Improved Superspiral Global Fast Terminal Sliding Mode Coordinated ESP Control Method for Red-billed Blue Magpie

Abstract

This invention discloses an improved superspiral global fast termination sliding mode coordinated ESP control method for the Red-billed Blue Magpie. A vehicle dynamics model is established, and a superspiral algorithm is used to suppress chattering. A global fast termination term is introduced to improve convergence speed, optimizing the sliding mode controller. The yaw rate and center-of-gravity sideslip angle control weights are dynamically coordinated based on phase plane stability criteria. Considering that the sliding mode controller is significantly affected by its inherent parameters, the Red-billed Blue Magpie optimization algorithm is used to optimize it. The Red-billed Blue Magpie optimization algorithm is further improved to obtain an improved algorithm, and its fitness is calculated. Based on the improved algorithm, the optimal fitness is selected after iterative processing, and the corresponding coordinate values ​​are assigned to the inherent parameters of the sliding mode controller. This algorithm is then applied to the constructed vehicle dynamics model to improve the vehicle's dynamic stability and anti-interference capability under complex conditions.

Description

Technical Field

[0001] This invention relates to the field of ESP control for automotive stability, specifically to an improved superspiral global fast terminal sliding mode coordinated ESP control method for the Red-billed Blue Magpie. Background Technology

[0002] Control strategy is a core issue in Electronic Stability Program (ESP). Currently, widely used control algorithms mainly cover sliding mode control, PID control, and fuzzy logic control. [1] In 2023, Yahya J et al. [2] A model predictive control method combining lateral stability is proposed, integrating lateral stability control, rollover prevention control, and traction braking control. A novel model predictive controller is designed, significantly improving vehicle stability control capabilities under typical highway top speed conditions. (Jiang Lin et al.) [3] An adaptive sliding mode control scheme was designed, utilizing the integral terminal algorithm and an adaptive law designed according to the system characteristics, to give the sliding mode controller higher robustness, faster convergence speed, and better control accuracy; Liang et al. [4] A hierarchical control scheme is proposed, which utilizes different regions of the tire slip angle phase plane and combines a time-varying model predictive controller to optimize the vehicle's yaw stability and energy efficiency, thereby enhancing the vehicle's handling and economy; Fang et al. [5] By integrating an active front-wheel steering system and a direct yaw torque control system, the vehicle's lateral movement capability was improved; Wu Jian et al., 2024 [6] Introducing a dynamic multi-objective mapping function to adjust the built-in parameters of the stability control strategy designed based on model prediction theory; Guan Quancai et al. [7] In 2025, by combining sliding mode controllers and PID controllers, the additional yaw moment was optimized while active rear-wheel steering was introduced, improving the lateral stability of the vehicle during driving. In conjunction with the development of swarm intelligence algorithms in recent years, Li et al. [8] Combining swarm intelligence algorithms with classic controllers solves the problem of limited control performance caused by poor parameter selection. However, traditional sliding mode controllers have many fixed parameters, high parameter requirements, and are often prone to problems such as chattering and slow convergence speed.

[0003] References: [1] National Motor Vehicle and Driver Data for 2024 [J]. Road Traffic Management, 2025, (01): 9. [2] A Review of Academic Research on Automotive Engineering in China · 2023 [J]. China Journal of Highway and Transport, 2023, 36(11): 1-192. DOI: 10.19721 / j.cnki.1001-7372.2023.11.001. [3] China Statistical Yearbook 2024 [EB / OL]. (2024-11-19) [2024-3-25]. https: / / www.stats.gov.cn / sj / ndsj / 2024 / indexch.htm . [4] Guidance Catalogue for Industrial Structure Adjustment (2024 Edition) [EB / OL]. (2023-12-27) [2024-3-25]. https: / / www.gov.cn / zhengce / 202401 / content_6924187.htm. [5] Key Points of Automotive Standardization Work in 2024 [EB / OL]. (2024-06-21) [2024-03-25]. https: / / www.miit.gov.cn / jgsj / zbys / gzdt / art / 2024 / art_d26cb7b3830845f3b3792ae7e3cf46e9.html. [6] A review of handling stability control for distributed drive vehicles [J]. Automotive Technology, 2024, (01): 1-12. DOI: 10.19620 / j.cnki.1000-3703.20230364. [7]Research on yaw stability control strategy for distributed driveelectric trucks[J]. Sensors, 2023, 23(16): 7222. [8] A review of the development of in-wheel motors for electric vehicles [J]. Practical Automotive Technology, 2022, 47(04):139-143. DOI:10.16638 / j.cnki.1671-7988.2022.004.033. Summary of the Invention The purpose of this invention is to provide an improved super-spiral global fast terminal sliding mode coordinated ESP control method for the Red-billed Blue Magpie, in order to overcome the problems existing in the prior art. This invention can significantly reduce the vehicle's yaw rate and center of gravity sideslip angle, effectively improve the dynamic stability and anti-interference ability under complex working conditions, and show obvious advantages over traditional control methods in terms of convergence speed and control accuracy.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: An improved method for coordinated ESP control of the red-billed blue magpie's superspiral global fast terminal sliding mode includes the following steps: Step 1: Establish a vehicle dynamics model, including a seven-degree-of-freedom model of the whole vehicle and an ideal two-degree-of-freedom model, and establish a sliding mode controller; Step 2: Use the superhelical algorithm to suppress chattering, introduce a global fast terminal term to improve convergence speed, optimize the sliding mode controller, and dynamically coordinate the control weights of yaw rate and centroid sideslip angle according to the phase plane stability criterion. Step 3: Based on the factors that greatly affect the sliding mode controller due to its inherent parameters, the Red-beaked Blue Magpie optimization algorithm is used to optimize the sliding mode controller; Step 4: Based on the need for precise control of automobiles under complex conditions, the Red-billed Blue Magpie optimization algorithm in Step 3 is improved to obtain the improved Red-billed Blue Magpie optimization algorithm, and the Red-billed Blue Magpie fitness is calculated. Step 5: Based on the improved Red-billed Blue Magpie optimization algorithm in Step 4, the optimal fitness is selected after iterative processing, and the corresponding coordinate values ​​are assigned to the inherent parameters in the sliding mode controller. The results are then applied to the constructed vehicle dynamics model to improve the dynamic stability and anti-interference capability of the vehicle under complex working conditions.

