Tire burst vehicle stability control method based on FPID-PO

Abstract

The invention discloses an FPID-PO-based tire burst vehicle stability control method, which comprises the following steps of: establishing a seven-degree-of-freedom vehicle dynamic model and a tire burst model based on a Dugoff tire model, and analyzing the mechanical property change of a tire after tire burst; fuzzy PID control is adopted in the upper layer, the deviation value of the actual side slip angle and the yaw velocity relative to the reference and the change rate of the deviation value serve as input, PID parameter increment is obtained through a fuzzy rule table, and additional yaw moment for maintaining the stability of the vehicle is output; the lower layer firstly uses an analytic hierarchy process to establish an objective function, determines a weight coefficient of a key dynamic response parameter, and then uses an improved parrot optimization algorithm to optimize a torque distribution coefficient of an additional yaw moment; and the stability control of the tire burst vehicle is realized through the double-layer cooperative control architecture. According to the method, the problems of nonlinearity and time lag of vehicle control under the tire burst working condition are solved, and stability and real-time performance superior to those of a traditional control strategy are shown in simulation.

Description

Technical Field

[0001] The invention relates to a stability control method for a tire burst vehicle based on FPID-PO. Background Art

[0002] During vehicle operation, tires are the only dynamic interface between the vehicle and the road, and their mechanical properties directly determine the vehicle's driving safety performance. Sudden tire blowouts, a typical high-risk driving condition, often lead to vehicle instability or even loss of control. After a blowout, the sudden failure of the tire causes a dramatic shift in the vehicle's dynamic load distribution and contact patch friction characteristics, resulting in asymmetric mechanical characteristics in the vehicle's dynamics system, which in turn induces abnormal changes in vehicle posture and severely impacts vehicle handling stability. Therefore, developing effective vehicle stability control strategies after a blowout has become an urgent issue. Summary of the Invention

[0003] The present invention aims to solve the above problems in the prior art and provides a stability control method for a vehicle with a tire blowout based on FPID-PO.

[0004] The technical solutions adopted in the present invention are:

[0005] A tire blowout vehicle stability control method based on FPID-PO includes the following steps:

[0006] S1: Establish a seven-degree-of-freedom vehicle dynamics model and a tire blowout model based on the Dugoff tire model to analyze the changes in tire mechanical properties after a tire blowout.

[0007] S2: Building a two-layer collaborative control architecture:

[0008] The upper layer uses fuzzy PID control, taking the deviation of the actual sideslip angle and yaw rate relative to the reference datum and the rate of change of the deviation as input, and deriving the PID parameter increment through the fuzzy rule table to output the additional yaw moment to maintain vehicle stability.

[0009] The lower layer first uses the hierarchical analysis method to establish the objective function and determine the weight coefficients of the key dynamic response parameters. Then, the improved Parrot optimization algorithm is used to optimize the torque distribution coefficient of the additional yaw moment.

[0010] S3: Achieve stability control of the vehicle with a tire blowout through the two-layer collaborative control architecture.

[0011] Furthermore, the upper layer adopts the fuzzy PID control process including:

[0012] The two-degree-of-freedom vehicle dynamics equation is used to perform steady-state analysis;

[0013] The two-degree-of-freedom vehicle dynamics equation is reconstructed into a state variable description through the vehicle's lateral displacement and rotation equation around the vertical axis;

[0014] Based on the assumption of steady-state driving conditions, the ideal state parameters that characterize the vehicle's lateral dynamic characteristics are solved;

[0015] Combined with road conditions, determine the maximum values of the vehicle's yaw rate and sideslip angle;

[0016] The final expected yaw rate and the final expected sideslip angle of the vehicle are obtained comprehensively;

[0017] The target yaw rate deviation and the target sideslip angle deviation of the center of mass are calculated and used as the input of the fuzzy PID controller to adjust the parameter increment of the fuzzy PID controller and output the additional yaw moment to maintain vehicle stability.

[0018] Furthermore, the Parrot optimization algorithm is improved with four improvements, corresponding to:

[0019] 1. Introducing dynamic weights into foraging behavior;

[0020] 2. Adaptive step size is added to the lingering behavior, and random perturbations are introduced instead of uniform perturbations;

[0021] 3. Dynamic adjustment of communication behavior probability;

[0022] 4. Introduce a safe distance mechanism for fearful behavior.

