A stability evaluation method and system for a linear steering execution system

Abstract

The application discloses a stability evaluation method and system for a linear steering execution system, and relates to the technical field of linear steering execution system optimization.The application solves the technical problems of a large deviation between a model and actuality caused by neglecting mechanical transmission nonlinearity in traditional linear steering execution system modeling, difficulty of a single optimization algorithm in giving consideration to global search and local precision, lack of quantitative evaluation standards for stability under multiple working conditions, etc., improves simulation reality by constructing a dynamic model containing nonlinearity characteristics, enhances the robustness and precision of a control strategy by using a PSO-BO hybrid optimization algorithm, ensures stable operation of the system under different scenes by combining multiple working condition simulation and quantitative evaluation, and finally realizes significant improvement of the control performance and reliability of the linear steering execution system.

Description

Technical Field

[0001] This invention relates to the field of linear steering system optimization technology, and in particular to a stability evaluation method and system for linear steering systems. Background Technology

[0002] In recent years, the development of autonomous vehicles has attracted much attention, and steer-by-wire (SBW) technology has gained importance due to its ease of integration and control. It consists of a steering control system and an actuation system, with no steering column or mechanical transmission; instead, it relies on electrical signal communication, and the actuator motor provides full power steering. SBW is a core technology for intelligent vehicle chassis control, and the accuracy of its actuation system's dynamic modeling and control strategy directly determines the front wheel steering angle tracking performance. However, mainstream modeling is mostly based on linear assumptions, failing to fully consider nonlinear characteristics such as backlash and LuGre friction, and not fully coupling the tire return torque with the dynamic interaction of the actuation system. This leads to deviations between the model and the actual system. For example, backlash in gears and racks can cause nonlinear dead zones in torque transmission, and the simplification of traditional single-mass rigid body models can easily cause inconsistencies between simulation and real-vehicle responses.

[0003] In terms of control strategy optimization, although the particle swarm optimization (PSO) algorithm has improved the efficiency of parameter tuning, PSO has the defect of premature convergence and is prone to getting trapped in local optima when searching for parameters of high-dimensional nonlinear systems. At the same time, traditional PID is not adaptable to time-varying conditions (such as road surfaces with different adhesion coefficients and variable vehicle speeds), and the fusion depth of fuzzy logic or reinforcement learning is limited, making it difficult to balance the robustness and real-time performance of the control strategy under extreme conditions. Summary of the Invention

[0004] The purpose of this invention is to provide a stability evaluation method and system for linear steering actuation systems to improve the above-mentioned technical problems.

[0005] To achieve the above-mentioned objectives, the embodiments of the present invention provide the following technical solutions:

[0006] A stability evaluation method for a linear steering actuation system, comprising:

[0007] The operating parameters of the vehicle's linear steering system are collected, and the dynamic equations of the linear steering system are constructed through the nonlinear mechanical principles and frictional principles of mechanical transmission; the linear steering system includes a steering motor, a reduction mechanism, and an actuator;

[0008] Based on the dynamic equations, the linear steering actuation system is simulated using the CarSim-Simulink co-simulation method to generate an initial control strategy;

[0009] Based on the initial control strategy, the PID controller is optimized using the PSO-BO hybrid optimization algorithm to obtain the control strategy;

[0010] Construct simulation environments under different operating conditions, simulate control strategies under different operating conditions, and obtain simulation results;

[0011] Based on the simulation results, the stability under different operating conditions is calculated, and the stability evaluation results are generated by combining the stability judgment criteria.

[0012] In the above solution, this invention solves the technical problems of large deviation between the model and reality caused by neglecting the nonlinearity of mechanical transmission (such as backlash and friction) in the modeling of traditional linear steering actuators, the difficulty of a single optimization algorithm to balance global search and local accuracy, and the lack of quantitative evaluation standards for stability under multiple working conditions. By constructing a dynamic model with nonlinear characteristics, the simulation realism is improved. The robustness and accuracy of the control strategy are enhanced by using the PSO-BO hybrid optimization algorithm. The combination of multi-working-condition simulation and quantitative evaluation ensures the stable operation of the system under different scenarios, and finally achieves a significant improvement in the control performance and reliability of the linear steering actuator.

[0013] Furthermore, the dynamic equations for constructing the linear steering actuation system include:

[0014] Collect the operating parameters of the vehicle's linear steering system;

[0015] Based on operating parameters, electromagnetic principles and Newton's second law, the electrical equations, electromagnetic torque equations and motor layer rotational dynamics equations of the steering actuator motor are constructed to generate a dynamic model of the steering actuator motor.

[0016] Based on the operating parameters, and combined with the kinematic principles and dynamic equivalence principles of gear transmission, a dynamic model of the reduction mechanism is constructed.

