: selecting the control variable u = [δ M1 M2]. T ;

[0025] By combining the dynamic model of steering and differential braking of the tractor and trailer with kinematic constraints, its state-space equations can be obtained:

[0026]

[0027] In the formula

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] The continuous state-space model is discretized using the forward Euler method, with a sampling time of T. The discrete state-space equations are:

[0034]

[0035] Among them: A c = (I+T)A, B c =TB;

[0036] set up: Δu=[Δδ ΔM1 ΔM2];

[0037] Combining equation (9) and the set state variable ξ(k), the control increment Δu,

[0038]

[0039] in,

[0040] Furthermore, step S2 above predicts the future state of the semi-trailer;

[0041] Set the prediction time domain to N p The control time domain is Nc By combining equation (15) to predict the future state of the semi-trailer, we can obtain:

[0042]

[0043] Combining equations (15) and (16), the relationship between the output quantity, state quantity, and control increment in the prediction time domain can be obtained:

[0044]

[0045] Y=Ψξ(k)+ΘΔU (18)

[0046] in:

[0047]

[0048]

[0049] C d =(CO 8×3 ),

[0050] To ensure that the vehicle state of the semi-trailer in the prediction time domain keeps up with the expected value, an objective function is set. To ensure vehicle stability while minimizing control input, an objective function is set. To ensure the equation has a solution and facilitate computation, we set the relaxation factor to ε and the weighting coefficient to ρ, resulting in the final optimization objective function:

[0051] J = J1 + J2 + ρε 2 (19),

[0052] In the formula, η(k+i) is the predicted output in the time domain, and η ref (k+i) is the expected value of the output in the prediction time domain, Δu(k+i) is the control increment of the vehicle turning angle and the yaw moment of the tractor and semi-trailer in the control time domain, Q is the semi-positive definite state weighting matrix, and R is the positive definite control weighting matrix.

[0053] Furthermore, step S3 above includes setting steering angle and yaw moment constraints based on the road surface adhesion coefficient:

[0054] Add tire adhesion limits to the constraints:

[0055]

[0056] In the formula, F xmax F is the maximum longitudinal force of the tire. z For the vertical load of the tire, F y This refers to the lateral force of the tire;

[0057] Maximum yaw moment of the tractor:

[0058]

[0059] Maximum yaw moment of trailer:

[0060]

[0061] In the formula M 1max M 2max Divided into the maximum yaw moment of the tractor and trailer, F 1xmax F 2xmax F 3xmax F is the maximum longitudinal force of the tractor tire. 4xmax F 5xmax F 6xmax l1 represents the maximum longitudinal force on the trailer tire, and l2 represents the wheelbase of the tractor and the trailer, respectively.

[0062] Furthermore, step S3 above includes using a quadratic programming algorithm to solve the constrained optimization problem to obtain the optimal control quantity:

[0063] Through a series of matrix derivations, the optimal objective function is transformed into:

[0064] J=(ΔU T ε)H(ΔU T ε) T +f(ΔU T ε) T +E T QE T (twenty three)

[0065] in, f = (2E T QΘ0), E=Ψξ(k)-Y ref ;

[0066] In summary, the objective function is solved using the quadratic programming method:

[0067] minJ=(ΔU T ε)H(ΔU T ε) T +f(ΔU T ε) T (twenty four),

[0068] Add constraints based on the road adhesion coefficient to the front wheel steering angle and the yaw moment of the tractor and trailer:

[0069] U min ≤U t +A t ΔU≤U max (25)

[0070] Among them U t For N c ×1 matrix, U max U min All are 3N c A matrix of size 1,

[0071] Constrain the control increment:

[0072] ΔU min ≤ΔU≤ΔU max (26),

[0073] Add constraints to vehicle status:

[0074] Y min -ε≤Ψξ(k)-ΘΔU≤Y max +ε (27),

[0075] A series of control increments are obtained by solving the constrained objective function using a quadratic programming algorithm:

[0076]

[0077] The current control input is obtained by adding the previously input control value to the first element of the control sequence.