[0023] Furthermore, the improvement point 1 is specifically as follows: in the foraging behavior, the improved position movement follows the following pattern:

[0024] ,

[0025] in, is the individual’s current position, X best represents the current optimal individual position, Used to represent the flying behavior of parrots, refers to the individual dimension, Indicates the position of observing the entire group, is the number of iterations, represents the maximum number of iterations, is a dynamic weight, which changes with the number of iterations Exponential decay, initial value , is the average value of the current position of the entire group, and the calculation formula is:

[0026] ,

[0027] is the population size.

[0028] Furthermore, improvement point 2 is specifically as follows:

[0029] The fixed step size is changed to an adaptive step size that decreases linearly with the number of iterations, and random perturbations are introduced instead of uniform perturbations to enhance local fine-tuning capabilities. In the lingering behavior, the improved position update follows the following pattern:

[0030] ,

[0031] in, For the The adaptive step coefficient at the iteration controls the parrot individual to the optimal individual position The step length of the movement, is the initial value of the step coefficient, is a fixed perturbation coefficient, Indicates generation dimensional standard normally distributed random numbers.

[0032] Furthermore, improvement point 3 is specifically as follows:

[0033] The improvement of communication behavior includes designing a dynamic probability threshold, which determines whether individuals should cooperate in groups or explore independently by comparing the random probability p with the dynamic probability threshold;

[0034] In the act of communication, when random probability When , individuals collaborate in groups, and the position update formula is:

[0035] ,

[0036] On the contrary, when When , individuals conduct independent exploration, and the position update formula is:

[0037] ,

[0038] Among them, the dynamic probability threshold The calculation formula is:

[0039] .

[0040] As the number of iterations t increases, the dynamic probability threshold p threshold Gradually decreases, in the initial stage, due to p threshold is set to a higher initial value, the random probability p is more likely to be less than p threshold , prompting individuals to collaborate in groups; and as the number of iterations t approaches the maximum number of iterations t max , p threshold Decreases, at this time the random probability p is more likely to be greater than pthreshold , prompting individuals to explore independently.

[0041] Furthermore, improvement point 4 is specifically as follows: a new safety distance parameter is added to dynamically adjust the escape step size according to the distance between the individual and the threat source to avoid deviation from the optimal solution and enhance search robustness; in fear behavior, the improved position update formula is:

[0042] ,

[0043] in, is the safety distance constant, For strangers' location, is the worst solution of the current population, is the linear attenuation factor.

[0044] Furthermore, in the two-layer collaborative control architecture, the lower-layer optimization process constructs an objective function through the hierarchical analysis method. The objective function is based on the root mean square error index of the key dynamic response parameters, and the specific expression is:

[0045]

[0046] Among them: ω1, ω2, ω3, ω4 are the weight coefficients of yaw rate, sideslip angle of center of mass, lateral displacement and lateral acceleration respectively;

[0047] RMSE γ ,RMSE β ,RMSE y ,RMSEa y are the root mean square errors of yaw rate, sideslip angle of center of mass, lateral displacement, and lateral acceleration respectively;

[0048] The weight coefficient vector ω is calculated by the judgment matrix B in the hierarchical analysis method.

[0049] Weight coefficient vector , the judgment matrix B is:

[0050] ,

[0051] Moreover, the consistency ratio of the judgment matrix B satisfies .

[0052] The present invention has the following beneficial effects:

[0053] A seven-degree-of-freedom vehicle tire blowout model, built using the Dugoff tire model, more accurately reflects the sudden changes in parameters such as tire stiffness and effective rolling radius after a blowout. A collaborative optimization approach based on a hierarchical control architecture is constructed. The upper decision layer utilizes FPID control to dynamically adjust the target additional yaw torque based on the deviation between the real-time values of the center of mass sideslip angle and yaw rate and their ideal values. This design combines fuzzy and PID control algorithms, leveraging the advantages of both controllers to improve the system's anti-interference capability, adaptability, dynamic response speed, and robustness. The lower execution layer incorporates the Analytic Hierarchy Process (AHP) and Parrot algorithm to optimize torque distribution. Compared to traditional differential braking or fixed distribution strategies, this approach more efficiently adapts to the multi-objective constraints of a tire blowout. This combination of high-precision modeling, hierarchical control, and optimization algorithms addresses the nonlinear and time-lag challenges of vehicle control under tire blowout conditions, demonstrating superior stability and real-time performance compared to traditional control strategies in simulations. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a seven-degree-of-freedom vehicle model.

