A stability analysis method for vehicle lateral motion control system considering coupling of steering system

Abstract

The application discloses a kind of vehicle lateral motion control system stability analysis method considering steering system coupling, this method is by building closed-loop analysis model including steering system coupling, combined with multidimensional stability analysis method, effectively solve the problems existing in prior art, such as insufficient analysis accuracy, steering system coupling effect is difficult to observe, mechanism reveals not in-depth etc.;The application method is by introducing the steering system dynamics model including equivalent moment of inertia, damping coefficient and tire return torque characteristics, constructs single rail-steering system coupling open-loop model, solves the problem that traditional single rail model ignores the structural characteristics of steering system, cannot reflect the real dynamics behavior of vehicle, makes the stability analysis model more close to actual vehicle, significantly improves the accuracy of analysis result.

Description

Technical Field

[0001] This invention belongs to the field of vehicle engineering technology, and in particular relates to a stability analysis method for a vehicle lateral motion control system that considers the coupling of the steering system. Background Technology

[0002] Active safety technology is the core of improving vehicle driving safety, focusing on preventing traffic accidents. Vehicle yaw stability, as a key indicator of vehicle handling stability, directly determines the vehicle's safety performance under extreme conditions such as high-speed cornering and emergency obstacle avoidance. The vehicle's yaw response is not only affected by the vehicle's own dynamic characteristics but also closely related to the dynamic behavior of the steering system. In-depth exploration of the coupling mechanism between the two has significant theoretical and engineering value for optimizing vehicle steering system design and improving the performance of stability control strategies.

[0003] Most existing vehicle stability analysis methods are based on the traditional two-degree-of-freedom monorail model. This model has a simple structure and clear physical meaning, and can describe the basic dynamic characteristics of a vehicle's lateral velocity and yaw rate, thus it is widely used in related research. However, the traditional monorail model usually treats the front wheel steering angle as an ideal input. In actual vehicles, the driver's steering input needs to be transmitted to the steering wheels through the steering system. The steering system itself has dynamic characteristics, making the response process of the front wheel steering angle have obvious dynamic features. Because the influence of steering system dynamics is not considered, existing models tend to underestimate or ignore the role of the steering system in regulating the vehicle's yaw motion under conditions such as high-speed steering, emergency obstacle avoidance, and active stability control. This includes key structural characteristics such as the equivalent moment of inertia, damping coefficient, and tire self-centering torque generated by the mechanical trail of the steering system. As a result, the analysis results, such as the distribution of system eigenvalues, the location of stability boundaries, and the range of stability domains, deviate from those of actual vehicles. Meanwhile, most existing studies focus on control algorithm design and control performance optimization, lacking systematic analysis of the coupling relationship between steering system dynamics and vehicle lateral motion. In particular, there is a lack of research on the influence of the steering system on the stability of the vehicle lateral motion control system, making it difficult to reveal the mechanism of the steering system dynamics on closed-loop stability. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes a stability analysis method for a vehicle lateral motion control system that considers the coupling of the steering system.

[0005] The technical solution of the present invention is as follows:

[0006] A stability analysis method for a vehicle lateral motion control system considering steering system coupling includes:

[0007] Obtain a two-degree-of-freedom vehicle monorail open-loop model and a monorail-steering system coupled open-loop model that includes the dynamic characteristics of the steering system;

[0008] For the two-degree-of-freedom vehicle monorail open-loop model and the monorail-steering system coupled open-loop model, a direct yaw moment (PD) control strategy with lateral velocity and yaw rate as feedback variables is introduced. This control strategy actively changes the modal structure of the vehicle lateral motion control system through state feedback to reduce the system stability margin and increase the sensitivity of the vehicle lateral motion control system to parameter changes. Thus, a closed-loop monorail model without a steering system and a closed-loop coupled model with a steering system are constructed.

[0009] A full-domain parameter scan is performed on the lateral velocity feedback gain and yaw rate feedback gain of the PD control strategy. The maximum real part of the system eigenvalue corresponding to each parameter point is calculated. The stability domain distribution diagrams of the closed-loop monorail model and the closed-loop coupled model are drawn with the maximum real part of the eigenvalue equal to zero as the stability boundary.

[0010] Based on the stability domain distribution map, typical parameter points are selected for time-domain response simulation. Sensitivity scanning is performed on key structural parameters of the steering system. The stability domain range and maximum real part of the eigenvalues ​​of the closed-loop single-track model and the closed-loop coupled model are compared to reveal the influence mechanism of the steering system dynamics on the vehicle yaw stability.