[0005] Furthermore, the vehicle dynamics model and sliding mode controller established in step 1 are as follows: The seven-DOF model of the entire vehicle is constructed using the following formula:

[0006]

[0007]

[0008] In the formula, m For the overall vehicle quality, V x For the longitudinal speed of the car, V y The lateral speed of the car, W z The yaw rate is angular velocity. F y_fl and F y_fr The lateral force is applied to the left and right front wheels; F y_rl and F y_rr The lateral force is applied to the left and right rear wheels. F x_fl and F x_fr The longitudinal force is applied to the left and right front wheels. F x_rl and F x_rr δ represents the longitudinal force on the left and right rear wheels; δ represents the steering angle of the two front wheels; Lf and L r This represents the distance from the center of mass to the front and rear axles, respectively. B f and B r The track width is the distance between the front and rear axles; F f_fl and F f_fr The rolling resistance of the left and right front wheels; F f_rl and F f_rr The rolling resistance of the left and right rear wheels; Tire rolling resistance F f_i , i=(fl,fr,rl,rr) The calculation is as follows:

[0009] In the formula, m For the overall vehicle weight; C This is the gain coefficient; f 0, f 1 and f 4 represents the tire drag coefficient; F z_i This refers to the vertical load on the corresponding wheel; V x For the car along X Axle travel speed; The formulas for the vertical load of each tire are as follows:

[0010] In the formula, m w This refers to the tire weight. m b For vehicle body weight; h g The height of the center of mass above the ground; L This refers to the wheelbase; a x For the car along x Axial acceleration; a y For the car along y Axial acceleration; Four tires rotating motion w i ( i=fl,fr,rl,rr The differential equation is as follows:

[0011] In the formula, R e For the effective rolling radius, OThis refers to the tire's moment of inertia. T di This refers to the driving torque of a car. T bi For the braking torque of the car, i=(fl,fr,rl,rr) The seven-DOF model of the vehicle uses hub motors for drive. The output torque of the four-wheel motors is determined using the motor characteristic curves as follows:

[0012] In the formula, q t This is the motor torque coefficient, ranging from [-1, 1], and its value represents the positive motor output driving torque. p t If the value is negative, the motor outputs braking torque; n i For the corresponding wheel speed, i=(fl,fr,rl,rr) It is obtained by conversion after calculation based on the seven degrees of freedom of the whole vehicle; The ideal two-degree-of-freedom model is constructed using the following formula:

[0013] In the formula, β The sideslip angle is the angle between the vehicle's center of gravity and its body. W z This refers to the yaw rate of the car. I z For cars to go around Z Moment of inertia of the shaft; C f , C r Using the front and rear wheel lateral stiffness coefficients of the car, the desired yaw rate of the car is derived. and the ideal center of gravity sideslip angle of the car The specific formula is as follows:

[0014] In the formula, K The stability coefficient; Due to the limitations imposed by the road surface friction coefficient, both the yaw rate and the sideslip angle of the vehicle have extreme values. Furthermore, considering the differences between the ideal model and actual conditions, the following formula is used to correct the output values:

[0015] In the formula, u The coefficient of friction of the road surface; g This is the acceleration due to gravity.

[0016] Furthermore, step 2 optimizes the sliding mode controller as follows:

[0017] In the formula, S wz For sliding surface functions, v Add a new variable to the sliding surface; K 1. K 2 represents the fixed parameters of the super-spiral sliding mode; Design a smoother switching function. M The specific expression is as follows:

[0018] In the formula, n A value greater than 0 is used to adjust the slope of the function. n The smaller the value, the smoother the function curve; The yaw rate tracking error and its derivative are defined as follows:

[0019] The differential equation of the original two-degree-of-freedom model can then be written as:

[0020] In the formula, ΔM z To add yaw moment; The design of the new sliding surface and its derivative are as follows:

[0021] In the formula, c ωz The correlation coefficient between the yaw rate error and the error derivative is given by the coefficient of variation. c ωz The larger the value, the more sensitive the controller is to errors, and the less sensitive it is to the rate of change of errors; λ , q and p It is a positive odd number;

[0022] By rearranging the improved approach rate formula and switching function formula of the superhelix method, the final additional yaw moment output is obtained as follows:

[0023] The additional yaw moment output by the slip mode controller for the center of gravity side slip angle is also calculated using the same method; Meanwhile, the joint coefficient allocation is designed, and the specific formula is as follows:

[0024]

[0025] In the formula, B 1, B2 represents the allocation coefficient. By allocating the joint coefficient, an additional yaw moment that conforms to the current vehicle conditions is output, thereby enabling more precise control and better control performance. The calculation of the additional yaw moment after adding the joint coefficient allocation is as follows:

[0026] In the formula, p 1 is the distributive factor.

[0027] Furthermore, the red-billed blue magpie optimization algorithm in step 3 includes the following steps: Step 3.1: Randomly initialize the red-billed blue magpie population; Step 3.2: Based on the red-billed blue magpie population obtained in Step 3.1, individual red-billed blue magpies in the population begin to search for food and update their locations accordingly; Step 3.3: Based on the red-billed blue magpie population obtained in Step 3.2, individual red-billed blue magpies begin to attack prey and update their positions accordingly; Step 3.5: Based on the red-billed blue magpie population obtained in Step 3.3, individual red-billed blue magpies begin to store physical objects and update their locations accordingly.

