Predictive Control Method for Four-Wheel Steering Vehicles Based on Nonlinear Tire Model

Abstract

The present invention discloses a predictive control method for a four-wheel steering vehicle based on a nonlinear tire model. First, a nonlinear tire model and a three-degree-of-freedom nonlinear four-wheel steering dynamics model are established. Then, according to the equivalent cornering stiffness in the nonlinear tire model, the working domain of the tire cornering characteristic curve is divided, and the working domain includes a linear region, a nonlinear region, and a saturation region. Finally, three four-wheel steering model predictive control subsystems corresponding to the linear region, the nonlinear region, and the saturation region are established respectively to describe the overall nonlinear four-wheel steering control system. According to the predictive control method of the present invention, the tire nonlinear problem can be transformed into a linear problem of the control system, improving the accuracy of the control system model and ensuring the tracking accuracy and stability of the four-wheel steering system.

Description

Technical Field

[0001] The present invention relates to the field of vehicle stability control, and particularly to a predictive control method for four-wheel steering vehicles based on a non-linear tire model. Background Art

[0002] Throughout the history of the automobile development over the past century, people's pursuit of automotive safety performance has never stopped. With the rapid development of road traffic in China, the domestic automobile ownership has increased significantly, and the automobile has become the main means of transportation for every household. However, with the increase in automobile ownership, traffic accidents occur frequently, often bringing irreparable losses. Therefore, it is necessary to design and research active safety systems to enhance driving safety. In terms of braking, the research on the safety of braking systems has been relatively mature, and anti-lock braking systems and electronic stability programs for vehicles have been widely applied. Compared with braking, there is still a lack of a steering active safety system that is generally applicable to most vehicles in the aspect of steering. Although the electric power steering system has also been well applied, the electric power steering system is mainly to provide a more relaxed and convenient driving experience for drivers, and the breakthrough in terms of safety is not sufficient. Therefore, in the aspect of steering, it is still necessary to conduct in-depth research on safety issues.

[0003] When the vehicle system is in an extreme working condition, the lateral force - slip angle curve of the tire enters the non-linear region. At this time, the lateral force that the tire can actually provide is often difficult to meet the lateral force of the tire obtained by solving the vehicle control system, and the corresponding steering wheel angle at this time also cannot meet the steering requirements. If the vehicle control system is open-loop, the actual lateral force of the vehicle cannot meet the steering requirements, and the tracking accuracy is reduced. If the control system is closed-loop, due to the error between the real tire lateral force and the ideal lateral force obtained by the controller, the vehicle cannot quickly reach the desired control effect. The controller will continuously adjust the steering wheel angle in error correction to achieve the ideal tracking effect, and the continuous adjustment will also lead to the appearance of chattering in the yaw rate response curve, affecting the comfort of passengers and making it difficult to ensure the stability of the vehicle system. Therefore, when designing a vehicle system stability controller for extreme working conditions, the non-linear problem of the tire at a large slip angle must be considered. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a predictive control method for four-wheel steering vehicles based on a non-linear tire model aiming at the defects involved in the background art.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] A predictive control method for four-wheel steering vehicles based on a non-linear tire model, comprising the following steps:

[0007] Step 1), establish a non-linear tire model and a three-degree-of-freedom non-linear four-wheel steering dynamics model;

[0008] Step 2), divide the working range of the tire cornering characteristic curve according to the equivalent cornering stiffness in the non-linear tire model, and the working range includes a linear region, a non-linear region, and a saturation region;

[0009] Step 2.1), draw the tire cornering characteristic curve according to the tire model, and obtain the corresponding relationship between the cornering angle and the tire lateral force value;

[0010] Step 2.2), calculate the corresponding relationship between the cornering angle and the equivalent cornering stiffness according to the tire cornering characteristic curve, select the cornering angle corresponding to the equivalent cornering stiffness of 0.9 times the initial equivalent stiffness as the first demarcation point between the linear region and the non-linear region, and select the cornering angle corresponding to the maximum value of the lateral force value as the second demarcation point between the non-linear region and the saturation region;

[0011] Step 2.3), divide the region from zero to the first demarcation point as the linear region; divide the region from the first demarcation point to the second demarcation point as the non-linear region; the remaining part is the saturation region;

[0012] Step 3), substitute the non-linear tire models of the linear region, the non-linear region, and the saturation region into the three-degree-of-freedom non-linear four-wheel steering dynamics model respectively, establish a four-wheel steering model predictive control subsystem for the linear region, the non-linear region, and the saturation region to describe the overall non-linear four-wheel steering control system, and perform predictive control accordingly.