[0017] Based on operating parameters, the nonlinear mechanical principle of mechanical transmission, and the tribological principle, a rack linear displacement dynamic model is constructed.

[0018] Based on the dynamic model of the steering actuator motor, the dynamic model of the reduction mechanism, and the dynamic model of the rack linear displacement, the dynamic equations of the linear steering actuator system are generated.

[0019] In the above scheme, this invention introduces a rack linear displacement dynamics model because the rack, as the core actuator connecting the reduction mechanism and the steering wheel, directly determines the front wheel steering angle through its linear displacement. Furthermore, during transmission, it is subjected to complex forces such as nonlinear torque from gear meshing (including backlash dead zone), load feedback from tire return torque, and its own friction. Traditional simplified models cannot accurately characterize the dynamic coupling relationship between these forces and linear displacement. The rack linear displacement dynamics model, built based on the principles of nonlinear mechanics and tribology of mechanical transmission, can fully capture the force-motion characteristics of the rack, filling the gap in the most critical link of the "motor-reduction mechanism-steering actuator" power chain. Ultimately, this makes the overall dynamic equations more consistent with the physical laws of the actual system, providing a high-precision model foundation for subsequent control strategy optimization and stability evaluation, and significantly improving the consistency between simulation and real vehicle dynamic response.

[0020] Furthermore, the obtained control strategy includes:

[0021] Based on the dynamic equations and initial control strategy, a closed-loop control model of a linear steering actuation system is established in the Simulink environment;

[0022] Run the closed-loop control model, obtain the simulation output results, calculate the initial performance index and normalize it to generate the performance index;

[0023] Based on performance metrics, a comprehensive performance objective function is constructed by weighted summation.

[0024] Based on the comprehensive performance objective function, the PSO optimization algorithm is used to perform global parameter search and generate a preliminary set of optimal solutions for the PID controller parameters.

[0025] Using the initial optimal solution set as the search boundary, the BO optimization algorithm is used for local optimization to generate a control strategy.

[0026] In the aforementioned schemes, traditional linear steering execution system control strategy optimization suffers from technical problems such as the difficulty of a single algorithm simultaneously addressing global parameter exploration and local accuracy (e.g., premature convergence of PSO and low efficiency of BO global search), as well as the loose integration of parameter optimization with the system dynamics model. This invention addresses these issues by constructing a comprehensive performance objective function that integrates multi-dimensional indicators (normalization avoids indicator conflicts). It utilizes PSO global search to quickly locate the potential optimal parameter range, and then combines this with BO for precise optimization within that range. This approach ensures both the comprehensiveness of the parameter search and improves local convergence accuracy. The resulting control strategy better aligns with the system dynamics, achieving balanced optimization in tracking accuracy, response speed, and anti-interference capabilities. This significantly enhances the adaptability of the control strategy to different operating conditions and the stability of the control effect.

[0027] Furthermore, the generated performance metrics include:

[0028] Run the closed-loop control model, generate simulation output results, and determine the time required for the output of the linear steering actuator to reach the steady-state value, which is then used as a dynamic speed indicator.

[0029] Based on the simulation output results, the proportion by which the maximum peak value of the linear steering execution system exceeds the steady-state value is calculated and used as a dynamic stability index.

[0030] Based on the simulation output results, the time required for the output of the linear steering actuation system to enter the steady-state error band is calculated and used as the stable convergence speed;

[0031] Based on the simulation output results, the absolute value of the difference between the output of the linear steering execution system and the target output is calculated and used as an indicator of tracking accuracy.

[0032] Based on the simulation output, the proportion of time when the torque is zero and the motor angular velocity changes in the linear steering system is calculated, and this proportion is used as the degree of backlash influence.

[0033] The dynamic speed index, dynamic stability index, tracking accuracy index, stable convergence speed, and backlash influence are normalized to generate performance indicators.

[0034] In the above scheme, the dynamic velocity index reflects the system's response speed, the dynamic stability index measures the degree of overshoot to assess dynamic stability, the stable convergence speed reflects the efficiency of entering steady state, the tracking accuracy index quantifies control accuracy, and the backlash effect specifically characterizes the interference of mechanical transmission nonlinearity (backlash) on the system. This invention, through the normalization of these multi-dimensional indices, achieves a comprehensive quantification of the system's dynamic response, stability, control accuracy, and nonlinear effects, avoiding the one-sidedness of single-index evaluation. It provides a precise and comprehensive performance benchmark for subsequent control strategy optimization, ensuring that the optimization direction can take into account multiple performance requirements of the system, and improving the pertinence and effectiveness of the control strategy.