[0028] Furthermore, the specific formula for initializing the red-billed blue magpie population in step 3.1 is as follows:

[0029] In the formula, x i,j For population location, ub and lb These represent the upper and lower boundaries of the solution domain, respectively. Rand 1 represents a random number between 0 and 1; In step 3.2, during the food search, red-billed blue magpies typically move in small groups of 2 to 5 individuals or in flocks of 10 or more. When small groups are exploring for food, the population iteration formula is as follows:

[0030] In the formula, t Indicates the current iteration number; X i ( t +1) indicates the first i A new search agent location; p2 This indicates the number of red-billed blue magpies randomly selected from 2 to 5 small groups across all search populations; (t) represents the randomly selected first... w Individual; (t) represents the th i Individual; X rs (t ) represents the search agent randomly selected in the current iteration; Rand 2 represents a random number between 0 and 1; When groups search for food, the population iteration formula is as follows:

[0031] In the formula, Rand 3 is a random number in the range [0,1]. q2 This indicates the number of search agents in the population when exploring for food, ranging from 10 to the total population size. In step 3.3, when attacking prey, in small group operations, the main targets are small prey or plants; the corresponding mathematical model is as follows:

[0032] When red-billed blue magpies move in flocks, they exhibit predatory hunting behavior, and the corresponding mathematical model is as follows:

[0033] In the formula, X food ( t () indicates the location of the food; Rand ni_ Let i = (1,2) represent the random numbers used to generate the standard normal distribution. CF It is the attenuation factor; T This represents the total number of iterations. t This represents the current iteration number. CF The formula is as follows:

[0034] In step 3.2, besides searching for and attacking food, the red-billed blue magpie also stores excess food in tree holes or other hidden places for future consumption, ensuring a stable food supply when food is scarce. This preserves location information to facilitate finding the global optimum, as shown in the following formula:

[0035] In the formula, This represents the fitness value from the previous iteration; This represents the fitness value of the current iteration.

[0036] Furthermore, step 4 involves improving the Red-billed Blue Magpie optimization algorithm to obtain an improved Red-billed Blue Magpie optimization algorithm, which specifically includes the following steps: Step 4.1: Randomly initialize the red-billed blue magpie population by designing an SPM chaotic mapping method incorporating cosine transform; Step 4.2: After establishing the initial location of the Red-billed Blue Magpie population, begin preparing for the Red-billed Blue Magpie algorithm iteration update; Step 4.3: A nonlinear time-varying inertia factor was designed for the food-finding stage of the red-billed blue magpie algorithm. c This will improve the search range and local development capabilities of the red-billed blue magpie. Step 4.4: During the prey attack phase, define "apprentice magpies" and "elite magpies" in the population to reduce the tendency to get stuck in local optima; Step 4.5: Calculate the fitness of the red-billed blue magpie population and select the best red-billed blue magpie based on the fitness level; Step 4.6: Determine if the maximum number of iterations has been reached. If yes, output the optimal red-billed blue magpie position coordinates and fitness. If no, return to step 4.3.

[0037] Furthermore, in step 4.1, a SPM chaotic mapping method incorporating cosine transform is designed to randomly initialize the red-billed blue magpie population. The specific formula is as follows:

[0038] In the formula, X(t+1), X(t) This indicates the position information at time t+1 and time t. η ∈(0,1); μ ∈(0,1); r A random number between 0 and 1; mod represents the modulo operation function.

[0039] Furthermore, in step 4.3, a nonlinear time-varying inertia factor was designed. c To improve the search range and local development capabilities of the red-billed blue magpie, the specific formula is as follows: The formula for the nonlinear time-varying inertia factor is as follows:

[0040] In the formula, a p If the parameters are adjustable, the formula for the food-finding stage of the Red-billed Blue Magpie algorithm is transformed into the following form: .

[0041] Furthermore, in step 4.4, "apprentice magpies" and "elite magpies" are defined in the population to reduce the tendency to get trapped in local optima. The specific formula is as follows:

[0042] In the formula: X i (t+1) For the first i Individuals t+1 Location information at any given time Indicates the learning location; r 1 and r2 are both random numbers that follow a uniform distribution in [0,1]. T This represents the maximum number of iterations. t This represents the current iteration number; This represents the average position of the population in the current iteration; ζ For adaptive step size; α For smoothness control parameters; p These are amplitude control parameters.

[0043] Furthermore, in step 5, the improved red-billed blue magpie optimization algorithm is used to optimize the sliding mode controller, calculate the coordinate parameters corresponding to the optimal fitness, and assign these parameters to the inherent parameters in the sliding mode controller. Specifically, the following method is used: Step 5.1: Use the method in Step 4.1 to obtain a chaotic map to initialize the red-billed blue magpie population; Step 5.2: Use the obtained red-billed blue magpie population from Step 4.2 to run the subsequent algorithm; Step 5.3: Optimize the food-finding stage of the Red-billed Blue Magpie optimization algorithm based on Step 4.3 to obtain the optimized Red-billed Blue Magpie population; Step 5.4: Optimize the prey attack stage of the red-billed blue magpie optimization algorithm through step 4.4 to obtain the optimized red-billed blue magpie population; Step 5.5: Continue running the Red-billed Blue Magpie optimization algorithm to finally obtain the global optimal solution; Step 5.6: Assign the population position corresponding to the obtained global optimal solution to the intrinsic parameters of the sliding mode controller to obtain the improved sliding mode controller; Step 5.7: Combine the optimized sliding mode controller obtained in Step 5.6 with the vehicle dynamics model constructed in Step 1, and use joint coefficients to allocate coefficients for the yaw rate and center of mass sideslip angle modules, finally obtaining the improved super-spiral global fast terminal sliding mode coordinated ESP control model of the Red-billed Blue Magpie.

[0044] Compared with the prior art, the present invention has the following beneficial technical effects: This invention proposes an improved optimization algorithm for the red-billed blue magpie. Specifically, it designs a SPM chaotic mapping incorporating cosine transform, resulting in a more uniform red-billed blue magpie population after initialization, thus improving the algorithm's early-stage optimization ability. A nonlinear time-varying inertia factor is proposed to optimize the food-finding stage of the algorithm, improving its local optimization ability. An adaptive Gaussian walk strategy based on "apprentice magpies" is also proposed to increase the ability of individual red-billed blue magpies to find the optimal solution and avoid getting trapped in local optima.