[0011] Furthermore, the expression for the control law of the direct yaw moment PD control strategy, with lateral velocity and yaw angular velocity as feedback variables, is as follows:

[0012] ;

[0013] in, , ; Normalized lateral velocity feedback gain; Normalized yaw rate feedback gain;

[0014] In the formula, Let t be the additional yaw moment acting on the vehicle at time t, where t is a time variable; This is the lateral velocity proportionality coefficient. The actual lateral speed of the vehicle. This is a reference value for lateral velocity. The differential coefficients of the yaw rate are... This refers to the vehicle's actual yaw rate. This is the reference value for yaw rate. This is the moment of inertia of the vehicle as it rotates about its longitudinal axis at its center of gravity.

[0015] Furthermore, the expression for the closed-loop monorail model without a steering system is:

[0016] ;

[0017] In the formula, and These are the longitudinal and lateral velocities, respectively. The yaw rate is angular velocity. , The lateral forces of the front and rear tires, For vehicle quality, This is the distance from the car's center of gravity to the front axle. This is the distance from the car's center of gravity to the rear axle. Let $\frac{ ... This refers to the front wheel steering angle. This refers to the front wheel lateral stiffness. For rear wheel lateral stiffness, This is the lateral velocity proportionality coefficient. The actual lateral speed of the vehicle. This is a reference value for lateral velocity. The differential coefficients of the yaw rate are... This refers to the vehicle's actual yaw rate. This is a reference value for the yaw rate.

[0018] Furthermore, the expression for the closed-loop coupling model including the steering system is:

[0019] ;

[0020] In the formula, and These are the longitudinal and lateral velocities, respectively. The yaw rate is angular velocity. , The lateral forces of the front and rear tires, For vehicle quality, This is the distance from the car's center of gravity to the front axle. The distance from the car's center of gravity to the rear axle. It is the moment of inertia of the vehicle as it rotates about its longitudinal axis at its center of gravity. This refers to the front wheel steering angle. This refers to the front wheel lateral stiffness. For rear wheel lateral stiffness, The equivalent rotational inertia of the steering system; The damping coefficient of the steering system; This refers to the input torque of the steering wheel; This is the steering gear ratio. For mechanical trailing distance, This is the lateral velocity proportionality coefficient. The actual lateral speed of the vehicle. This is a reference value for lateral velocity. The differential coefficients of the yaw rate are... This refers to the vehicle's actual yaw rate. This is a reference value for the yaw rate.

[0021] Furthermore, the method for drawing the stability domain distribution diagrams of the closed-loop single-track model and the closed-loop coupled model includes:

[0022] Lateral velocity feedback gain Feedback gain with yaw rate On the constructed two-dimensional parameter plane, the eigenvalues ​​of the system state matrix corresponding to each parameter combination are solved, and the maximum real part of the system eigenvalues ​​is calculated. The maximum real part of the system eigenvalues ​​is used as the stability criterion. When the maximum real part of the eigenvalues ​​is less than zero, the corresponding parameter point is determined to be a stable region. When the maximum real part of the eigenvalues ​​is greater than zero, the corresponding parameter point is determined to be an unstable region. The parameter points with the maximum real part of the eigenvalues ​​equal to zero are connected to form the system stability boundary, thereby obtaining the stability domain distribution map of the closed-loop single-track model and the closed-loop coupled model.

[0023] Furthermore, the specific method for selecting typical parameter points based on the stability domain distribution map to perform time-domain response simulation includes:

[0024] Three sets of parameter points were selected in the stable region distribution map, located inside the stable region, on the stable boundary, and in the unstable region, respectively. The same initial conditions were applied to the closed-loop monorail model and the closed-loop coupled model, respectively. The time-domain response curves of the lateral velocity and yaw rate were obtained by simulation, and the dynamic response characteristics of the closed-loop monorail model and the closed-loop coupled model were compared and analyzed.

[0025] Furthermore, the specific method for performing sensitivity scanning on the key structural parameters of the steering system includes:

[0026] Select the equivalent moment of inertia of the steering system Damping coefficient and mechanical trail As key parameters, a parameter combination domain is constructed, the maximum real part of the system eigenvalue corresponding to each parameter combination is calculated, a stability distribution cloud map of the parameter combination is plotted, and the influence of key structural parameters of the shifting system on the system stability is quantitatively analyzed.

[0027] Furthermore, the specific methods for comparing the stability domain range and the maximum real part of the eigenvalues ​​of the closed-loop single-track model and the closed-loop coupled model include:

[0028] Under the same vehicle speed and control gain, the stability domain area and the maximum real part of the eigenvalues ​​of the closed-loop monorail model and the closed-loop coupled model are calculated respectively. The effect of steering system dynamics on improving vehicle yaw stability is quantitatively evaluated by numerical comparison.

[0029] Furthermore, the single-rail-steering system coupled open-loop model that incorporates the dynamic characteristics of the steering system considers the equivalent moment of inertia, damping coefficient, and tire self-centering torque characteristics generated by the mechanical trail of the steering system.

[0030] Furthermore, the steering system dynamics characteristics included in the single-rail-steering system coupled open-loop model include at least the tire return torque generated by the mechanical trail.