[0035] Furthermore, the obtained simulation results include:

[0036] Select a representative set of operating parameters and set different operating conditions;

[0037] In the Simulink and CarSim co-simulation platform, a full closed-loop simulation model including a linear steering actuation system and a PID controller was constructed.

[0038] Based on the control strategy, the simulation is carried out under different operating conditions using a full closed-loop simulation model to obtain the simulation results for each operating condition.

[0039] In the above-described scheme, actual vehicle driving scenarios are highly diverse, and different operating conditions directly alter the load characteristics, dynamic response requirements (such as steering sensitivity), and intensity of external disturbances of the steering system. Simulating different operating conditions aims to cover these scenarios that may be encountered in real-world driving, capturing the performance differences of the control strategy under diverse conditions. Performance fluctuations may occur under other operating conditions due to sudden load changes and variations in response requirements. Therefore, this invention's simulation of control strategies under different operating conditions is beneficial for determining the universality and safety of the control strategy.

[0040] Furthermore, the generation of stability evaluation results includes:

[0041] Calculate the integral of the deviation between the actual displacement angle and the target displacement angle of the rack under each working condition, and use it as the integral of the angle error for each working condition;

[0042] Calculate the standard deviation of the angular velocity of the motor or rack under each working condition, and use it as the velocity variation fluctuation under each working condition;

[0043] Select the maximum and minimum torque signals for each working condition, and calculate the average torque signal value for each working condition;

[0044] Based on the average value of each torque signal, each maximum torque signal, and each minimum torque signal, the torque fluctuation index for each operating condition is calculated.

[0045] The stability of the control strategy is obtained by weighted summation and mean calculation of the integral of angle error, speed change fluctuation and torque fluctuation index under each working condition;

[0046] Based on stability and stability judgment criteria, stability evaluation results of the control strategy are generated.

[0047] In the above scheme, this invention quantifies the cumulative deviation of rack displacement tracking through angle error integration, reflects the stability of the dynamic response of the motor or rack through speed variation fluctuations, and characterizes the stability of force transmission through torque fluctuation index. It constructs a multi-dimensional stability quantification index from three core dimensions: displacement, speed, and torque, avoiding the one-sidedness of single-index evaluation. Combined with clear stability judgment criteria, the final evaluation result is objective and quantifiable, effectively ensuring the practicality and guidance of the evaluation results.

[0048] A stability evaluation system for linear steering actuation systems includes:

[0049] The dynamics construction module is used to collect the operating parameters of the vehicle's linear steering system and construct the dynamic equations of the linear steering system through the nonlinear mechanical principles and frictional principles of mechanical transmission; the linear steering system includes a steering motor, a reduction mechanism, and an actuator;

[0050] The first strategy module is used to simulate the linear steering actuation system based on the dynamic equations and generate an initial control strategy using the CarSim-Simulink co-simulation method.

[0051] The second strategy module is used to optimize the PID controller based on the initial control strategy using the PSO-BO hybrid optimization algorithm to obtain the control strategy.

[0052] The simulation module is used to build simulation environments under different operating conditions, simulate control strategies under different operating conditions, and obtain simulation results.

[0053] The stability evaluation module is used to calculate the stability under different operating conditions based on the simulation results, and generate stability evaluation results by combining the stability judgment criteria.

[0054] In the above scheme, the system forms a closed loop throughout the entire process through the collaboration of various modules, realizing the integration of accurate modeling, optimized control, multi-condition verification and quantitative evaluation, effectively ensuring the stability and practicality of the linear steering execution system control strategy, and meeting the reliable steering requirements of the vehicle in actual driving.

[0055] Furthermore, the dynamics building block includes:

[0056] The data acquisition unit is used to collect the operating parameters of the vehicle's linear steering system.

[0057] The steering mechanism unit is used to construct the electrical equations, electromagnetic torque equations, and motor layer rotational dynamics equations of the steering actuator motor based on operating parameters, electromagnetic principles, and Newton's second law, thereby generating a dynamic model of the steering actuator motor.

[0058] The speed reduction mechanism unit is used to construct a dynamic model of the speed reduction mechanism based on operating parameters and the kinematic and dynamic equivalence principles of gear transmission.

[0059] The rack displacement element is used to construct a rack linear displacement dynamic model based on operating parameters, the nonlinear mechanical principle of mechanical transmission, and the tribological principle.

[0060] The dynamics building unit is used to generate the dynamic equations of the linear steering system based on the dynamics model of the steering actuator motor, the dynamics model of the reduction mechanism, and the dynamics model of the rack linear displacement.