[0013] As a further optimization scheme of the four-wheel steering vehicle predictive control method based on the non-linear tire model of the present invention, the detailed steps of the step 1) are as follows:

[0014] Step 1.1), establish a non-linear tire model using the Dugoff model:

[0015]

[0016]

[0017]

[0018] In the formula, F y is the tire lateral force; C α is the tire cornering stiffness; α is the tire cornering angle; F z is the tire vertical load; s is the longitudinal slip ratio;

[0019] Step 1.2), establish a three-degree-of-freedom non-linear four-wheel steering dynamics model:

[0020]

[0021] In the formula, is the lateral displacement speed in the global coordinate system; is the longitudinal displacement speed in the global coordinate system; is the lateral speed in the vehicle body coordinate system; is the longitudinal speed in the vehicle body coordinate system; is the heading angle; is the yaw angular velocity; δ f is the front wheel steering angle; δ r is the rear wheel steering angle; m is the total vehicle mass; I z is the moment of inertia about the z-axis; is the longitudinal acceleration in the vehicle body coordinate system; is the lateral acceleration in the vehicle body coordinate system C sf 、C sr are the longitudinal stiffness of the front wheel and the longitudinal stiffness of the rear wheel respectively; s f 、s r are the front wheel slip ratio and the rear wheel slip ratio respectively; C αf 、C αr are the equivalent front wheel cornering stiffness and the equivalent rear wheel cornering stiffness respectively; a is the distance between the front axle and the center of mass; b is the distance between the rear axle and the center of mass.

[0022] As a further optimization scheme of the four-wheel steering vehicle predictive control method based on the non-linear tire model of the present invention, the detailed steps of step 3) are as follows:

[0023] Step 3.1), select the lateral position in the global coordinate system, the longitudinal position in the global coordinate system, the lateral speed in the vehicle body coordinate system, the longitudinal speed in the vehicle body coordinate system, the heading angle and the yaw angular velocity as state variables, and select the front wheel steering angle and the rear wheel steering angle as control variables:

[0024]

[0025] u = [δ f δ r T

[0026] In the formula, ψ is the state variable; Y is the lateral position in the global coordinate system; X is the longitudinal position in the global coordinate system; u is the control variable; linearize the three-degree-of-freedom non-linear four-wheel steering dynamics model:

[0027]

[0028]

[0029]

[0030] ​

[0031]

[0032]

[0033] In the formula, is the derivative of the state quantity at time t; ψ(t) is the state quantity at time t; u(t) is the control quantity at time t; is the heading angle at time t; is the longitudinal speed of the vehicle body coordinate system at time t; is the lateral speed of the vehicle body coordinate system at time t;

[0034] Step 3.2), discretize the linearized model:

[0035] ψ(k + 1) = A 2 ψ(k) + B 2 u(k)

[0036] y(k) = C 2 ψ(k)

[0037] In the formula, ψ(k + 1) is the state quantity at time k + 1; ψ(k) is the state quantity at time k; u(k) is the control quantity at time k; y(k) is the output quantity at time k;

[0038]

[0039]

[0040] C 2 = C 1

[0041] Step 3.3), expand the dimension of the discretized model:

[0042]

[0043]

[0044] Δu(k) = u(k) - u(k - 1)

[0045] η(k + 1|k) = ψ(k + 1|k)

[0046]

[0047] In the formula, ξ(k) is the state quantity at time k after dimension expansion; ξ(k + 1|k) is the predicted state quantity at time k + 1 at time k after dimension expansion; η(k + 1|k) is the predicted output quantity at time k + 1 at time k after dimension expansion; u(k - 1) is the control quantity at time k - 1;

[0048] Step 3.4), iterate the dimension-expanded model:

[0049] Φ(k) = Zξ(k) + ΘΔU(k)

[0050]

[0051]

[0052]

[0053]

[0054] In the formula, N c is the control time domain; N p is the prediction time domain;

[0055] Step 3.5), construct the objective function:

[0056]

[0057] In the formula, J is the objective function; R is the reference path sequence; P is the tracking matrix; Q is the control matrix; ρ is the relaxation factor matrix; ε is the relaxation factor;

[0058] Step 3.6), substitute the initial equivalent cornering stiffness and the equivalent stiffness at the two demarcation points into the model to obtain sub-models for three working domains, and select the corresponding sub-model according to the working conditions to solve the controller.