[0045] This paper proposes a sliding mode control method that combines the principles of superhelical global fast termination with an improved sliding surface and switching function to optimize the chattering and convergence speed issues of traditional sliding mode controllers. A weighting method for two sliding mode controllers is designed to output the optimal additional torque. Then, three improved strategies of the Red-beaked Blue Magpie algorithm are developed to improve the convergence speed and accuracy of algorithm parameter tuning, thereby enhancing overall performance. Results show that the sliding mode control method optimized using the superhelical global fast termination and the Red-beaked Blue Magpie algorithm can stably control the yaw rate and sideslip angle of a vehicle, demonstrating significant application value.

[0046] Compared to existing red-beaked blue magpie optimization algorithms, this invention has a faster convergence speed and higher convergence accuracy, resulting in better stability of the optimized car. Attached Figure Description

[0047] The accompanying drawings are provided to further understand the invention and constitute a part of this invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0048] Figure 1 This is a flowchart illustrating the present invention; Figure 2 This is an overall block diagram of the control system involved in the present invention; Figure 3 The image shows a comparison of the algorithm of the present invention applied to a complete vehicle (step condition). Figure 4 The image shows a comparison of the algorithm of the present invention applied to a complete vehicle (sine wave condition). Detailed Implementation

[0049] The present invention will now be described in further detail with reference to the accompanying drawings: This invention proposes a multi-strategy SuperTwisting Global Fast Terminal Sliding Mode Control (STGFTSMC). It utilizes multiple strategies to optimize fixed parameters in the sliding mode controller and combines a global fast terminal strategy to improve the controller's convergence speed. A super-twisting strategy is designed to reduce chattering inherent to the controller and other chattering that may be caused by the global fast terminal strategy. Based on vehicle instability criteria, a two-stage sliding mode coordinated controller is established for yaw rate and sideslip angle. The designed controller exhibits superior performance, faster convergence, and more precise control under various complex conditions.

[0050] See Figure 1 The flowchart of this invention shows that the basic red-billed blue magpie optimization algorithm has been improved and applied to a sliding mode controller. The final system block diagram is as follows. Figure 2As shown, firstly, by establishing a seven-DOF vehicle dynamics model and a two-DOF ideal reference model, a super-spiral global fast terminal sliding mode controller (STGFTSMC) is designed. The super-spiral algorithm is used to suppress chattering, a global fast terminal term is introduced to improve convergence speed, and the yaw rate and centroid sideslip angle control weights are dynamically coordinated based on the phase plane stability criterion. Secondly, an improved red-beaked blue magpie optimization algorithm (AP red-beaked blue magpie) is proposed, integrating chaotic mapping initialization, nonlinear inertia factors, and an adaptive Gaussian walk strategy to achieve collaborative optimization of sliding mode controller parameters. Finally, a torque optimal allocation module is constructed by combining the road surface adhesion load function, integrating differential braking and active steering fuzzy control strategies. From Figure 3 and Figure 4 It can be seen that the proposed method can significantly reduce the vehicle's yaw rate and sideslip angle, effectively improve the dynamic stability and anti-interference ability under complex working conditions, and show obvious advantages over traditional control methods in terms of convergence speed and control accuracy.

[0051] The specific steps are as follows: Step 1: Establish the vehicle dynamics model, including a seven-degree-of-freedom model of the whole vehicle and an ideal two-degree-of-freedom model, and establish a sliding mode controller as follows: The seven-DOF model of the entire vehicle is constructed using the following formula:

[0052]

[0053]

[0054] In the formula, m For the overall vehicle quality, V x For the longitudinal speed of the car, V y The lateral speed of the car, W z The yaw rate is angular velocity. F y_fl and F y_fr The lateral force is applied to the left and right front wheels; F y_rl and F y_rr The lateral force is applied to the left and right rear wheels. F x_fl and F x_fr The longitudinal force is applied to the left and right front wheels. F x_rl and F x_rr δ represents the longitudinal force on the left and right rear wheels; δ represents the steering angle of the two front wheels; L fand L r This represents the distance from the center of mass to the front and rear axles, respectively. B f and B r The track width is the distance between the front and rear axles; F f_fl and F f_fr The rolling resistance of the left and right front wheels; F f_rl and F f_rr The rolling resistance of the left and right rear wheels; a fl and a fr The rolling resistance of the tires at the left and right front wheel slip angles. F f_i , i=(fl,fr,rl,rr) The calculation is as follows:

[0055] In the formula, m For the overall vehicle weight; C The gain coefficient is set to 1.2; f 0, f 1 and f 4 represents the tire drag coefficient; F z_i This refers to the vertical load on the corresponding wheel; V x For the car along X Axle travel speed. The formulas for the vertical load on each tire are as follows:

[0056] In the formula, m w This refers to the tire weight. m b For vehicle body weight; h g The height of the center of mass above the ground; L This refers to the wheelbase; a x For the car along x Axial acceleration; a y For the car along y Axial acceleration. Rotational motion of four tires. w i ( i=fl,fr,rl,rr The differential equation is as follows:

[0057] In the formula, R eFor the effective rolling radius, O This refers to the tire's moment of inertia. T di This refers to the driving torque of a car. T bi This refers to the braking torque of the vehicle. The vehicle model uses in-wheel motors for drive, and the output torque of the four motors is determined using the motor characteristic curves as follows:

[0058] In the formula, q t This is the motor torque coefficient, ranging from [-1, 1], and its value represents the positive motor output driving torque. p t If the value is negative, the motor outputs braking torque; n i i=(fl,fr,rl,rr) The corresponding wheel speed is calculated using equation (6) and then converted.