[0061] In the above scheme, the dynamics construction module acquires comprehensive operating parameters through the acquisition unit, and then models the core components such as motors, reduction mechanisms, and racks in units according to their physical characteristics and working principles. In particular, it fully incorporates the nonlinearity and friction characteristics of mechanical transmission, avoiding the simplification deviation of traditional modeling. Finally, by integrating the models of each component, a system-level dynamic equation is generated, ensuring the model's fit to the actual transmission law.

[0062] Furthermore, the second strategy module includes:

[0063] Closed-loop control unit, used to build a closed-loop control model of a linear steering actuation system in the Simulink environment based on dynamic equations and initial control strategy;

[0064] The performance index unit is used to run the closed-loop control model, obtain the simulation output results, calculate the initial performance index, normalize it, and generate the performance index.

[0065] The objective function unit is used to construct a comprehensive performance objective function based on performance metrics through weighted summation.

[0066] The initial optimization unit is used to perform a global parameter search based on the comprehensive performance objective function using the PSO optimization algorithm to generate a preliminary set of optimal solutions for the PID controller parameters.

[0067] The secondary optimization unit is used to take the initial optimal solution set as the search boundary and perform local optimization through the BO optimization algorithm to generate a control strategy.

[0068] In the above scheme, the second strategy module, relying on the dynamic characteristics and initial control strategy of the linear steering actuator, constructs a comprehensive objective function by integrating multi-dimensional normalized performance indicators. It then uses a PSO-BO hybrid optimization algorithm to achieve global search and local fine-tuning of the PID controller parameters, ultimately generating a control strategy adapted to the system's nonlinear characteristics. This control strategy balances steering response speed, tracking accuracy, and operational stability, avoiding the limitations of a single optimization algorithm and ensuring the reliability and adaptability of the control effect in complex transmission scenarios.

[0069] Furthermore, the performance indicator unit includes:

[0070] The speed index subunit is used to run the closed-loop control model, generate simulation output results, and determine the time required for the output of the linear steering actuation system to reach the steady-state value, which is then used as a dynamic speed index.

[0071] The stability index subunit is used to calculate the proportion by which the maximum peak value of the output of the linear steering execution system exceeds the steady-state value based on the simulation output results, and to serve as a dynamic stability index.

[0072] The stable convergence subunit is used to calculate the time required for the output of the linear steering actuation system to enter the steady-state error band based on the simulation output results, and to use this as the stable convergence speed.

[0073] The tracking accuracy subunit is used to calculate the absolute value of the difference between the output of the linear steering actuation system and the target output based on the simulation output results, and use it as a tracking accuracy index.

[0074] The backlash influence subunit is used to calculate the proportion of time when the linear steering system experiences zero torque and changes in motor angular velocity based on the simulation output results, and to use this as the degree of backlash influence.

[0075] The normalization sub-unit is used to normalize the dynamic speed index, dynamic stability index, tracking accuracy index, stable convergence speed, and backlash influence to generate performance indicators.

[0076] In the above scheme, the system can extract key indicators reflecting the dynamic response, tracking accuracy and nonlinear effects of the linear steering execution system from the closed-loop simulation results and normalize them. This avoids the one-sidedness of evaluation by a single indicator and unifies the order of magnitude of indicators of different dimensions. It ensures that the optimization of the control strategy can balance the system response speed, stability, tracking accuracy and anti-backlash interference capability, laying a reliable foundation for generating high-performance control strategies. Attached Figure Description

[0077] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0078] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention;

[0079] Figure 2 This is a flowchart of the method in Embodiment 1 of the present invention;

[0080] Figure 3 This is a system diagram from Embodiment 1 of the present invention;

[0081] Figure 4 This is a simulation diagram of the front wheel steering angle of condition 1 in embodiment 2 of the present invention, which is 10°.

[0082] Figure 5 This is a simulation diagram of the front wheel steering angle of condition 1 in embodiment 2 of the present invention being 30°;

[0083] Figure 6This is a simulation diagram of the front wheel steering angle of condition 1 in embodiment 2 of the present invention, which is 45°.

[0084] Figure 7 This is a schematic diagram of the front wheel steering angle curve in scenario 1 of working condition 2 in embodiment 3 of the present invention;

[0085] Figure 8 This is a schematic diagram of the front wheel steering angle error curve in scenario 1 of working condition 2 in embodiment 3 of the present invention;

[0086] Figure 9 This is a schematic diagram of the front wheel steering angle curve in scenario 2 of working condition 2 in embodiment 3 of the present invention;

[0087] Figure 10 This is a schematic diagram of the front wheel steering angle error curve in scenario 2 of working condition 2 in embodiment 3 of the present invention; Detailed Implementation

[0088] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0089] Example 1:

[0090] Please see Figure 1 This embodiment provides a stability evaluation method and system for linear steering execution systems. Figure 1 The execution entity of the method shown can be a software and / or hardware device. The execution entity of this application can include, but is not limited to, at least one of the following: user equipment, network equipment, etc. User equipment can include, but is not limited to, computers, smartphones, personal digital assistants (PDAs), and the aforementioned electronic devices. Network equipment can include, but is not limited to, a single network server, a server group consisting of multiple network servers, or a cloud based on cloud computing consisting of a large number of computers or network servers. Cloud computing is a type of distributed computing, consisting of a super virtual computer composed of a group of loosely coupled computers. This embodiment does not impose any limitations on this.