[0059] Compared with the prior art, the present invention adopts the above technical solutions and has the following technical effects:

[0060] When the vehicle system is in an extreme working condition, the tire lateral force - slip angle curve enters the non-linear region. At this time, the lateral force that the tire can actually provide often fails to meet the tire lateral force obtained by solving the vehicle control system, and the corresponding steering wheel angle at this time also cannot meet the steering requirements. Existing research often ignores the non-linear problem of the tire. The present invention takes into account the non-linear factors of the tire, divides the working domain of the tire cornering characteristic curve, designs sub-models and controllers for different working domains, and the designed non-linear multi-model predictive controller can ensure the stability of the four-wheel steering vehicle system without losing the tracking accuracy. Brief Description of the Drawings

[0061] Figure 1 is the regional division diagram of the tire cornering characteristic curve provided by the present invention;

[0062] Figure 2 is the working domain division diagram of the equivalent cornering stiffness provided by the present invention. Detailed Embodiment

[0063] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings:

[0064] The present invention can be implemented in many different forms and should not be considered limited to the embodiments described herein. On the contrary, these embodiments are provided so that this disclosure is thorough and complete, and will fully convey the scope of the present invention to those skilled in the art. In the drawings, components are enlarged for clarity.

[0065] As Figure 1 shown, the present invention discloses a predictive control method for a four-wheel steering vehicle based on a non-linear tire model, including the following steps:

[0066] Step 1), establish a non-linear tire model and a three-degree-of-freedom non-linear four-wheel steering dynamics model;

[0067] Step 1.1), establish a non-linear tire model using the Dugoff model:

[0068]

[0069]

[0070]

[0071] In the formula, F y is the lateral force of the tire; C α is the cornering stiffness of the tire; α is the slip angle of the tire; F z is the vertical load of the tire; s is the longitudinal slip ratio;

[0072] Step 1.2), establish a three-degree-of-freedom non-linear four-wheel steering dynamics model:

[0073]

[0074] In the formula, is the lateral displacement speed in the global coordinate system; is the longitudinal displacement speed in the global coordinate system; is the lateral speed in the body coordinate system; is the longitudinal speed in the body coordinate system; is the heading angle; is the yaw rate; δ f is the front wheel steering angle; δ r is the rear wheel steering angle; m is the vehicle mass; I z is the moment of inertia about the z-axis; is the longitudinal acceleration in the body coordinate system; is the lateral acceleration in the body coordinate system C sf 、C sr are the longitudinal stiffness of the front wheel and the longitudinal stiffness of the rear wheel respectively; s f, s r are the front-wheel slip ratio and the rear-wheel slip ratio respectively; C αf , C αr are the equivalent cornering stiffness of the front wheels and the equivalent cornering stiffness of the rear wheels respectively; a is the distance between the front axle and the center of mass; b is the distance between the rear axle and the center of mass;

[0075] Step 2), divide the working range of the tire cornering characteristic curve according to the equivalent cornering stiffness in the nonlinear tire model, and the working range includes a linear region, a nonlinear region, and a saturation region;

[0076] Step 2.1), draw the tire cornering characteristic curve according to the tire model to obtain the corresponding relationship between the cornering angle and the tire lateral force value;

[0077] Step 2.2), calculate the corresponding relationship between the cornering angle and the equivalent cornering stiffness according to the tire cornering characteristic curve, and select the cornering angle corresponding to the equivalent cornering stiffness of 0.9 times the initial equivalent stiffness as the first demarcation point between the linear region and the nonlinear region, and select the cornering angle corresponding to the maximum value of the lateral force value as the second demarcation point between the nonlinear region and the saturation region;

[0078] Step 2.3), divide the region from zero to the first demarcation point as the linear region; divide the region from the first demarcation point to the second demarcation point as the nonlinear region; the remaining part is the saturation region; Figure 2 is the working range division diagram of the equivalent cornering stiffness;