[0078]

[0079] Advantages of this invention:

[0080] (1) This invention incorporates the dynamic road surface adhesion coefficient into the constraints of the front wheel turning angle and trailer yaw moment, thereby reducing the risk of rollover caused by tire slippage on low-adhesion road surfaces.

[0081] (2) This invention provides a combined active steering and braking integrated anti-rollover control strategy, which further enhances the anti-rollover performance of the vehicle and solves the technical problem that the existing semi-trailer tractors have insufficient steering or differential braking control effects when implemented alone.

[0082] (3) In view of the fact that existing vehicle rollover prevention control methods are prone to saturation in the current period, this invention introduces a model predictive control algorithm to set the controller, predict the future state of the vehicle in advance, and improve the driving safety of the vehicle. Attached Figure Description

[0083] Fig. 1 A flowchart of the active steering and differential braking integrated anti-rollover control method provided by the present invention;

[0084] Fig. 2 MPC flowchart of the integrated anti-rollover control method based on road adhesion coefficient for the present invention;

[0085] Fig. 3 The tractor-trailer dynamics model of the integrated anti-rollover control method based on road adhesion coefficient and active steering and differential braking provided by the present invention. Detailed Implementation

[0086] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention.

[0087] Reference Figs. 1 to 3 This invention proposes an integrated anti-rollover control method combining active steering and differential braking, which mainly includes the following steps:

[0088] S1. Construct a tractor-trailer steering and braking anti-rollover model, including dynamic models of the tractor and trailer;

[0089] S2. A rollover prevention controller is established using model prediction methods to predict the future state of the semi-trailer during the prediction phase.

[0090] S3. Based on the road surface adhesion coefficient, set the turning angle and yaw moment constraints, and use the quadratic programming algorithm to solve the constraint optimization problem to obtain the optimal control output.

[0091] In a preferred embodiment of the present invention, in step S1 above, a dynamic model of the steering and differential braking of the tractor is established:

[0092] Integrated dynamic equations for tractor steering and differential braking:

[0093]

[0094]

[0095]

[0096] In the formula: m1 is the mass of the tractor, u1 is the instantaneous velocity of the tractor's center of gravity, β1 is the sideslip angle of the tractor's center of gravity, ψ1 is the yaw angle of the tractor, and m 1sLet f be the sprung mass of the tractor, h1 be the distance from the center of gravity of the tractor to the roll axis, φ1 be the roll angle of the tractor, F1 be the lateral force on the front axle, δ be the steering angle of the front wheels of the tractor, F2 be the lateral force on the rear axle of the tractor, F4 be the force at the articulation point, and I be the lateral force on the rear axle of the tractor. 1zz Let I be the moment of inertia of the tractor unit about the Z-axis. 1xz Let I be the product of yaw and roll inertia of the sprung mass of the tractor unit, a be the distance from the center of gravity of the tractor unit to the front axle, b be the distance from the center of gravity of the tractor unit to the rear axle, c be the distance from the center of gravity of the tractor unit to the articulation point, and I be the distance from the sprung mass of the tractor unit to the articulation point. xx Let g be the moment of inertia of the tractor about the X-axis, g be the acceleration due to gravity, and k be the moment of inertia of the tractor about the X-axis. r1 Let c1 be the lateral stiffness of the tractor unit, c1 be the lateral roll damping of the tractor unit, and k be the lateral stiffness of the tractor unit. 12 φ2 is the lateral stiffness at the articulation point, h is the trailer roll angle, and h is the lateral stiffness at the articulation point. 1c This is the distance from the articulation point to the tilt axis of the tractor.