[0031] The expression for the coupled open-loop model of the monorail-steering system is as follows:

[0032] ;

[0033] In the formula, and These are the longitudinal and lateral velocities, respectively. The yaw rate is angular velocity. , The lateral forces of the front and rear tires, For vehicle quality, This is the distance from the car's center of gravity to the front axle. The distance from the car's center of gravity to the rear axle. It is the moment of inertia of the vehicle as it rotates about its longitudinal axis at its center of gravity. This refers to the front wheel steering angle. This refers to the front wheel lateral stiffness. For rear wheel lateral stiffness, The equivalent rotational inertia of the steering system; The damping coefficient of the steering system; This refers to the input torque of the steering wheel; This is the steering gear ratio. For mechanical trailing distance;

[0034] The expression for the two-degree-of-freedom vehicle monorail open-loop model is as follows:

[0035] ;

[0036] In the formula, and These are the longitudinal and lateral velocities, respectively. The yaw rate is angular velocity. , The lateral forces of the front and rear tires, For vehicle quality, This is the distance from the car's center of gravity to the front axle. The distance from the car's center of gravity to the rear axle. It is the moment of inertia of the vehicle as it rotates about its longitudinal axis at its center of gravity. This refers to the front wheel steering angle. This refers to the front wheel lateral stiffness. This refers to the rear wheel lateral stiffness.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] This invention proposes a stability analysis method for a vehicle lateral motion control system considering steering system coupling. This method, by constructing a closed-loop analysis model incorporating steering system coupling and combining it with multi-dimensional stability analysis methods, effectively solves the problems of insufficient analysis accuracy, difficulty in observing steering system coupling effects, and insufficient understanding of the underlying mechanisms in existing technologies. Specifically:

[0039] The method of this invention introduces a steering system dynamic model that includes equivalent moment of inertia, damping coefficient, and tire self-centering torque characteristics, and constructs a coupled open-loop model of the single-rail steering system. This solves the problem that the traditional single-rail model ignores the structural characteristics of the steering system and cannot reflect the real dynamic behavior of the vehicle, making the stability analysis model closer to the actual vehicle and significantly improving the accuracy of the analysis results.

[0040] The method of this invention designs a direct yaw moment (PD) control strategy specifically for stability analysis. It generates an additional yaw moment by using lateral velocity and yaw angular velocity as feedback variables, and actively changes the system modal structure to appropriately reduce the system stability margin. This solves the problems of excessive stability margin and difficulty in showing the effects of parameter changes in traditional open-loop models. It significantly improves the system's sensitivity to changes in control parameters and structural parameters, and makes the coupling effect of steering system dynamics clearly observable.

[0041] This invention constructs a closed-loop monorail model without a steering system and a closed-loop coupled model including a steering system, forming a comparable analysis system. This effectively separates the influence of vehicle dynamics and steering system dynamics on stability, providing a reference for quantitatively evaluating the coupling effect of the steering system. The method employs a multi-dimensional analysis approach combining full-domain stability domain scanning, time-domain response simulation at typical parameter points, and steering system parameter sensitivity scanning to comprehensively evaluate system stability, improving the systematicity and reliability of stability analysis. Furthermore, by quantitatively comparing the two closed-loop models from two core dimensions—stability domain range and the maximum real part of the system's eigenvalues—this invention addresses the problem of traditional analysis methods relying primarily on qualitative descriptions and lacking quantitative evidence. It clarifies that the steering system can significantly expand the stability domain of the closed-loop system and reduce the maximum real part of the system's eigenvalues, thereby improving the vehicle's stability margin under high-speed conditions. Attached Figure Description

[0042] Figure 1 This is the root locus diagram for the open-loop system.

[0043] Figure 2 This is a control block diagram for a closed-loop monorail-steering coupling system.

[0044] Figure 3 Stability domain diagrams of a closed-loop monorail system at different vehicle speeds;

[0045] Figure 4 Stability domain diagrams of a closed-loop monorail-steering coupling system at different vehicle speeds;

[0046] Figure 5 The time-domain response of a closed-loop monorail system;

[0047] Figure 6 The time-domain response of the closed-loop monorail-steering coupled system;

[0048] Figure 7 Stability domain distribution diagram of steering system parameter combination;

[0049] Figure 8 A comparison of the stability regions of the two closed-loop models;

[0050] Figure 9 The maximum real part and time-domain response of the two closed-loop models are compared. Detailed Implementation

[0051] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0052] Example 1:

[0053] The present invention provides a stability analysis method for a vehicle lateral motion control system considering steering system coupling. The vehicle lateral motion control system and the steering system are dynamically physically coupled through tire return force rectangles. The method includes:

[0054] Obtain a two-degree-of-freedom vehicle monorail open-loop model and a monorail-steering system coupled open-loop model that includes the dynamic characteristics of the steering system;

[0055] For the two-degree-of-freedom vehicle monorail open-loop model and the monorail-steering system coupled open-loop model, a direct yaw moment (PD) control strategy with lateral velocity and yaw rate as feedback variables is introduced. This control strategy actively changes the modal structure of the vehicle lateral motion control system through state feedback to reduce the system stability margin and increase the sensitivity of the vehicle lateral motion control system to parameter changes. Thus, a closed-loop monorail model without a steering system and a closed-loop coupled model with a steering system are constructed.