[0059] The ideal two-degree-of-freedom model is constructed using the following formula:

[0060] In the formula, β The sideslip angle is the angle between the vehicle's center of gravity and its body. W z This refers to the yaw rate of the car. I z For cars to go around Z Moment of inertia of the shaft; C f , C r Let be the lateral stiffness coefficients of the front and rear wheels of the vehicle. The desired yaw rate of the vehicle is derived from equation (8). and centroid side slip angle The specific formula is as follows:

[0061] In the formula, K This is the stability coefficient.

[0062] Due to the limitations imposed by the road surface friction coefficient, both the yaw rate and the sideslip angle of the vehicle have extreme values. Furthermore, considering the differences between the ideal model and actual conditions, the following formula is used to correct the output values:

[0063] In the formula, u The coefficient of friction of the road surface; g This is the acceleration due to gravity.

[0064] Step 2: Suppress chattering using the superspiral algorithm, introduce a global fast termination term to improve convergence speed, optimize the sliding mode controller, and dynamically coordinate the control weights of yaw rate and centroid sideslip angle based on the phase plane stability criterion, as detailed below:

[0065] In the formula, S wz For sliding surface functions, v Add a new variable to the sliding surface in the system; K 1. K 2 represents the fixed parameters of the super-spiral sliding mode.

[0066] A smoother switching function was designed, with the following expression:

[0067] In the formula, n A value greater than 0 is used to adjust the slope of the function. n The smaller the value, the smoother the function curve.

[0068] The yaw rate tracking error and its derivative are defined as follows:

[0069] The differential equation of the original two-degree-of-freedom model can be written as:

[0070] In the formula, ΔM z To add yaw moment.

[0071] The design of the new sliding surface and its derivative are as follows:

[0072] In the formula, c ωz The correlation coefficient between the yaw rate error and the error derivative is given by the coefficient of variation. c ωz The larger the value, the more sensitive the controller is to errors, and the less sensitive it is to the rate of change of errors; λ , q and p It is a positive odd number.

[0073]

[0074] By rearranging the improved approach rate formula and switching function formula of the superhelix method, the final additional yaw moment output is obtained as follows:

[0075] The additional yaw moment output by the sliding mode controller for the center of gravity side slip angle is also calculated using the same method.

[0076] Meanwhile, the joint coefficient allocation is designed, and the specific formula is as follows:

[0077]

[0078] By assigning joint coefficients, an additional yaw moment is output that matches the current vehicle conditions, thereby enabling more precise and effective vehicle control. The additional yaw moment after adding the joint coefficients is as follows:

[0079] In the formula, p 1 is the allocation coefficient.

[0080] Step 3: Based on the factors that significantly affect the sliding mode controller due to its inherent parameters, the Red-billed Blue Magpie optimization algorithm is used to optimize the sliding mode controller. The basic Red-billed Blue Magpie optimization algorithm includes the following steps: (1) Population initialization

[0081] In the formula, x i,j Population location ub and lb These represent the upper and lower boundaries of the solution domain, respectively. Rand 1 represents a random number between 0 and 1.

[0082] (2) Searching for food In the search for food, red-billed blue magpies typically move in small groups (2 to 5 individuals) or large flocks (10 or more) to improve search efficiency. The population iteration formula when small groups are exploring for food is as follows:

[0083] In the formula, t Indicates the current iteration number; X i ( t +1) indicates the first i A new search agent location; p2 This indicates the number of red-billed blue magpies randomly selected from 2 to 5 small groups across all search populations; Indicates the randomly selected first w Individual; Indicates the first i Individual; X rs ( t) represents the search agent randomly selected in the current iteration; Rand 2 represents a random number between 0 and 1. The population iteration formula for searching for food in a group is as follows:

[0084] In the formula, Rand 3 is a random number in the range [0,1]. q2 This indicates the number of search agents a population uses when exploring for food, ranging from 10 to the total population size.

[0085] (3) Attacking prey Red-billed blue magpies exhibit a high level of hunting skill and cooperation when pursuing prey. In small group operations, the primary targets are typically small prey or plants. The corresponding mathematical model is as follows:

[0086] When red-billed blue magpies move in flocks, they exhibit predatory hunting behavior. This behavior highlights the multiple strategies and skills they possess, enabling them to successfully obtain food in various situations. The corresponding mathematical model is as follows:

[0087] In the formula, X food ( t () indicates the location of the food; Rand n， i=(1,2), representing the random numbers used to generate the standard normal distribution; CF It is the attenuation factor; T This represents the total number of iterations. t This represents the current iteration number. CF The formula is as follows:

[0088] (4) Storing food Besides foraging for food, the red-billed blue magpie also stores surplus food in tree hollows or other hidden places for future consumption, ensuring a stable food supply during times of scarcity. This process preserves information about the solution, facilitating the finding of the global optimum, as shown in the following formula:

[0089] In the formula, This represents the fitness value from the previous iteration; This represents the fitness value of the current iteration.

[0090] Step 4: Based on the need for more precise control of automobiles under complex conditions, the Red-billed Blue Magpie optimization algorithm in Step 3 is improved to obtain the improved Red-billed Blue Magpie optimization algorithm. The Red-billed Blue Magpie fitness is then calculated, as follows: A SPM chaotic mapping method incorporating cosine transform is designed to randomly initialize a population of red-billed blue magpies. The specific formula is as follows:

[0091] In the formula, X(t+1), X(t) This indicates the position information at time t+1 and time t. η ∈(0,1); μ ∈(0,1); r A random number between 0 and 1; mod represents the modulo operation function.