[0097] Integrated dynamic model of trailer steering and differential braking:

[0098]

[0099]

[0100]

[0101] In the formula: m2 is the trailer mass, β2 is the trailer's sideslip angle, ψ2 is the trailer's yaw angle, u2 is the instantaneous velocity of the trailer's center of gravity, and m 2x h1 is the sprung mass of the trailer, h2 is the distance from the trailer's center of gravity to the trailer axle, F3 is the lateral force on the trailer's rear axle, Γ is the hinge angle, and I is the lateral force on the trailer's rear axle. 2zz Let I be the moment of inertia of the trailer about the Z-axis. 2xz Let d be the product of yaw and tilt inertia of the trailer sprung mass, d be the distance between the trailer center of gravity and the trailer axle, e be the distance between the trailer center of gravity and the articulation point, and I be the distance between the trailer center of gravity and the articulation point. 2xx Let k be the moment of inertia of the trailer about the X-axis. r2 c1 is the trailer roll stiffness, c2 is the trailer roll damping, and h is the trailer roll resistance. 2c This is the distance from the articulation point to the trailer's tilt axis;

[0102] Kinematic constraints of tractor and trailer:

[0103]

[0104] Using a linear tire model, the tire slip angle does not exceed 5°; therefore, the lateral force on each axle of the trailer is equal to the product of the lateral stiffness and the slip angle.

[0105]

[0106] In a preferred embodiment of the present invention, step S2 above uses a model prediction method to design the controller, specifically including: selecting the control quantity u = [δ M1 M2] T ;

[0107] By combining the dynamic model of steering and differential braking of the tractor and trailer with kinematic constraints, its state-space equations can be obtained:

[0108]

[0109] In the formula

[0110]

[0111]

[0112]

[0113]

[0114] The continuous state-space model is discretized using the forward Euler method, with a sampling time of T. The discrete state-space equations are:

[0115]

[0116] Among them: A c = (I+T)A, B c =TB;

[0117] set up: Δu=[Δδ ΔM1 ΔM2];

[0118] Combining equation (9) and the set state variable ξ(k), the control increment Δu,

[0119]

[0120] in,

[0121] In a preferred embodiment of the present invention, step S2 above predicts the future state of the semi-trailer;

[0122] Set the prediction time domain to N p The control time domain is N c By combining equation (15) to predict the future state of the semi-trailer, we can obtain:

[0123]

[0124] Combining equations (15) and (16), the relationship between the output quantity, state quantity, and control increment in the prediction time domain can be obtained:

[0125]

[0126] Y=Ψξ(k)+ΘΔU (18)

[0127] in:

[0128]

[0129]

[0130] C d =(CO 8×3 ),

[0131] To ensure that the vehicle state of the semi-trailer in the prediction time domain keeps up with the expected value, an objective function is set. To ensure vehicle stability while minimizing control input, an objective function is set. To ensure the equation has a solution and facilitate computation, we set the relaxation factor to ε and the weighting coefficient to ρ, resulting in the final optimization objective function:

[0132] J = J1 + J2 + ρε 2 (19),

[0133] In the formula, η(k+i) is the predicted output in the time domain, and η ref (k+i) is the expected value of the output in the prediction time domain, Δu(k+i) is the control increment of the vehicle turning angle and the yaw moment of the tractor and semi-trailer in the control time domain, Q is the semi-positive definite state weighting matrix, and R is the positive definite control weighting matrix.

[0134] In a preferred embodiment of the present invention, step S3 includes setting rotation angle and yaw moment constraints based on the road surface adhesion coefficient:

[0135] Add tire adhesion limits to the constraints:

[0136]

[0137] In the formula, F xmax F is the maximum longitudinal force of the tire. z For the vertical load of the tire, F y This refers to the lateral force of the tire;

[0138] Maximum yaw moment of the tractor:

[0139]

[0140] Maximum yaw moment of trailer:

[0141]

[0142] In the formula M1max M 2max Divided into the maximum yaw moment of the tractor and trailer, F 1xmax F 2xmax F 3xmax F is the maximum longitudinal force of the tractor tire. 4xmax F 5xmax F 6xmax l1 represents the maximum longitudinal force on the trailer tire, and l2 represents the wheelbase of the tractor and the trailer, respectively.