[0091] like Figure 1 As shown, a stability evaluation method for a linear steering actuation system includes:

[0092] S1. Collect the operating parameters of the vehicle's linear steering system, and construct the dynamic equations of the linear steering system using the nonlinear mechanical principles and frictional principles of mechanical transmission; the linear steering system includes a steering motor, a reduction mechanism, and actuators (rack and pinion steering gear and steering tie rod), such as... Figure 2 As shown.

[0093] S1 includes:

[0094] S11. Collect the operating parameters of the vehicle's linear steering system; the operating parameters include the motor angle. Output shaft angle of the reduction mechanism rack linear displacement Electromagnetic torque The torque transmitted from the reduction mechanism to the rack side Rack torque Reduction ratio Pitch circle radius of the pinion half-angle of tooth gap meshing stiffness Meshing damping Moment of inertia of the motor Moment of inertia of the reduction mechanism Motor damping Damping of the deceleration mechanism .

[0095] S12. Based on operating parameters, electromagnetic principles and Newton's second law, construct the electrical equations, electromagnetic torque equations and motor layer rotational dynamics equations of the steering actuator motor, and generate the dynamics model of the steering actuator motor.

[0096] Specifically, the formula corresponding to the electrical equation is:

[0097] ;

[0098] The formula corresponding to the electromagnetic torque equation is:

[0099] ;

[0100] The formula corresponding to the rotational dynamics equation of the motor layer is:

[0101] ;

[0102] in, This indicates the resistance of the motor that drives the steering mechanism. Indicates at time The current of the motor that drives the steering input. Represents current The first derivative, Indicates the inductance of the motor that drives the steering mechanism. , These represent the back electromotive force coefficient and the motor torque coefficient, respectively. , They represent the times respectively. The first derivative (motor angular velocity) and the second derivative (motor angular acceleration) of the motor angle. Indicates at time The input voltage of the downward steering actuator motor. Indicates at time Lower electromagnetic torque, Indicates at time The torque transmitted from the steering motor to the gears is used for downward steering.

[0103] S13. Based on the operating parameters, and combined with the kinematic principles and dynamic equivalence principles of gear transmission, a dynamic model of the reduction mechanism is constructed; the dynamic model of the reduction mechanism includes the calculation of angle mapping relationship and equivalent inertia conversion equation;

[0104] Specifically, the formula corresponding to the angle mapping relationship is:

[0105] ;

[0106] ;

[0107] ;

[0108] The formula corresponding to the equivalent inertia reduction equation is:

[0109] ;

[0110] ;

[0111] in, , , They represent the times respectively. The output shaft angle of the lower reduction mechanism and its first and second derivatives. Indicates at time Lower motor angle, This represents the equivalent moment of inertia referred to the motor side. It represents the equivalent moment of inertia referred to the gear side.

[0112] S14. Based on the operating parameters, the nonlinear mechanical principle of mechanical transmission, and the tribological principle, construct a rack linear displacement dynamic model;

[0113] Specifically, current dynamic models of linear steering systems often focus on linear dynamic characteristics, such as the motor's moment of inertia and viscous damping, the meshing stiffness and damping of the gear and rack, and the linear mapping of tire return torque. They often assume the transmission system is an ideal rigid connection, neglecting actual mechanical characteristics such as backlash and frictional nonlinearity. However, in actual operation, there is backlash between the gears and rack. When the input angle is small, the "torque transmission dead zone" causes a deviation between the actual and desired steering angle, resulting in a decrease in the control accuracy of the linear steering system. Furthermore, frequent reversals cause "free travel," leading to steering response delay and increased overshoot, resulting in distorted response of the linear steering system and making it prone to oscillation or instability in actual backlash-laden systems.

[0114] Therefore, based on the nonlinear mechanical principle of mechanical transmission, a rack linear displacement dynamic model is constructed and introduced into the dynamic equation of the linear steering system. Due to the physical clearance (backlash) in the gear-rack meshing, no torque is transmitted when the relative angle is within the backlash range; only when it exceeds the backlash does torque is transmitted according to the elastic damping relationship.