[0092] A nonlinear time-varying inertia factor was designed. c To improve the search range and local development capabilities of the red-billed blue magpie, the specific formula is as follows: The formula for the nonlinear time-varying inertia factor is as follows:

[0093] In the formula, a p Since these are adjustable parameters, the formula for the food-finding phase of the Red-billed Blue Magpie algorithm is transformed into the following form:

[0094] "Apprentice magpies" and "elite magpies" were defined in the population to reduce the tendency to get trapped in local optima. The specific formula is as follows:

[0095] In the formula: X i (t+1) For the first i Individuals t+1 Location information at any given time Indicates the learning location; r 1 and r 2 are both random numbers that follow a uniform distribution in [0,1]. T This represents the maximum number of iterations. t This represents the current iteration number; This represents the average position of the population in the current iteration; ζ For adaptive step size; α For smoothness control parameters, α =2; p For amplitude control parameters, p =0.05. In the initial stage of iteration, ζ The algorithm has a large size and strong exploratory ability; in the later stages of iteration... ζ The gradual reduction enhances the algorithm's local development capabilities. The introduction of the "apprentice magpie" weakens the fixed-direction guidance effect and improves the overall performance of the algorithm.

[0096] Step 5: Based on the improved Red-billed Blue Magpie optimization algorithm from Step 4, the optimal fitness is selected after iterative processing, and the corresponding coordinate values ​​are assigned to the inherent parameters in the sliding mode controller model. This is then applied to the constructed vehicle dynamics model, effectively improving the dynamic stability and anti-interference capability of the vehicle under complex conditions. Specifically, this includes the following steps: Step 5.1: Use the method in Step 4.1 to obtain a chaotic map to initialize the red-billed blue magpie population; Step 5.2: Use the obtained red-billed blue magpie population from Step 4.2 to run the subsequent algorithm; Step 5.3: Optimize the food-finding stage of the Red-billed Blue Magpie optimization algorithm based on Step 4.3 to obtain the optimized Red-billed Blue Magpie population; Step 5.4: Optimize the prey attack stage of the red-billed blue magpie optimization algorithm through step 4.4 to obtain the optimized red-billed blue magpie population; Step 5.5: Continue running the Red-billed Blue Magpie optimization algorithm to finally obtain the global optimal solution; Step 5.6: Assign the population position corresponding to the obtained global optimal solution to the intrinsic parameters of the sliding mode controller to obtain the improved sliding mode controller.

[0097] Step 5.7: Combine the optimized sliding mode controller obtained in Step 5.6 with the vehicle dynamics model constructed in Step 1. Use joint coefficients to allocate coefficients for the yaw rate and center of gravity sideslip angle modules, ultimately obtaining the improved super-spiral global fast terminal sliding mode coordinated ESP control model for the Red-billed Blue Magpie. Observe the control effect as follows: Figure 3 and Figure 4 As shown.

[0098] Figure 3 The diagram shows the comparison results of the algorithm of this invention applied to a complete vehicle (step test condition). Figure 3 (a) is the front wheel steering angle under step-load conditions. Figure 3 (b) is a comparison curve of yaw rate under step conditions; Figure 3 (c) is a comparison curve of the centroid sideslip angle under step conditions.

[0099] As shown in the figure, the yaw rate curve of the sliding mode control exhibits large overall fluctuations. After the car turns, the yaw rate shows amplitude decay and oscillation, reaching a peak of 0.322 rad / s at 1.14s, and then gradually stabilizing at 3.3s, approaching the ideal value. The sideslip angle loses control after the turn and cannot be stabilized. Using the superspiral global fast optimization sliding mode control, the yaw rate gradually approaches the ideal value at 7.54s at the same speed; the control of the sideslip angle reaches its maximum value of -0.0452 rad at 1.72s, and tends to stabilize at 5.6s, but chattering still exists.

[0100] The yaw rate of the sliding mode control optimized by the superspiral global fast and red-beaked blue magpie algorithm reached its maximum value of 0.218 rad / s at 1.15s, then slowly decreased and stabilized at 2.4s; the centroid sideslip angle reached its maximum value of 0.0347 rad at 1.57s and stabilized at 3.89s. Neither of the two controlled variables showed obvious chattering, and both had smaller errors and shorter settling times.

[0101] Figure 4 The diagram shows the comparison results (sine wave condition) of the algorithm involved in this invention applied to a complete vehicle. Figure 4 (a) is the front wheel steering angle under sinusoidal operating conditions. Figure 4 (b) is a comparison curve of yaw rate under sinusoidal working conditions; Figure 4 (c) is a comparison curve of the centroid sideslip angle under sinusoidal working conditions.

[0102] As shown in the figure, the yaw rate curve under sliding mode control exhibits more severe chattering between 3 and 7 seconds, with the actual value continuously oscillating around the ideal value, reaching a maximum deviation of 0.21 rad / s. The four prominent peaks indicate poor adaptability of the system to changes. The maximum deviation of the centroid sideslip angle from the ideal value reaches 0.051 rad. Sliding mode control using superspiral global fast optimization reduces the chattering and peak values ​​of the yaw rate and centroid sideslip angle curves, decreases the negative growth of the yaw rate curve, and reduces the response time hysteresis of the centroid sideslip angle curve.

[0103] The yaw rate curve and centroid sideslip angle curve of the sliding mode control optimized by superspiral global fast and red-beaked blue magpie algorithms are smoother and have weaker chattering amplitude than the sliding mode control optimized by superspiral global fast. It can suppress curve growth and thus has a higher degree of approximation to the ideal value, resulting in excellent overall performance.

[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit its scope of protection. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading the present invention, they can still make various changes, modifications or equivalent substitutions to the specific implementation of the invention, but these changes, modifications or equivalent substitutions are all within the scope of protection of the pending claims of the invention.