[0143] In a preferred embodiment of the present invention, step S3 includes solving the constrained optimization problem using a quadratic programming algorithm to obtain the optimal control quantity:

[0144] Through a series of matrix derivations, the optimal objective function is transformed into:

[0145] J=(ΔU T ε)H(ΔU T ε) T +f(ΔU T ε) T +E T QE T (twenty three)

[0146] in, f = (2E T QΘ0), E=Ψξ(k)-Y ref ;

[0147] In summary, the objective function is solved using the quadratic programming method:

[0148] minJ=(ΔU T ε)H(ΔU T ε) T +f(ΔU T ε) T (twenty four),

[0149] Add constraints based on the road adhesion coefficient to the front wheel steering angle and the yaw moment of the tractor and trailer:

[0150] U min ≤U t +A t ΔU≤U max (25)

[0151] Among them U t For N c ×1 matrix, U max U min All are 3N c A matrix of size 1,

[0152] Constrain the control increment:

[0153] ΔU min ≤ΔU≤ΔU max (26),

[0154] Add constraints to vehicle status:

[0155] Y min -ε≤Ψξ(k)-ΘΔU≤Y max +ε (27),

[0156] A series of control increments are obtained by solving the constrained objective function using a quadratic programming algorithm:

[0157]

[0158] The current control input is obtained by adding the previously input control value to the first element of the control sequence.

[0159]

[0160] In summary, this invention proposes an integrated anti-rollover control method combining active steering and differential braking. It introduces a dynamic estimate of the road surface adhesion coefficient into the front wheel steering angle and trailer yaw moment constraints, effectively reducing tire slippage due to insufficient adhesion on low-adhesion roads and addressing the problem that static values ​​cannot adapt to all operating conditions in real time. Simultaneously, a model prediction method is used to set the controller, predicting the vehicle's future state in advance and improving driving safety. This invention effectively improves the adaptability of anti-rollover control for articulated vehicles on low-adhesion roads, significantly enhancing the anti-rollover control effect through an integrated approach. Compared to traditional methods, this invention improves the anti-rollover stability of heavy-duty semi-trailers, setting yaw moment constraints based on the road surface adhesion coefficient to prevent braking slippage and improve the active safety of semi-trailers.

[0161] The above description is merely an embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related system fields, are similarly included within the scope of protection of the present invention.