[0115] Since backlash is an inherent characteristic of mechanical systems, neglecting it will lead to a significant deviation between the model and the real system, thus causing the control strategy to fail. Piecewise functions can intuitively and accurately characterize the physical essence of "dead zone-elastic transmission," and parameters such as backlash half-angle, meshing stiffness, and meshing damping can be identified experimentally (e.g., small-amplitude bidirectional reciprocating steering tests), making them engineering feasible. Therefore, a piecewise nonlinear function method is chosen for construction, i.e., when the relative angle between the gear and rack... At that time, the torque is transmitted The value is 0; otherwise, according to:

[0116] ;

[0117] Calculate the transmitted torque .in, Represents a symbolic function. , These represent the first derivatives of the angular displacements on the output shaft angle and rack side of the reduction mechanism, respectively. The relative angle refers to the difference between the output shaft angle and the equivalent angle on the rack side of the reduction mechanism.

[0118] The equations constructed using the piecewise nonlinear function method are embedded in the torque transmission link of the gear and rack; then, the torque is combined with the force balance or rotational balance equation of the rack to obtain the linear displacement dynamic model of the rack, namely:

[0119] ;

[0120] ;

[0121] Expressed in degrees ,but:

[0122] ;

[0123] in, , , They represent the times respectively. The displacement of the lower steering rack relative to the center position along its direction of motion, and its first and second derivatives. , , These represent the equivalent mass of the rack, the linear damping of the rack, and the linear stiffness of the rack, respectively. , They represent the times respectively. The equivalent linear force obtained from the meshing torque conversion, and the combined linear force generated by the left and right tie rods and the wheel end. Indicates at time Torque is transmitted downwards. Indicates at time The rack under the load has a torque. , These represent the first and second parameters, respectively, after the equivalent mass of the rack is converted into moment of inertia. , They represent the times respectively. equivalent angle of the lower rack side The first and second derivatives.

[0124] By introducing a backlash model, the dynamic model of this invention can accurately reproduce the actual transmission behavior of gears and racks (such as idle travel and torque dead zone during small-angle commutation); it enables the control strategy to specifically compensate for the influence of backlash, significantly reducing the angle tracking error; it can also support online monitoring of backlash parameters and provide early warning of gear wear and other faults.

[0125] S16. Based on the dynamic model of the steering actuator motor, the dynamic model of the reduction mechanism, and the dynamic model of the rack linear displacement, the dynamic equation of the linear steering actuator system is generated.

[0126] S2. Based on the dynamic equations, the linear steering actuation system is simulated using the CarSim-Simulink co-simulation method to generate an initial control strategy;

[0127] Specifically, the dynamic equations of the linear steering actuator system are transformed into a modular structural model in the Simulink environment, forming a simulation model of the actuator system that can be used for real-time response calculation. Subsequently, the vehicle dynamics model is called in the CarSim platform, and the actuator system model is coupled with the vehicle's yaw, sideslip, tire lateral forces, and other dynamic characteristics to establish a closed-loop dynamic simulation relationship between the vehicle and the actuator system. This co-simulation platform can comprehensively reflect the energy transfer and response processes between the motor, reduction mechanism, rack and pinion transmission, and front wheel motion, realistically reproducing the dynamic behavior characteristics of the linear steering actuator system under different steering angle inputs, vehicle speeds, and road adhesion coefficients.

[0128] During the co-simulation process, different forms of steering input signals (including step signals, sinusoidal scanning signals, and random input signals) are applied to the system, and the system's output response data is recorded. The data includes key state quantities (simulation output results) such as motor torque, current change, rack displacement, front wheel angle, and return torque.

[0129] Based on key state variables, control law analysis is performed on the motor drive, torque transmission, and self-aligning force feedback stages of the actuator system to establish the mapping relationship between motor input voltage and output torque. By adjusting the proportional parameters of motor voltage input and torque output, dead zone compensation parameters, and self-aligning torque feedback weights, the initial control gain and feedback structure of the linear steering actuator system are determined, forming the initial control strategy.

[0130] Finally, the mapping process from dynamic equations to control law parameters was realized through the CarSim–Simulink co-simulation method, enabling the generated initial control strategy to reflect the dynamic law of the system based on the real physical characteristics, and providing effective initial values ​​and performance benchmarks for subsequent optimization of control parameters.