[0079] Step 3), substitute the nonlinear tire models of the linear region, the nonlinear region, and the saturation region into the three-degree-of-freedom nonlinear four-wheel steering dynamics model respectively, establish the four-wheel steering model predictive control subsystems of the linear region, the nonlinear region, and the saturation region to describe the overall nonlinear four-wheel steering control system, and perform predictive control accordingly;

[0080] Step 3.1), select the lateral position in the global coordinate system, the longitudinal position in the global coordinate system, the lateral speed in the vehicle body coordinate system, the longitudinal speed in the vehicle body coordinate system, the heading angle, and the yaw rate as the state variables, and select the front-wheel steering angle and the rear-wheel steering angle as the control variables:

[0081]

[0082] u = [δ f δ r T

[0083] In the formula, ψ is the state variable; Y is the lateral position in the global coordinate system; X is the longitudinal position in the global coordinate system; u is the control variable;

[0084] Linearize the three-degree-of-freedom nonlinear four-wheel steering dynamics model: ​

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091] In the formula, is the derivative of the state variable at time t; ψ(t) is the state variable at time t; u(t) is the control variable at time t; is the heading angle at time t; is the longitudinal speed of the vehicle body coordinate system at time t; is the lateral speed of the vehicle body coordinate system at time t;

[0092] Step 3.2), discretize the linearized model:

[0093] ψ(k + 1) = A 2 ψ(k) + B 2 u(k)

[0094] y(k) = C 2 ψ(k)

[0095] In the formula, ψ(k + 1) is the state variable at time k + 1; ψ(k) is the state variable at time k; u(k) is the control variable at time k; y(k) is the output variable at time k;

[0096]

[0097]

[0098] C 2 = C 1

[0099] Step 3.3), expand the dimension of the discretized model:

[0100]

[0101]

[0102] Δu(k) = u(k) - u(k - 1)

[0103] η(k + 1|k) = ψ(k + 1|k)

[0104]

[0105] Where ξ(k) is the state quantity at time k after dimension expansion; ξ(k + 1|k) is the predicted state quantity at time k + 1 after dimension expansion; η(k + 1|k) is the predicted output quantity at time k + 1 after dimension expansion; u(k - 1) is the control quantity at time k - 1;

[0106] Step 3.4), perform iteration on the expanded model:

[0107] Φ(k) = Zξ(k) + ΘΔU(k)

[0108]

[0109]

[0110]

[0111]

[0112] Where N c is the control time domain; N p is the prediction time domain;

[0113] Step 3.5), construct the objective function:

[0114]

[0115] Where J is the objective function; R is the reference path sequence; P is the tracking matrix; Q is the control matrix; ρ is the relaxation factor matrix; ε is the relaxation factor;

[0116] Step 3.6), substitute the initial equivalent cornering stiffness and the equivalent stiffness at the two demarcation points into the model to obtain sub - models for three working domains, and select the corresponding sub - model according to the working conditions to solve the controller.

[0117] The present invention provides a predictive control method for a four - wheel steering vehicle based on a non - linear tire model to solve the problem in the prior art that it is difficult to achieve stability control under extreme working conditions due to neglecting the non - linearity of the tire. The present invention takes into account the non - linear factors of the tire, divides the working domain of the tire cornering characteristic curve, designs sub - models and controllers for different working domains. The designed non - linear multi - model predictive controller can ensure the stability of the four - wheel steering vehicle system without losing the tracking accuracy.

[0118] Those skilled in the art can understand that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as the general understanding of those of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in a general dictionary should be understood to have a meaning consistent with their meaning in the context of the prior art, and will not be interpreted in an idealized or overly formal sense unless defined as such here.