Claims

1. A rollover prevention control method integrating active steering and differential braking, characterized in that, Includes the following steps: S1. Construct a tractor-trailer steering and braking anti-rollover model, including dynamic models of the tractor and trailer; S2. A rollover prevention controller is established using model prediction methods to predict the future state of the semi-trailer during the prediction phase. S3. Based on the real-time estimated road adhesion coefficient, the constraints of the front wheel steering angle, tractor yaw moment and trailer yaw moment are dynamically set in a coordinated manner, and the constraint optimization problem is solved by using a quadratic programming algorithm to obtain the optimal control output. Based on the real-time estimated road adhesion coefficient, constraints on the front wheel steering angle, tractor yaw moment, and trailer yaw moment are dynamically set collaboratively, specifically as follows: Add tire adhesion limits to the constraints: (20)， In the formula, This is the maximum longitudinal force of the tire. For the vertical load of the tire, This refers to the lateral force of the tire; Maximum yaw moment of the tractor: (21)， Maximum yaw moment of trailer: (22)， In the formula , Divided into the maximum yaw moment of tractor and trailer, , , This represents the maximum longitudinal force on the tractor tires. , , This represents the maximum longitudinal force on the trailer tires. , These are the wheelbases of the tractor and trailer, respectively. The optimal control quantity is obtained by solving the constrained optimization problem using a quadratic programming algorithm, specifically: Through a series of matrix derivations, the optimal objective function is transformed into: (23) in, , , ; In summary, the objective function is solved using the quadratic programming method: (24)， Add constraints based on the road adhesion coefficient to the front wheel steering angle and the yaw moment of the tractor and trailer: (25) in for matrix, , , All are The matrix, , , , Constrain the control increment: (26)， Add constraints to vehicle status: (27)， A series of control increments are obtained by solving the constrained objective function using a quadratic programming algorithm: (28)， The current control input is obtained by adding the previously input control value to the first element of the control sequence. (29)。 2. The method for integrated active steering and differential braking to prevent rollover as described in claim 1, characterized in that: In step S1, a dynamic model of the steering and differential braking of the tractor is established: Integrated dynamic equations for tractor steering and differential braking: (1) (2) (3) In the formula: For the quality of the tractor, The instantaneous speed of the center of gravity of the tractor unit. The sideslip angle of the tractor's center of gravity. The yaw angle of the tractor unit. For the sprung mass of the tractor, This is the distance from the center of gravity of the tractor to the roll axis. The tractor's side tilt angle, To pull the lateral force of the front axle, For the steering angle of the front wheels of the tractor, The lateral force on the rear axle of the tractor. Force acting at the hinge point For the tractor Moment of inertia of the shaft, The product of yaw and roll inertia of the tractor's sprung mass. This is the distance from the center of gravity of the tractor to the front axle. This is the distance from the rear axle of the tractor's center of gravity. This is the distance from the center of gravity of the tractor to the articulation point. For the tractor Moment of inertia of the shaft, It is the acceleration due to gravity. For the lateral stiffness of the tractor, For the tractor roll damping, For the lateral stiffness of the hinge point, This refers to the trailer's tilt angle. This is the distance from the articulation point to the tilt axis of the tractor. Integrated dynamic model of trailer steering and differential braking: (4) (5) (6) In the formula: For trailer quality, The trailer's center of gravity sideslip angle. This refers to the yaw angle of the trailer. The instantaneous speed of the trailer's center of gravity. For the sprung mass of the trailer, The distance between the trailer's center of gravity and the trailer axle. This refers to the lateral force on the rear axle of the trailer. Hinged angle, For trailers to go around Moment of inertia of the shaft, The product of yaw and roll inertia of the trailer's sprung mass. The distance between the trailer's center of gravity and the trailer axle. This is the distance between the hinge point and the center of gravity of the trailer. For trailers to go around Moment of inertia of the shaft, For trailer roll stiffness, For trailer roll damping, This is the distance from the articulation point to the trailer's tilt axis; Kinematic constraints of tractor and trailer: (7)， Using a linear tire model, the tire slip angle does not exceed Therefore, the lateral force on each axle of the trailer is equal to the product of the lateral stiffness and the lateral slip angle. (8)。 3. The method for integrated active steering and differential braking to prevent rollover as described in claim 2, characterized in that: Step S2 employs a model prediction method to design the controller, specifically including: selecting the control variable. ; By combining the dynamic model of steering and differential braking of the tractor and trailer with kinematic constraints, its state-space equations can be obtained: (9) In the formula , (10) (11) (12) (13)， The continuous state-space model is discretized using the forward Euler method, with a sampling time of... The discrete state-space equation is: (14) in: , ; set up: , ; Combining equation (9) and the set state variables Control increment , (15) in, , .

4. The method for integrated active steering and differential braking to prevent rollover as described in claim 3, characterized in that: Step S2 predicts the future state of the semi-trailer; Set the prediction time domain as Control time domain is By combining equation (15) to predict the future state of the semi-trailer, we can obtain: (16)， Combining equations (15) and (16), the relationship between the output quantity, state quantity, and control increment in the prediction time domain can be obtained: (17) (18) in: ， ， ， ， To ensure that the vehicle state of the semi-trailer in the prediction time domain keeps up with the expected value, an objective function is set. To ensure vehicle stability while minimizing control input, an objective function is set. To ensure the equation has a solution and facilitate calculation, the relaxation factor is set to 1. The weighting coefficient is The final optimization objective function is obtained as follows: (19)， In the formula, Predict the output in the time domain. To predict the expected value of the output in the time domain, To control the vehicle's turning angle and the yaw moment increment of the tractor and semi-trailer in the time domain, The state weighting matrix is ​​a positive semi-definite matrix. It is a positive definite control weighting matrix.

Images