[0055] Figure 2 The tire parameters change before and after the tire burst.

[0056] Figure 3 It is a two-degree-of-freedom vehicle dynamics model.

[0057] Figure 4 is the sideslip angle of the center of mass in the straight-ahead tire blowout condition.

[0058] Figure 5 is the yaw angular velocity of the straight-ahead tire blowout condition.

[0059] Figure 6 It is the lateral acceleration of the straight-ahead tire blowout condition.

[0060] Figure 7 It is the lateral displacement of the straight-ahead tire blowout condition. DETAILED DESCRIPTION

[0061] The present invention will be further described below with reference to the accompanying drawings.

[0062] Aiming at the dynamic response characteristics of vehicles under tire blowout conditions, based on the theoretical framework of Dugoff tire model, a tire blowout model considering the transient process of tire blowout is established by introducing tire mechanical characteristic parameters, and a hierarchical control is proposed. The upper layer adopts FPID control, and outputs the additional yaw torque to maintain vehicle stability through the deviation of the actual sideslip angle and yaw angular velocity relative to the reference benchmark; the lower layer first establishes the objective function through the hierarchical analysis method, and then uses the improved Parrot optimization algorithm to optimize the torque distribution. Finally, simulation experiments are carried out to verify the effectiveness of the proposed control strategy.

[0063] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0064] like Figure 1 , establish a vehicle dynamics model and build a seven-degree-of-freedom vehicle model based on the Dugoff tire model;

[0065] Longitudinal force balance equation:

[0066] ,

[0067] Lateral force balance equation:

[0068] ,

[0069] The moment balance equation around the Z axis is:

[0070] ,

[0071] The torque balance equation of the four wheels:

[0072] ,

[0073] in, is the yaw angular velocity, is the wheel angle, is the vehicle's forward speed, is the sideslip angle at the center of mass, is the longitudinal velocity, is the lateral velocity, is the horizontal distance from the center of mass to the front axle, is the horizontal distance from the center of mass to the rear axle, and are the tire longitudinal force and lateral force, is the wheel slip angle, is the driving torque of the wheel, is the wheel braking torque.

[0074] The tire model uses the Dugoff tire model;

[0075] Longitudinal force formula:

[0076] ,

[0077] Lateral force formula:

[0078] ,

[0079] in

[0080] ,

[0081] ,

[0082] Where: and are the longitudinal and lateral stiffness of the tire, respectively; is the tire slip rate; are the parameters introduced; is the sideslip angle; is the road adhesion coefficient.

[0083] According to the experimental results of tire mechanical properties at normal tire pressure and zero tire pressure, it is assumed that the changes of various parameters are linear, and the change process is as follows: Figure 2 As shown in Figure 3, a mechanical characteristic model of the tire during a tire blowout is established.

[0084] Longitudinal stiffness is the parameter that describes the relationship between the force and deformation generated by longitudinal stress:

[0085] ,

[0086] Where: is the normalized load; is the normalized load factor obtained from the test fitting.

[0087] Longitudinal stiffness is shown in the formula:

[0088] ,

[0089] Where: is the longitudinal stiffness of the tire under normal conditions; The time when the tire blowout started; The duration of the tire blowout.

[0090] The lateral stiffness is shown in the formula:

[0091] ,

[0092] Where: is the longitudinal stiffness of the tire under normal conditions.

[0093] The effective rolling radius is shown in the formula:

[0094] ,

[0095] Where: It is the effective rolling radius of the tire under normal conditions.

[0096] The rolling resistance coefficient of paved road was experimentally measured and parameter identification was performed, and a universal semi-empirical fitting formula was established:

[0097] ,

[0098] In the formula are the test fitting parameters.