[0056] A full-domain parameter scan is performed on the lateral velocity feedback gain and yaw rate feedback gain of the PD control strategy. The maximum real part of the system eigenvalue corresponding to each parameter point is calculated. The stability domain distribution diagrams of the closed-loop monorail model and the closed-loop coupled model are drawn with the maximum real part of the eigenvalue equal to zero as the stability boundary.

[0057] Based on the stability domain distribution map, typical parameter points are selected for time-domain response simulation. Sensitivity scanning is performed on key structural parameters of the steering system. The stability domain range and maximum real part of the eigenvalues ​​of the closed-loop single-track model and the closed-loop coupled model are compared to reveal the influence mechanism of the steering system dynamics on the vehicle yaw stability.

[0058] In the single-rail-steering system coupled open-loop model, the steering wheel input torque needs to overcome the equivalent rotational inertia and damping coefficient of the steering system. Simultaneously, the tire return torque is fed back to the steering system via mechanical trail, forming a closed-loop dynamic coupling between the vehicle and steering system. It is twice the moment of inertia of a single wheel about its kingpin; under small steering angle conditions, the tire self-centering torque is solely due to the mechanical trailing distance. produce.

[0059] Furthermore, the PD control strategy adopted in this embodiment is different from the conventional PD control used for vehicle driving performance optimization. Its design purpose is not to improve vehicle handling or comfort, but to actively adjust the system modal distribution so that the coupling effect of steering system dynamics can be clearly observed.

[0060] Furthermore, the expression for the control law of the direct yaw moment (PD) control strategy, with lateral velocity and yaw angular velocity as feedback variables, is as follows:

[0061] ;

[0062] in, , ;

[0063] In the formula, Let t be the additional yaw moment acting on the vehicle at time t, where t is a time variable; This is the lateral velocity proportionality coefficient. The actual lateral speed of the vehicle. This is a reference value for lateral velocity. The differential coefficients of the yaw rate are... This refers to the vehicle's actual yaw rate. This is the reference value for yaw rate. It is the moment of inertia of a vehicle as it rotates around its longitudinal axis at its center of gravity.

[0064] In this control law, the lateral velocity feedback term is used to suppress vehicle yaw motion by weakening the increasing trend of lateral velocity and limiting the vehicle's lateral deviation; the yaw rate feedback term is used to dampen vehicle motion by adding a counter-yaw moment to suppress yaw oscillations and instability tendencies. This control strategy does not require the introduction of an additional reference trajectory or ideal vehicle model; feedback control can be achieved solely based on the vehicle's real-time state variables.

[0065] Preferably, the lateral velocity reference value Reference value of yaw rate Take the target values ​​corresponding to the vehicle's stable equilibrium state respectively; during the stability analysis process... and All are set to zero.

[0066] Furthermore, the expression for the closed-loop monorail model without a steering system is:

[0067] ;

[0068] In the formula, and These are the longitudinal and lateral velocities, respectively. The yaw rate is angular velocity. , The lateral forces of the front and rear tires, For vehicle quality, This is the distance from the car's center of gravity to the front axle. The distance from the car's center of gravity to the rear axle. It is the moment of inertia of a vehicle as it rotates around its longitudinal axis at its center of gravity.

[0069] The vehicle model is linearized under small steering angle conditions, and the linearized tire force relationship can be expressed as:

[0070] ;

[0071] This linearized tire model allows us to study the steady-state steering of a vehicle, and further investigate small steering angles. Stability under [condition / condition]. Derivation and simplification yield:

[0072] ;

[0073] ;

[0074] In the formula, This refers to the front wheel steering angle; This refers to the front wheel slip angle; This refers to the rear wheel slip angle; This refers to the front wheel lateral stiffness. This refers to the rear wheel lateral stiffness.

[0075] Then there is ;

[0076] In the formula, and These are the longitudinal and lateral velocities, respectively. The yaw rate is angular velocity. , The lateral forces of the front and rear tires, For vehicle quality, This is the distance from the car's center of gravity to the front axle. The distance from the car's center of gravity to the rear axle. It is the moment of inertia of the vehicle as it rotates about its longitudinal axis at its center of gravity. This refers to the front wheel steering angle. This refers to the front wheel lateral stiffness. For rear wheel lateral stiffness, This is the lateral velocity proportionality coefficient. The actual lateral speed of the vehicle. This is a reference value for lateral velocity. The differential coefficients of the yaw rate are... This refers to the vehicle's actual yaw rate. This is a reference value for the yaw rate.