[0131] S3. Based on the initial control strategy, the PID controller is optimized using the PSO-BO hybrid optimization algorithm to obtain the control strategy;

[0132] Specifically, in the optimization of control strategies for existing steer-by-wire systems, global optimization methods such as genetic algorithms (GA), particle swarm optimization (PSO), or differential evolution (DE) are commonly used. However, when applied to systems with strong nonlinear factors such as backlash, friction, and feedback coupling, traditional algorithms have significant limitations. First, traditional optimization algorithms rely on large-scale population search, requiring complete simulation for each set of parameters, resulting in high computational costs and slow convergence. Second, since the performance index function is usually multi-peaked, the algorithm is prone to getting trapped in local optima in later iterations, leading to a decline in control performance. Third, these algorithms are sensitive to noise and model uncertainty, lack the ability to probabilistically model the performance function, and have insufficient stability of optimization results. Finally, traditional methods often only optimize the PID gain at a single point, without considering the coupling and matching between the control law and the dynamic characteristics of the execution system, resulting in the theoretically optimal parameters performing poorly in practical systems.

[0133] To address the technical problems of the aforementioned global optimization methods, this embodiment employs a combined algorithm of PID control and PSO-BO hybrid optimization to optimize the initial control strategy. Within the PID control framework, this method utilizes Particle Swarm Optimization (PSO) for global search, followed by Bayesian Optimization (BO) for local fine-tuning. The PSO algorithm, through its collaborative mechanism, possesses excellent global optimization capabilities, enabling rapid location of near-optimal regions in a multi-dimensional parameter space. Subsequently, the BO algorithm, based on a Gaussian process model, predicts the distribution trend of the performance function and establishes an Acquisition Function to perform precise sampling and optimization within the preferred region determined by PSO, thereby further improving parameter optimization accuracy. Furthermore, the PID control structure offers engineering advantages such as simplicity, stability, and ease of implementation. Combined with PSO-BO hybrid optimization, it can achieve adaptive parameter optimization and performance self-tuning while maintaining controller structural stability.

[0134] In this embodiment, the PID controller is the outer control unit, responsible for outputting drive signals based on the deviation between the target steering angle and the feedback angle. The linear steering actuation system is the inner power unit, converting the control signals into physical angle changes. The linear steering actuation system exhibits nonlinear characteristics due to backlash and feedback coupling; these nonlinearities are fed back to the PID controller through the system's dynamic equations. Therefore, during optimization, the PSO-BO hybrid algorithm does not directly optimize the motor's movement, but rather indirectly corrects the actuation system's response characteristics by adjusting the PID controller parameters.

[0135] Therefore, S3 includes:

[0136] S3-1. Based on the dynamic equations and initial control strategy, establish a closed-loop control model of the linear steering execution system in the Simulink environment;

[0137] Specifically, the initial control strategy is a set of initial control parameters and control logic obtained from the dynamic equations in simulation. For example, it determines how the motor should follow the direction of turn, how quickly to respond, and how to distribute torque. A PID controller is a method for implementing this control logic, automatically adjusting the control input based on the error (the difference between the target angle and the actual angle). The initial control strategy is essentially an "initial version of PID control," only the parameters (proportional, integral, and derivative) have not yet been optimized. In other words, the initial control strategy is the starting point for PID control, while the PID algorithm is the tool for implementing and optimizing this control strategy.

[0138] The closed-loop control model uses a PID controller as its core, with the input signal being the steering angle command and the output signal being the actual steering angle. Closed-loop control is achieved by comparing the error between the two. The PID control parameters (proportional gain, integral gain, and derivative gain) are provided by the initial control strategy and serve as the initial solution for subsequent optimization.

[0139] S3-2. Run the closed-loop control model, obtain the simulation output results, calculate the initial performance index and normalize it to generate the performance index.

[0140] It should be noted that, to comprehensively reflect the dynamic characteristics and control performance of the linear steering actuator under closed-loop control, the initial performance indicators include dynamic speed indicators (rise time), dynamic stability indicators (overshoot), tracking accuracy indicators (steady-state error), stable convergence speed (setup time), and backlash influence. Among these, rise time refers to the time required for the closed-loop control model output to reach its steady-state value, reflecting the response speed of the closed-loop system; overshoot refers to the maximum magnitude by which the closed-loop system output first exceeds the steady-state value, reflecting the smoothness of the system's transient response; steady-state error refers to the deviation between the target angle and the actual angle when the closed-loop system reaches steady state, reflecting control accuracy; and backlash influence indicates the degree of impact on output accuracy and dynamic response when mechanical backlash (such as gear backlash or coupling backlash) exists in the closed-loop system. It reflects the degree to which backlash disrupts the tracking accuracy, commutation smoothness, and force transmission continuity of the closed-loop control model, and is a comprehensive indicator for measuring the system's mechanical nonlinear characteristics.