[0099] The rolling resistance coefficient is shown in the formula:

[0100] ,

[0101] Where: is the tire rolling resistance coefficient under normal conditions.

[0102] The upper layer uses fuzzy PID control. The controller input is the deviation of the actual sideslip angle and yaw rate relative to the reference benchmark, as well as the rate of change of the deviation. The output is the PID parameter increment obtained through the fuzzy rule table, which then determines the yaw torque applied to restore the vehicle system to stability.

[0103] Use Figure 3 The two-degree-of-freedom vehicle dynamics framework shown is used for steady-state analysis.

[0104] Vehicle lateral displacement:

[0105] ,

[0106] Rotation about the vertical axis:

[0107] ,

[0108] Restructure the dynamic equations into a state variable description:

[0109] ,

[0110] ,

[0111] In the vehicle two-degree-of-freedom dynamic model, based on the assumption of steady-state driving conditions, let , , the ideal state parameters that characterize the vehicle's lateral dynamics characteristics can be solved by analytical derivation:

[0112] ,

[0113] ,

[0114] During actual vehicle operation, subject to the constraints of road conditions (such as road adhesion coefficient, road surface smoothness, slope, etc.), the vehicle's yaw rate and sideslip angle both have a maximum value, which are:

[0115] ,

[0116] ,

[0117] Combining the above formulas, we can get the expressions of the final expected yaw rate and the final expected sideslip angle of the vehicle:

[0118] ,

[0119] ,

[0120] The target yaw rate deviation is shown in the formula:

[0121] ,

[0122] The target center of mass sideslip angle deviation is shown in the formula:

[0123] ,

[0124] The lower layer uses an improved Parrot Optimization Algorithm for optimal control. This algorithm simulates the four basic behaviors of domesticated green-cheeked conures: foraging, sojourning, communication, and fear of strangers. It features behavioral diversity, high performance, and strong parameter adaptability. The improved Parrot Optimization Algorithm is used to solve the lower layer's torque coefficient optimization problem.

[0125] Foraging behavior: Green-cheeked Conures exhibit unique group behavior patterns when searching for food. These domesticated parrots prefer to forage in small groups with abundant food. They observe the locations of their feeders and companions to infer the possible location of food, and then fly to their own foraging spots. The original foraging behavior relied solely on the group mean to guide the search, resulting in insufficient exploration in the early stages of the algorithm and low efficiency in later development. A new dynamic weight mechanism has been added to balance individual autonomous exploration with group collaboration. The weight value decays exponentially with the number of iterations, focusing on individual exploration in the early stages and group experience in the later stages. This prevents the algorithm from falling into local optimality too early and accelerates convergence in the later stages. The movement of the improved position follows a specific pattern:

[0126]

[0127]

[0128] in, is the individual’s current position, representing the current best individual position, Used to represent the flying behavior of parrots, refers to the individual dimension, Indicates the position of observing the entire group, is the number of iterations, represents the maximum number of iterations, is a dynamic weight, which changes with the number of iterations Exponential decay, initial value , is the average value of the current position of the entire group, is the population size.

[0129] Lingering behavior: Green-cheeked conures are highly social creatures and exhibit a unique lingering behavior, where they suddenly fly to any part of their owner's body and remain there for a period of time. The original lingering behavior used a fixed random step size, which easily led to invalid oscillations in the later stages. We changed the fixed step size to an adaptive step size that decreases linearly with the number of iterations. We introduced random perturbations instead of uniform perturbations to enhance local fine-tuning capabilities. This behavior can be described by the following formula:

[0130] ,

[0131] in, For the The adaptive step coefficient at the iteration time controls the parrot individual to the optimal individual The step length of the movement, is the initial value of the step coefficient, is a fixed perturbation coefficient, Indicates generation dimensional standard normally distributed random numbers.

[0132] Communication Behavior: Green-cheeked Conures are naturally gregarious, and social interactions within their flocks are a key feature of their survival strategy. They exhibit two basic behaviors during group interactions: first, flight toward the flock, and second, independent movements away from the flock, with roughly equal probability of occurrence. The original communication behavior used a fixed probability switching strategy, which was unable to adapt to the needs of different search phases. A dynamic probability threshold was designed to favor group collaboration in the early stages and independent exploration in the later stages. This allows for rapid identification of potential areas through group collaboration in the early stages, followed by detailed development through independent exploration in the later stages.