[0119] The specific embodiments described above further elaborate on the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. Predictive control method for four-wheel steering vehicle based on non-linear tire model, Characterized in that, It includes the following steps: Step 1), establish a non-linear tire model and a three-degree-of-freedom non-linear four-wheel steering dynamics model; Step 1.1), establish a non-linear tire model using the Dugoff model: where F y is the lateral force of the tire; C α is the cornering stiffness of the tire; α is the slip angle of the tire; F z is the vertical load of the tire; s is the longitudinal slip ratio; Step 1.2), establish a three-degree-of-freedom non-linear four-wheel steering dynamics model: In the formula, is the lateral displacement velocity in the global coordinate system; is the longitudinal displacement velocity in the global coordinate system; is the lateral velocity in the vehicle body coordinate system; is the longitudinal velocity in the vehicle body coordinate system; is the heading angle; is the yaw angular velocity; δ f is the front wheel steering angle; δ r is the rear wheel steering angle; m is the total vehicle mass; I z is the moment of inertia about the z-axis; is the longitudinal acceleration in the vehicle body coordinate system; is the lateral acceleration in the vehicle body coordinate system C sf 、C sr are the longitudinal stiffness of the front wheel and the longitudinal stiffness of the rear wheel respectively; s f 、s r are the front wheel slip ratio and the rear wheel slip ratio respectively; C αf 、C αr are the equivalent cornering stiffness of the front wheel and the equivalent cornering stiffness of the rear wheel respectively; a is the distance between the front axle and the center of mass; b is the distance between the rear axle and the center of mass; Step 2), divide the working range of the tire cornering characteristic curve according to the equivalent cornering stiffness in the non-linear tire model, and the working range includes a linear region, a non-linear region and a saturation region; Step 2.1), draw the tire cornering characteristic curve according to the tire model, and obtain the corresponding relationship between the cornering angle and the tire lateral force value; Step 2.2), calculate the corresponding relationship between the cornering angle and the equivalent cornering stiffness according to the tire cornering characteristic curve, select the cornering angle corresponding to the equivalent cornering stiffness of 0.9 times the initial equivalent stiffness as the first demarcation point between the linear region and the non-linear region, and select the cornering angle corresponding to the lateral force value reaching the maximum as the second demarcation point between the non-linear region and the saturation region; Step 2.3), divide the region from zero to the first demarcation point as the linear region; divide the region from the first demarcation point to the second demarcation point as the non-linear region; the remaining part is the saturation region; Step 3), substitute the non-linear tire models of the linear region, the non-linear region and the saturation region into the three-degree-of-freedom non-linear four-wheel steering dynamics model respectively, establish four-wheel steering model predictive control subsystems for the linear region, the non-linear region and the saturation region to describe the overall non-linear four-wheel steering control system, and perform predictive control accordingly; Step 3.1), select the lateral position in the global coordinate system, the longitudinal position in the global coordinate system, the lateral velocity in the body coordinate system, the longitudinal velocity in the body coordinate system, the heading angle and the yaw rate as state variables, and select the front wheel steering angle and the rear wheel steering angle as control variables: u = [δ f δ r T ​ In the formula, ψ is the state variable; Y is the lateral position in the global coordinate system; X is the longitudinal position in the global coordinate system; u is the control variable; Perform linearization processing on the three-degree-of-freedom non-linear four-wheel steering dynamics model: In the formula, is the derivative of the state variable at time t; ψ(t) is the state variable at time t; u(t) is the control variable at time t; is the heading angle at time t; is the longitudinal velocity of the vehicle body coordinate system at time t; is the lateral velocity of the vehicle body coordinate system at time t; Step 3.2), perform discretization processing on the linearized model: ψ(k + 1) = A 2 ψ(k) + B 2 u(k) y(k) = C 2 ψ(k) In the formula, ψ(k + 1) is the state variable at time k + 1; ψ(k) is the state variable at time k; u(k) is the control variable at time k; y(k) is the output variable at time k; C 2 = C 1 Step 3.3), expand the dimension of the discretized model: Δu(k) = u(k) - u(k - 1) In the formula, ξ(k) is the state variable at time k after dimension expansion; ξ(k + 1|k) is the predicted state variable at time k + 1 after dimension expansion; η(k + 1|k) is the predicted output variable at time k + 1 after dimension expansion; u(k - 1) is the control variable at time k - 1; Step 3.4), perform iteration on the model after dimension expansion: Φ(k) = Zξ(k) + ΘΔU(k) where, N c is the control time domain; N p is the prediction time domain; Step 3.5), construct the objective function: In the formula, J is the objective function; R is the reference path sequence; P is the tracking matrix; Q is the control matrix; ρ is the relaxation factor matrix; ε is the relaxation factor; Step 3.6), substitute the initial equivalent cornering stiffness and the equivalent stiffnesses at the two demarcation points into the model to obtain sub-models for the three working domains, and select the corresponding sub-model according to the working conditions to solve the controller.

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