[0077] The state-space equations for a closed-loop single-track model without a steering system are as follows:

[0078] ;

[0079] ;

[0080] ;in, , . Normalized lateral velocity feedback gain; This is the normalized yaw rate feedback gain.

[0081]

[0082] The closed-loop monorail model without a steering system has 2 degrees of freedom, and the selected state variables are shown in the equation:

[0083] ;

[0084] The state variables of the state-space equations for a closed-loop monorail model without a steering system include lateral velocity. yaw rate , Steering angle ; State variables The first derivative, including lateral acceleration yaw acceleration .

[0085] Furthermore, the expression for the closed-loop coupling model including the steering system is:

[0086] ;

[0087] In the formula, and These are the longitudinal and lateral velocities, respectively. The yaw rate is angular velocity. , The lateral forces of the front and rear tires, For vehicle quality, This is the distance from the car's center of gravity to the front axle. The distance from the car's center of gravity to the rear axle. It is the moment of inertia of the vehicle as it rotates about its longitudinal axis at its center of gravity. This refers to the front wheel steering angle. This refers to the front wheel lateral stiffness. For rear wheel lateral stiffness, The equivalent rotational inertia of the steering system; The damping coefficient of the steering system; This refers to the input torque of the steering wheel; This is the steering gear ratio. For mechanical trailing distance, This is the lateral velocity proportionality coefficient. The actual lateral speed of the vehicle. This is a reference value for lateral velocity. The differential coefficients of the yaw rate are... This refers to the vehicle's actual yaw rate. This is a reference value for the yaw rate.

[0088] The state-space equations of the closed-loop coupled model including the steering system are as follows:

[0089] ;

[0090] ;

[0091] ;in, , . Normalized lateral velocity feedback gain; This is the normalized yaw rate feedback gain.

[0092]

[0093] The closed-loop coupled model including the steering system has 3 degrees of freedom, and the state variables are selected as follows:

[0094]

[0095] The state variables in the state-space equations of the closed-loop coupled model containing the steering system include lateral velocity. yaw rate Steering angle angular velocity of steering , State variables The first derivative, including lateral acceleration yaw acceleration angular velocity of steering angular acceleration , Input torque of the steering wheel .

[0096] Furthermore, the methods for plotting the stability domain distribution diagrams of the closed-loop single-track model and the closed-loop coupled model include:

[0097] Lateral velocity feedback gain Feedback gain with yaw rate On the constructed two-dimensional parameter plane, the eigenvalues ​​of the system state matrix corresponding to each parameter combination are solved, and the maximum real part of the system eigenvalues ​​is calculated. The maximum real part of the system eigenvalues ​​is used as the stability criterion. When the maximum real part of the eigenvalues ​​is less than zero, the corresponding parameter point is determined to be a stable region. When the maximum real part of the eigenvalues ​​is greater than zero, the corresponding parameter point is determined to be an unstable region. The parameter points with the maximum real part of the eigenvalues ​​equal to zero are connected to form the system stability boundary, thereby obtaining the stability domain distribution map of the closed-loop single-track model and the closed-loop coupled model.

[0098] Furthermore, specific methods for selecting typical parameter points based on the stability domain distribution map to perform time-domain response simulation include:

[0099] Three sets of parameter points were selected in the stable region distribution map, located inside the stable region, on the stable boundary, and in the unstable region, respectively. The same initial conditions were applied to the closed-loop monorail model and the closed-loop coupled model, respectively. The time-domain response curves of the lateral velocity and yaw rate were obtained by simulation, and the dynamic response characteristics of the closed-loop monorail model and the closed-loop coupled model were compared and analyzed.

[0100] Furthermore, specific methods for sensitivity scanning of key structural parameters of the steering system include:

[0101] Select the equivalent moment of inertia of the steering system Damping coefficient and mechanical trail As key parameters, a parameter combination domain is constructed, the maximum real part of the system eigenvalue corresponding to each parameter combination is calculated, a stability distribution cloud map of the parameter combination is plotted, and the influence of key structural parameters of the shifting system on the system stability is quantitatively analyzed.

[0102] Furthermore, specific methods for comparing the stability domain range and the maximum real part of the eigenvalues ​​of the closed-loop single-track model and the closed-loop coupled model include:

[0103] Under the same vehicle speed and control gain, the stability domain area and the maximum real part of the eigenvalues ​​of the closed-loop monorail model and the closed-loop coupled model are calculated respectively. The effect of the steering system dynamics on the improvement of vehicle yaw stability is quantitatively evaluated by numerical comparison.

[0104] Furthermore, the single-rail-steering system coupled open-loop model, which incorporates the dynamic characteristics of the steering system, considers the equivalent moment of inertia, damping coefficient, and tire self-centering torque characteristics generated by the mechanical trailing distance of the steering system.