[0133] When random probability hour

[0134] ,

[0135] on the contrary ,

[0136] ,

[0137] ,

[0138] in, is a dynamic probability threshold, initially tending towards group collaboration ( ), and later tends to explore independently ( ).

[0139] Fear of strangers: Green-cheeked conures are naturally wary of strangers, often avoiding unfamiliar people and seeking safety from their caretakers. Originally, this fear behavior was controlled solely through a cosine function, which could lead to excessive deviations from the optimal solution. A new safety distance parameter dynamically adjusts the escape step size based on the individual's distance from the threat source. This effectively avoids local extrema while avoiding disrupting the convergence path, enhancing search robustness. This behavior can be expressed as follows:

[0140] ,

[0141] in, is the safety distance constant, For strangers' location, is the worst solution of the current population, is the linear attenuation factor.

[0142] The Parrot optimization algorithm is used to construct a torque vectoring multi-objective collaborative decision-making mechanism under the distributed drive architecture. The decision targets are three parameters: left rear wheel torque, right front wheel torque, and right rear wheel torque.

[0143] The algorithm group is set to consist of 30 parrots, the number of iterations is 100, and the optimization boundary condition is set to dynamically adjust the margin with the average torque distribution as the reference standard.

[0144] The root mean square error (RMSE) indicator is used to calculate the difference. This indicator is consistent with the original data unit and can intuitively reflect the actual size of the error. For the vehicle dynamic stability control under tire blowout conditions, a multi-modal coupling analysis framework is established. Key dynamic response parameters are selected; The four characteristic quantities are given weight coefficients according to their importance through the hierarchical analysis method.

[0145] Therefore, the objective function is:

[0146] ,

[0147] Based on the hierarchical analysis method, the judgment matrix B is constructed according to the importance of each factor:

[0148] ,

[0149] Calculate the coefficient matrix based on the judgment matrix , after consistency test, the weight vector of the matrix satisfies , the consistency degree of the matrix is within a reasonable range.

[0150] Assume that the vehicle is traveling at a constant speed of 80km / h in a straight line, the road adhesion coefficient is 0.85, and the left front tire of the vehicle bursts after 3s of driving time. The simulation results of no intervention and PO-FPID control are shown as follows: Figures 4-7As shown in the figure. After the tire blowout, the vehicle's slip angle, yaw rate, and lateral acceleration undergo a sudden change. The yaw rate and lateral acceleration have similar changing trends, while the trend is opposite to that of the slip angle. At the end of the simulation, at 10 seconds, the vehicle's lateral displacement reaches 8.2m. After control intervention, the changes in the vehicle's slip angle, yaw rate, and lateral acceleration are reduced by approximately 50% compared to the uncontrolled condition. At the end of the simulation, the vehicle's lateral displacement is reduced to 4.5m. This control method significantly improves the vehicle's stability after a tire blowout.

[0151] The above description is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principles of the present invention. These improvements should also be regarded as the scope of protection of the present invention.

Claims

1. A tire blowout vehicle stability control method based on FPID-PO, characterized by: The steps include: S1: Establish a seven-degree-of-freedom vehicle dynamics model and a tire blowout model based on the Dugoff tire model to analyze the changes in tire mechanical properties after a tire blowout. S2: Building a two-layer collaborative control architecture: The upper layer uses fuzzy PID control, taking the deviation of the actual sideslip angle and yaw rate relative to the reference datum and the rate of change of the deviation as input, and deriving the PID parameter increment through the fuzzy rule table to output the additional yaw moment to maintain vehicle stability. The lower layer first uses the hierarchical analysis method to establish the objective function and determine the weight coefficients of the key dynamic response parameters. Then, the improved Parrot optimization algorithm is used to optimize the torque distribution coefficient of the additional yaw moment. S3: Achieve stability control of the vehicle with a tire blowout through the two-layer collaborative control architecture.