Claims

1. An improved method for coordinated ESP control of the superspiral global fast terminal sliding mode of the red-billed blue magpie, characterized in that, Includes the following steps: Step 1: Establish a vehicle dynamics model, including a seven-degree-of-freedom model of the whole vehicle and an ideal two-degree-of-freedom model, and establish a sliding mode controller; Step 2: Use the superhelical algorithm to suppress chattering, introduce a global fast terminal term to improve convergence speed, optimize the sliding mode controller, and dynamically coordinate the control weights of yaw rate and centroid sideslip angle according to the phase plane stability criterion. Step 3: Based on the factors that greatly affect the sliding mode controller due to its inherent parameters, the Red-beaked Blue Magpie optimization algorithm is used to optimize the sliding mode controller; Step 4: Based on the requirements for precise control of automobiles under complex conditions, the Red-billed Blue Magpie optimization algorithm in Step 3 is improved to obtain the improved Red-billed Blue Magpie optimization algorithm, and the Red-billed Blue Magpie fitness is calculated; specifically including: Step 4.1: Randomly initialize the red-billed blue magpie population by designing an SPM chaotic mapping method incorporating cosine transform; Step 4.2: After establishing the initial location of the Red-billed Blue Magpie population, begin preparing for the Red-billed Blue Magpie algorithm iteration update; Step 4.3: A nonlinear time-varying inertia factor was designed for the food-finding stage of the red-billed blue magpie algorithm. c This will improve the search range and local development capabilities of the red-billed blue magpie. Step 4.4: During the prey attack phase, define "apprentice magpies" and "elite magpies" in the population to reduce the tendency to get trapped in local optima. The specific formula is as follows: In the formula: X i (t+1) For the first i Individuals t+1 Location information at any given time Indicates the learning location; r 1 and r 2 are both random numbers that follow a uniform distribution in [0,1]. T This represents the maximum number of iterations. t This represents the current iteration number; This represents the average position of the population in the current iteration; ζ For adaptive step size; α For smoothness control parameters; p For amplitude control parameters; Step 4.5: Calculate the fitness of the red-billed blue magpie population and select the best red-billed blue magpie based on the fitness level; Step 4.6: Determine if the maximum number of iterations has been reached. If yes, output the optimal red-billed blue magpie position coordinates and fitness. If no, return to step 4.

3. Step 5: Based on the improved Red-billed Blue Magpie optimization algorithm in Step 4, the optimal fitness is selected after iterative processing, and the corresponding coordinate values ​​are assigned to the inherent parameters in the sliding mode controller. The results are then applied to the constructed vehicle dynamics model to improve the dynamic stability and anti-interference capability of the vehicle under complex working conditions.

2. The improved superspiral global rapid terminal sliding mode coordinated ESP control method for the red-billed blue magpie according to claim 1, characterized in that, The vehicle dynamics model and sliding mode controller established in step 1 are as follows: The seven-DOF model of the entire vehicle is constructed using the following formula: In the formula, m For the overall vehicle quality, V x For the longitudinal speed of the car, V y The lateral speed of the car, W z The yaw rate is angular velocity. F y_fl and F y_fr The lateral force is applied to the left and right front wheels; F y_rl and F y_rr The lateral force is applied to the left and right rear wheels. F x_fl and F x_fr The longitudinal force is applied to the left and right front wheels. F x_rl and F x_rr δ represents the longitudinal force on the left and right rear wheels; δ represents the steering angle of the two front wheels. L f and L r This represents the distance from the center of mass to the front and rear axles, respectively. B f and B r The track width is the distance between the front and rear axles; F f_fl and F f_fr The rolling resistance of the left and right front wheels; F f_rl and F f_rr The rolling resistance of the left and right rear wheels; Tire rolling resistance F f_i , i=(fl,fr,rl,rr) The calculation is as follows: In the formula, m For the overall vehicle weight; C This is the gain coefficient; f 0, f 1 and f 4 represents the tire drag coefficient; F z_i This refers to the vertical load on the corresponding wheel; V x For the car along X Axle travel speed; The formulas for the vertical load of each tire are as follows: In the formula, m w This refers to the weight of the tire. m b For vehicle body weight; h g The height of the center of mass above the ground; L Wheelbase; a x For the car along x Axial acceleration; a y For the car along y Axial acceleration; Four tires rotating motion w i ( i=fl,fr,rl,rr The differential equation is as follows: In the formula, R e For the effective rolling radius, O This refers to the tire's moment of inertia. T di This refers to the driving torque of a car. T bi For the braking torque of the car, i=(fl,fr,rl,rr) The seven-DOF model of the vehicle uses hub motors for drive. The output torque of the four-wheel motors is determined using the motor characteristic curves as follows: In the formula, q t This is the motor torque coefficient, ranging from [-1, 1], and its value represents the positive motor output driving torque. p t If the value is negative, the motor outputs braking torque; n i For the corresponding wheel speed, i=(fl,fr,rl,rr) It is obtained by conversion after calculation based on the seven degrees of freedom of the whole vehicle; The ideal two-degree-of-freedom model is constructed using the following formula: In the formula, β The sideslip angle is the angle between the vehicle's center of gravity and its body. W z This refers to the yaw rate of the car. I z For cars to go around Z Moment of inertia of the shaft; C f , C r Using the front and rear wheel lateral stiffness coefficients of the car, the desired yaw rate of the car is derived. And the ideal center of gravity of the car's sideslip angle The specific formula is as follows: In the formula, K The stability coefficient; Due to the limitations imposed by the road surface friction coefficient, both the yaw rate and the sideslip angle of the vehicle have extreme values. Furthermore, considering the differences between the ideal model and actual conditions, the following formula is used to correct the output values: In the formula, u The coefficient of friction of the road surface; g This is the acceleration due to gravity.

3. The improved superspiral global fast terminal sliding mode coordinated ESP control method for the red-billed blue magpie according to claim 1, characterized in that, Step 2 involves optimizing the sliding mode controller, as detailed below: In the formula, S wz For sliding surface functions, v Add a new variable to the sliding surface; K 1. K 2 represents the fixed parameters of the super-spiral sliding mode; Design a smoother switching function. M The specific expression is as follows: In the formula, n A value greater than 0 is used to adjust the slope of the function. n The smaller the value, the smoother the function curve; The yaw rate tracking error and its derivative are defined as follows: The differential equation of the original two-degree-of-freedom model can then be written as: In the formula, ΔM z To add yaw moment; The design of the new sliding surface and its derivative are as follows: In the formula, c ωz The correlation coefficient between the yaw rate error and the error derivative is given by the coefficient of variation. c ωz The larger the value, the more sensitive the controller is to errors, and the less sensitive it is to the rate of change of errors; λ , q and p It is a positive odd number; By rearranging the improved approach rate formula and switching function formula of the superhelix method, the final additional yaw moment output is obtained as follows: The additional yaw moment output by the slip mode controller for the center of gravity side slip angle is also calculated using the same method; Meanwhile, the joint coefficient allocation is designed, and the specific formula is as follows: In the formula, B 1, B 2 represents the allocation coefficient. By allocating the joint coefficient, an additional yaw moment that conforms to the current vehicle conditions is output, thereby enabling more precise control and better control performance. The calculation of the additional yaw moment after adding the joint coefficient allocation is as follows: In the formula, p 1 is the distributive factor.