[0105] Furthermore, the steering system dynamics included in the single-rail-steering system coupled open-loop model include at least the tire return torque generated by the mechanical trail.

[0106] The expression for the coupled open-loop model of the monorail-steering system is as follows:

[0107] ;

[0108] In the formula, and These are the longitudinal and lateral velocities, respectively. The yaw rate is angular velocity. , The lateral forces of the front and rear tires, For vehicle quality, This is the distance from the car's center of gravity to the front axle. The distance from the car's center of gravity to the rear axle. It is the moment of inertia of the vehicle as it rotates about its longitudinal axis at its center of gravity. This refers to the front wheel steering angle. This refers to the front wheel lateral stiffness. For rear wheel lateral stiffness, The equivalent rotational inertia of the steering system; The damping coefficient of the steering system; This refers to the input torque of the steering wheel; This is the steering gear ratio. For mechanical trailing distance.

[0109] The expression for the two-degree-of-freedom vehicle monorail open-loop model is as follows:

[0110] ;

[0111] In the formula, and These are the longitudinal and lateral velocities, respectively. The yaw rate is angular velocity. , The lateral forces of the front and rear tires, For vehicle quality, This is the distance from the car's center of gravity to the front axle. The distance from the car's center of gravity to the rear axle. It is the moment of inertia of the vehicle as it rotates about its longitudinal axis at its center of gravity. This refers to the front wheel steering angle. This refers to the front wheel lateral stiffness. This refers to the rear wheel lateral stiffness.

[0112] The following example verifies the method of the present invention. In this example, the closed-loop monorail model without a steering system is denoted as Model 2, and the closed-loop coupled model including a steering system is denoted as Model 3. All dynamic models in this example are constructed based on the assumptions of small front wheel steering angle and small tire slip angle, and a linear tire model is used to describe the relationship between slip force and slip angle. The control structure of the closed-loop coupled model corresponds to... Figure 2 This demonstrates the connection between the direct yaw moment PD controller and the vehicle-steering system coupling model. Figure 2 The Plant Model in this context is the reference model, which is the coupled model of the closed-loop monorail-steering system. The actual lateral speed of the vehicle. This is a reference value for lateral velocity. This refers to the vehicle's actual yaw rate. This is a reference value for the yaw rate.

[0113] Furthermore, after obtaining the two-degree-of-freedom vehicle single-track open-loop model and the single-track-steering system coupled open-loop model including the dynamic characteristics of the steering system, the open-loop stability verification of the two open-loop models is also included: keeping the basic vehicle parameters constant, continuously changing the vehicle speed, using Matlab to calculate the eigenvalues ​​of the system at each vehicle speed, and plotting the trajectory of the eigenvalues ​​in the complex plane (root locus plot, corresponding to...) Figure 1 The verification results show that both the traditional open-loop monorail model and the coupled model have large stability margins, the system characteristic roots are far from the imaginary axis, and the impact of changes in vehicle structural parameters on stability is difficult to manifest, which is consistent with the problems existing in the prior art.

[0114] This example plots the stability domain distribution diagrams of Model 2 and Model 3 at six typical vehicle speeds: 90km / h, 108km / h, 126km / h, 144km / h, 162km / h, and 180km / h (e.g., Figure 3 , 4 The analysis results show that as the vehicle speed increases, the stability regions of both closed-loop models gradually shrink, and at the same vehicle speed, the stability region of model 3 is larger than that of model 2.

[0115] Specifically, for Model 2, parameter points A(1,5.8) (inside the stable region), B(1,2.8) (stable boundary), and C(1,0.8) (inside the unstable region) are selected, as follows: Figure 5 As shown; for Model 3, parameter points A(1.3, 2.5) (inside the stable region), B(1.9, 2.5) (stable boundary), and C(2.2, 2.5) (inside the unstable region) are selected, as follows: Figure 6 All simulations used the same initial perturbation conditions: initial lateral velocity v(0) = -0.1 m / s, initial yaw rate r(0) = 0 rad / s, and simulation duration was 10 s.

[0116] The time-domain response results show that the parameter point responses within the stable region converge rapidly, the parameter point responses on the stable boundary converge critically, and the parameter point responses within the unstable region diverge, which is completely consistent with the results of the stability domain analysis.

[0117] Specifically, this example pairs the three parameters to form a two-dimensional parameter plane. - flat, - flat, - Construct a parameter combination domain (plane). Plot the resulting parameter combination stability distribution cloud map (e.g., plane). Figure 7 In the diagram, the color intensity corresponds to the magnitude of the maximum real part of the eigenvalue. The darker the color, the smaller the maximum real part of the eigenvalue, and the higher the system stability.