2. The tire blowout vehicle stability control method based on FPID-PO according to claim 1, characterized in that: The upper layer adopts the fuzzy PID control process including: The two-degree-of-freedom vehicle dynamics equation is used to perform steady-state analysis; The two-degree-of-freedom vehicle dynamics equation is reconstructed into a state variable description through the vehicle's lateral displacement and rotation equation around the vertical axis; Based on the assumption of steady-state driving conditions, the ideal state parameters that characterize the vehicle's lateral dynamic characteristics are solved; Combined with road conditions, determine the maximum values of the vehicle's yaw rate and sideslip angle; The final expected yaw rate and the final expected sideslip angle of the vehicle are obtained comprehensively; The target yaw rate deviation and the target sideslip angle deviation of the center of mass are calculated and used as the input of the fuzzy PID controller to adjust the parameter increment of the fuzzy PID controller and output the additional yaw moment to maintain vehicle stability.

3. The tire blowout vehicle stability control method based on FPID-PO according to claim 1, characterized in that: The Parrot optimization algorithm is improved with four improvements, corresponding to: (1) Introducing dynamic weights into foraging behavior; (2) Adaptive step size is added to the stay behavior, and random perturbations are introduced to replace uniform perturbations; (3) Dynamic adjustment of the probability of communication behavior; (4) Introducing a safe distance mechanism for fearful behavior.

4. The FPID-PO based stability control method for a tire blowout vehicle according to claim 3, wherein: Improvement point 1 is as follows: During foraging behavior, the improved position movement follows the following pattern: ， in, is the individual’s current position, X best represents the current optimal individual position, Used to represent the flying behavior of parrots, refers to the individual dimension, Indicates the position of observing the entire group, is the number of iterations, represents the maximum number of iterations, is a dynamic weight, which changes with the number of iterations Exponential decay, initial value , is the average value of the current position of the entire group, and the calculation formula is: ， is the population size.

5. The FPID-PO based tire blowout vehicle stability control method according to claim 3, characterized in that: Improvement point 2 is as follows: The fixed step size is changed to an adaptive step size that decreases linearly with the number of iterations, and random perturbations are introduced instead of uniform perturbations to enhance local fine-tuning capabilities. In the lingering behavior, the improved position update follows the following pattern: ， in, For the The adaptive step coefficient at the iteration controls the parrot individual to the optimal individual position The step length of the movement, is the initial value of the step coefficient, is a fixed perturbation coefficient, Indicates generation dimensional standard normally distributed random numbers.

6. The FPID-PO based stability control method for a tire blowout vehicle according to claim 3, wherein: Improvement point 3 is as follows: The improvement of communication behavior includes designing a dynamic probability threshold, which determines whether individuals should cooperate in groups or explore independently by comparing the random probability p with the dynamic probability threshold; In the act of communication, when random probability When , individuals collaborate in groups, and the position update formula is: ， On the contrary, when When , individuals conduct independent exploration, and the position update formula is: ， Among them, the dynamic probability threshold The calculation formula is: 。 7. The FPID-PO based stability control method for a tire blowout vehicle according to claim 3, wherein: Improvement 4 specifically includes: adding a safety distance parameter to dynamically adjust the escape step size based on the distance between the individual and the threat source to avoid deviation from the optimal solution and enhance search robustness; in fear behavior, the improved position update formula is: ， in, is the safety distance constant, For strangers' location, is the worst solution of the current population, is the linear attenuation factor.

8. The FPID-PO based stability control method for a tire blowout vehicle according to claim 1, wherein: In the two-layer collaborative control architecture, the lower-layer optimization process constructs the objective function through the hierarchical analysis method. The objective function is based on the root mean square error index of the key dynamic response parameters, and the specific expression is: Among them: ω1, ω2, ω3, ω4 are the weight coefficients of yaw rate, sideslip angle of center of mass, lateral displacement and lateral acceleration respectively; RMSE γ ,RMSE β ,RMSE y ,RMSEa y are the root mean square errors of yaw rate, sideslip angle of center of mass, lateral displacement, and lateral acceleration respectively; The weight coefficient vector ω is calculated by the judgment matrix B in the hierarchical analysis method. Weight coefficient vector , the judgment matrix B is: ， Moreover, the consistency ratio of the judgment matrix B satisfies .

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