4. The improved superspiral global fast terminal sliding mode coordinated ESP control method for the red-billed blue magpie according to claim 3, characterized in that, Step 3 of the Red-billed Blue Magpie optimization algorithm includes the following steps: Step 3.1: Randomly initialize the red-billed blue magpie population; Step 3.2: Based on the red-billed blue magpie population obtained in Step 3.1, individual red-billed blue magpies in the population begin to search for food and update their locations accordingly; Step 3.3: Based on the red-billed blue magpie population obtained in Step 3.2, individual red-billed blue magpies begin to attack prey and update their positions accordingly; Step 3.5: Based on the red-billed blue magpie population obtained in Step 3.3, individual red-billed blue magpies begin to store physical objects and update their locations accordingly.

5. The improved superspiral global fast terminal sliding mode coordinated ESP control method for the red-billed blue magpie according to claim 4, characterized in that, The formula for initializing the red-billed blue magpie population in step 3.1 is as follows: In the formula, x i,j For population location, ub and lb These represent the upper and lower boundaries of the solution domain, respectively. Rand 1 represents a random number between 0 and 1; In step 3.2, during the food search, red-billed blue magpies typically move in small groups of 2 to 5 individuals or in flocks of 10 or more. When small groups are exploring for food, the population iteration formula is as follows: In the formula, t Indicates the current iteration number; X i ( t +1) indicates the first i A new search agent location; p 2 indicates the number of red-billed blue magpies randomly selected from 2 to 5 small groups from all the search populations; (t) represents the randomly selected first... w Individual; (t) represents the th i Individual; X rs ( t ) represents the search agent randomly selected in the current iteration; Rand 2 represents a random number between 0 and 1; When groups search for food, the population iteration formula is as follows: In the formula, Rand 3 is a random number in the range [0,1]. q 2 indicates the number of search agents in the population when exploring for food, ranging from 10 to the total population size; In step 3.3, when attacking prey, in small group operations, the main targets are small prey or plants; the corresponding mathematical model is as follows: When red-billed blue magpies move in flocks, they exhibit predatory hunting behavior, and the corresponding mathematical model is as follows: In the formula, X food ( t () indicates the location of the food; Rand ni_ Let i = (1,2) represent the random numbers used to generate the standard normal distribution. CF It is the attenuation factor; T This represents the total number of iterations. t This represents the current iteration number. CF The formula is as follows: In step 3.2, besides searching for and attacking food, the red-billed blue magpie also stores excess food in tree holes or other hidden places for future consumption, ensuring a stable food supply when food is scarce. This preserves location information to facilitate finding the global optimum, as shown in the following formula: In the formula, This represents the fitness value from the previous iteration; This represents the fitness value of the current iteration.

6. The improved superspiral global fast terminal sliding mode coordinated ESP control method for the red-billed blue magpie according to claim 1, characterized in that, In step 4.1, a SPM chaotic mapping method incorporating cosine transform is designed to randomly initialize the red-billed blue magpie population. The specific formula is as follows: In the formula, X(t+1), X(t) This indicates the position information at time t+1 and time t. η ∈(0,1); μ ∈(0,1); r A random number between 0 and 1; mod represents the modulo operation function.

7. The improved superspiral global fast terminal sliding mode coordinated ESP control method for the red-billed blue magpie according to claim 1, characterized in that, Step 4.3 involves designing a nonlinear time-varying inertia factor. c To improve the search range and local development capabilities of the red-billed blue magpie, the specific formula is as follows: The formula for the nonlinear time-varying inertia factor is as follows: In the formula, a p If the parameters are adjustable, the formula for the food-finding stage of the Red-billed Blue Magpie algorithm is transformed into the following form: 。 8. The improved superspiral global fast terminal sliding mode coordinated ESP control method for the red-billed blue magpie according to claim 1, characterized in that, In step 5, the improved red-billed blue magpie optimization algorithm is used to optimize the sliding mode controller, calculate the coordinate parameters corresponding to the optimal fitness, and assign these parameters to the inherent parameters in the sliding mode controller. Specifically, the following method is used: Step 5.1: Use the method in Step 4.1 to obtain a chaotic map to initialize the red-billed blue magpie population; Step 5.2: Use the obtained red-billed blue magpie population from Step 4.2 to run the subsequent algorithm; Step 5.3: Optimize the food-finding stage of the Red-billed Blue Magpie optimization algorithm based on Step 4.3 to obtain the optimized Red-billed Blue Magpie population; Step 5.4: Optimize the prey attack stage of the red-billed blue magpie optimization algorithm through step 4.4 to obtain the optimized red-billed blue magpie population; Step 5.5: Continue running the Red-billed Blue Magpie optimization algorithm to finally obtain the global optimal solution; Step 5.6: Assign the population position corresponding to the obtained global optimal solution to the intrinsic parameters of the sliding mode controller to obtain the improved sliding mode controller; Step 5.7: Combine the optimized sliding mode controller obtained in Step 5.6 with the vehicle dynamics model constructed in Step 1, and use joint coefficients to allocate coefficients for the yaw rate and center of mass sideslip angle modules, finally obtaining the improved super-spiral global fast terminal sliding mode coordinated ESP control model of the Red-billed Blue Magpie.

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