[0118] Sensitivity analysis results show that:

[0119] The system is most sensitive to stability. A larger mechanical trail enhances the recovery of yaw disturbances by the self-aligning torque, maintaining a larger negative real part of the system's dominant eigenvalue, thus exhibiting stronger stability. Conversely, when the mechanical trail decreases, the steering system's ability to recover from vehicle state disturbances weakens, making the system more prone to crossing stability boundaries. Simultaneously, the moment of inertia... With steering damping Proper matching also plays an important role in maintaining system stability.

[0120] Specifically, under the same vehicle speed and control gain conditions, the area of ​​the stable region and the maximum real part of the eigenvalues ​​of Model 2 and Model 3 are calculated respectively (corresponding to the specification). Figure 8 , Figure 9Quantitative comparison results show that, compared with Model 2, Model 3, which incorporates a steering system, has a larger system stability domain area (an average increase of about 30%), and the maximum real part of the system characteristic roots shows a decreasing trend within the overall parameter range (a decrease of about 20%), resulting in a significant improvement in the vehicle's yaw stability margin.

[0121] This embodiment achieves a visual representation of the system's stability boundary by combining root locus and stability domain analysis, significantly improving the efficiency of vehicle stability assessment. Furthermore, the stability analysis results are cross-validated through time-domain response simulation and parameter sensitivity analysis, enhancing the reliability and engineering application value of the analysis method.

[0122] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A stability analysis method for a vehicle lateral motion control system considering steering system coupling, characterized in that, include: Obtain a two-degree-of-freedom vehicle monorail open-loop model and a monorail-steering system coupled open-loop model that includes the dynamic characteristics of the steering system; For the two-degree-of-freedom vehicle monorail open-loop model and the monorail-steering system coupled open-loop model, respectively, a direct yaw moment PD control strategy with lateral velocity and yaw rate as feedback variables is introduced. This control strategy actively changes the modal structure of the vehicle lateral motion control system through state feedback to reduce the system stability margin and increase the sensitivity of the vehicle lateral motion control system to parameter changes. Thus, a closed-loop monorail model without a steering system and a closed-loop coupled model with a steering system are constructed. A full-domain parameter scan is performed on the lateral velocity feedback gain and yaw rate feedback gain of the PD control strategy. The maximum real part of the system eigenvalue corresponding to each parameter point is calculated. The stability domain distribution diagrams of the closed-loop monorail model and the closed-loop coupled model are drawn with the maximum real part of the eigenvalue equal to zero as the stability boundary. Based on the stability domain distribution map, typical parameter points are selected for time-domain response simulation. Sensitivity scanning is performed on key structural parameters of the steering system. The stability domain range and maximum real part of the eigenvalues ​​of the closed-loop single-track model and the closed-loop coupled model are compared to reveal the influence mechanism of the steering system dynamics on the vehicle yaw stability.

2. The stability analysis method for a vehicle lateral motion control system considering steering system coupling according to claim 1, characterized in that, The expression for the control law of the direct yaw moment PD control strategy, which uses lateral velocity and yaw angular velocity as feedback variables, is as follows: ； in, , ; Normalized lateral velocity feedback gain; Normalized yaw rate feedback gain; In the formula, Let t be the additional yaw moment acting on the vehicle at time t, where t is a time variable; This is the lateral velocity proportionality coefficient. The actual lateral speed of the vehicle. This is a reference value for lateral velocity. The differential coefficients of the yaw rate are... This refers to the vehicle's actual yaw rate. This is the reference value for yaw rate. This is the moment of inertia of the vehicle as it rotates about its longitudinal axis at its center of gravity.

3. The stability analysis method for a vehicle lateral motion control system considering steering system coupling according to claim 1, characterized in that, The expression for the closed-loop monorail model without a steering system is: ； In the formula, and These are the longitudinal and lateral velocities, respectively. The yaw rate is angular velocity. , The lateral forces of the front and rear tires, For vehicle quality, This is the distance from the car's center of gravity to the front axle. This is the distance from the car's center of gravity to the rear axle. Let this be the moment of inertia of the vehicle as it rotates about its longitudinal axis at its center of gravity. This refers to the front wheel steering angle. This refers to the front wheel lateral stiffness. For rear wheel lateral stiffness, This is the lateral velocity proportionality coefficient. The actual lateral speed of the vehicle. This is a reference value for lateral velocity. The differential coefficients of the yaw rate are... This refers to the vehicle's actual yaw rate. This is a reference value for the yaw rate.

4. The stability analysis method for a vehicle lateral motion control system considering steering system coupling according to claim 1, characterized in that, The expression for the closed-loop coupling model including the steering system is: ； In the formula, and These are the longitudinal and lateral velocities, respectively. The yaw rate is angular velocity. , The lateral forces of the front and rear tires, For vehicle quality, This is the distance from the car's center of gravity to the front axle. The distance from the car's center of gravity to the rear axle. It is the moment of inertia of the vehicle as it rotates about its longitudinal axis at its center of gravity. This refers to the front wheel steering angle. This refers to the front wheel lateral stiffness. For rear wheel lateral stiffness, The equivalent rotational inertia of the steering system; The damping coefficient of the steering system; This refers to the input torque of the steering wheel; This is the steering gear ratio. For mechanical trailing distance, This is the lateral velocity proportionality coefficient. The actual lateral speed of the vehicle. This is a reference value for lateral velocity. The differential coefficients of the yaw rate are... This refers to the vehicle's actual yaw rate. This is a reference value for the yaw rate.

5. The stability analysis method for a vehicle lateral motion control system considering steering system coupling according to claim 1, characterized in that, The methods for plotting the stability domain distribution diagrams of the closed-loop monorail model and the closed-loop coupled model include: Lateral velocity feedback gain Feedback gain with yaw rate On the constructed two-dimensional parameter plane, the eigenvalues ​​of the system state matrix corresponding to each parameter combination are solved, and the maximum real part of the system eigenvalues ​​is calculated. The maximum real part of the system eigenvalues ​​is used as the stability criterion. When the maximum real part of the eigenvalues ​​is less than zero, the corresponding parameter point is determined to be a stable region. When the maximum real part of the eigenvalues ​​is greater than zero, the corresponding parameter point is determined to be an unstable region. The parameter points with the maximum real part of the eigenvalues ​​equal to zero are connected to form the system stability boundary, thereby obtaining the stability domain distribution map of the closed-loop single-track model and the closed-loop coupled model.

6. The stability analysis method for a vehicle lateral motion control system considering steering system coupling according to claim 1, characterized in that, The specific method for selecting typical parameter points based on the stability domain distribution map to perform time-domain response simulation includes: Three sets of parameter points were selected in the stable region distribution map, located inside the stable region, on the stable boundary, and in the unstable region, respectively. The same initial conditions were applied to the closed-loop monorail model and the closed-loop coupled model, respectively. The time-domain response curves of the lateral velocity and yaw rate were obtained by simulation, and the dynamic response characteristics of the closed-loop monorail model and the closed-loop coupled model were compared and analyzed.

7. The stability analysis method for a vehicle lateral motion control system considering steering system coupling according to claim 1, characterized in that, The specific method for performing sensitivity scanning on key structural parameters of the steering system includes: Select the equivalent moment of inertia of the steering system Damping coefficient and mechanical trail As key parameters, a parameter combination domain is constructed, the maximum real part of the system eigenvalue corresponding to each parameter combination is calculated, a stability distribution cloud map of the parameter combination is plotted, and the influence of key structural parameters of the shifting system on the system stability is quantitatively analyzed.

8. The stability analysis method for a vehicle lateral motion control system considering steering system coupling according to claim 1, characterized in that, The specific methods for comparing the stability domain range and the maximum real part of the eigenvalues ​​of the closed-loop monorail model and the closed-loop coupled model include: Under the same vehicle speed and control gain, the stability domain area and the maximum real part of the eigenvalues ​​of the closed-loop monorail model and the closed-loop coupled model are calculated respectively. The effect of steering system dynamics on improving vehicle yaw stability is quantitatively evaluated by numerical comparison.

9. The stability analysis method for a vehicle lateral motion control system considering steering system coupling according to claim 1, characterized in that, The single-rail-steering system coupled open-loop model, which incorporates the dynamic characteristics of the steering system, considers the equivalent rotational inertia, damping coefficient, and tire self-centering torque characteristics generated by the mechanical trailing distance of the steering system.

10. The stability analysis method for a vehicle lateral motion control system considering steering system coupling according to claim 1, characterized in that, The steering system dynamics characteristics included in the single-rail-steering system coupled open-loop model include at least the tire self-centering torque generated by the mechanical trail. The expression for the coupled open-loop model of the monorail-steering system is as follows: ； In the formula, and These are the longitudinal and lateral velocities, respectively. The yaw rate is angular velocity. , The lateral forces of the front and rear tires, For vehicle quality, This is the distance from the car's center of gravity to the front axle. The distance from the car's center of gravity to the rear axle. It is the moment of inertia of the vehicle as it rotates about its longitudinal axis at its center of gravity. This refers to the front wheel steering angle. This refers to the front wheel lateral stiffness. For rear wheel lateral stiffness, The equivalent rotational inertia of the steering system; The damping coefficient of the steering system; This refers to the input torque of the steering wheel; This is the steering gear ratio. For mechanical trailing distance; The expression for the two-degree-of-freedom vehicle monorail open-loop model is as follows: ； In the formula, and These are the longitudinal and lateral velocities, respectively. The yaw rate is angular velocity. , The lateral forces of the front and rear tires, For vehicle quality, This is the distance from the car's center of gravity to the front axle. The distance from the car's center of gravity to the rear axle. It is the moment of inertia of the vehicle as it rotates about its longitudinal axis at its center of gravity. This refers to the front wheel steering angle. This refers to the front wheel lateral stiffness. This refers to the rear wheel lateral stiffness.

Images