[0141] S3-2-1. Run the closed-loop control model, generate simulation output results, and determine the time required for the output of the linear steering actuator to reach the steady-state value, which is used as a dynamic speed index. In this embodiment, the dynamic speed index is the time required for the output of the linear steering actuator to rise from 10% to 90% of the steady-state value.

[0142] S3-2-2. Based on the simulation output results, calculate the proportion by which the maximum peak value of the linear steering actuation system exceeds the steady-state value, and use it as a dynamic stability index.

[0143] S3-2-3. Based on the simulation output results, calculate the time required for the output of the linear steering execution system to enter the steady-state error band, and use it as the stable convergence speed; in this embodiment, the settings of the steady-state value and the steady-state error band are determined according to the actual situation.

[0144] S3-2-4. Based on the simulation output results, calculate the absolute value of the difference between the output of the linear steering actuation system and the target output, and use it as an indicator of tracking accuracy.

[0145] S3-2-5. Based on the simulation output results, calculate the proportion of time when the torque is zero and the motor angular velocity changes in the linear steering system, and use this as the degree of backlash influence.

[0146] Specifically, when studying the impact of backlash on linear steering systems, the core focus is on quantitatively describing the "idle travel" effect caused by backlash. Backlash is not directly reflected in the absolute value of force or angle, but rather manifests through dynamic behavior: when the angle of the system input (motor or reduction gear output shaft) changes, but the output (rack or front wheel) has not yet responded and the torque transmission path has not been established, the system is in a state of "motor moving, load not moving, torque near zero." Therefore, the degree of backlash influence can be defined as the proportion of time this state occurs throughout the entire simulation cycle; that is, the longer its duration and the higher its frequency, the greater the interference of backlash on system control. This method identifies the backlash effect through system dynamic characteristics rather than geometric parameters, using motor angular velocity as the criterion for "angle change" and near-zero transmitted torque as the criterion for "ineffective engagement," thereby dynamically and quantitatively characterizing the degree of backlash influence during system operation.

[0147] Therefore, the degree of influence of backlash The corresponding formula is:

[0148] ;

[0149] ;

[0150] in, This indicates the duration during which the linear steering system experiences zero torque and a change in motor angular velocity. Indicates the total simulation duration. Represents absolute value. This indicates an indicator function (it takes the value 1 if the condition is met, and 0 otherwise). This indicates the integration operation. Indicates the torque threshold. This represents the minimum speed threshold at which the motor's angular velocity changes. In practice, torque only needs to be close to 0 to be considered as zero; that is, when the torque is less than the torque threshold, the torque is determined to be zero.

[0151] S3-2-6. Normalize the dynamic speed index, dynamic stability index, tracking accuracy index, stable convergence speed, and backlash influence to generate performance indicators.

[0152] S3-3. Based on performance indicators, construct a comprehensive performance objective function through weighted summation. The corresponding formula is:

[0153] ;

[0154] in, Indicates the first Each performance metric weight, Indicates the first One performance metric, This represents the minimum value function.

[0155] S3-4. Based on the comprehensive performance objective function, the PSO optimization algorithm is used to perform a global parameter search to generate a preliminary set of optimal solutions for the PID controller parameters.

[0156] S3-4 includes:

[0157] S3-4-1. Initialize the particle swarm, set the particle swarm size and maximum number of iterations; the position vector of each particle represents a set of PID controller parameters.

[0158] S3-4-2. Input each particle into the closed-loop control model and calculate the corresponding fitness based on the comprehensive performance objective function.

[0159] S3-4-3. Based on fitness, iterate the velocity and position of the particle swarm until the maximum number of iterations is reached or the convergence condition is met, to obtain the preliminary optimal solution set of the PID controller parameters.

[0160] Specifically, in each iteration, fitness is used to guide the search direction. For each particle, it is determined whether the current fitness is smaller than the historical best position of each particle. If so, the current fitness is taken as the individual best position of that particle; otherwise, the historical best position is taken as the individual best position. Then, the particle with the smallest current fitness is found from the particle swarm and taken as the global best position. Based on the individual best position and the global best position, the velocity and position vectors of each particle are updated using the velocity and position update formulas of the traditional PSO algorithm, and the iteration count is incremented by 1. The process of updating the velocity and position vectors is repeated until the number of iterations reaches the maximum number of iterations, or the global best fitness is less than a set threshold (convergence condition). The global best position is then taken as the initial optimal solution set for the PID controller parameters. The initial value of the iteration count is 0.

[0161] S3-5. Using the initial optimal solution set as the search boundary, perform local optimization using the BO optimization algorithm to generate a control strategy.

[0162] S3-5 includes:

[0163] S3-5-1. Use the preliminary optimal solution set as the search boundary, and use the preliminary optimal solution set and its fitness as the initial sample set;

[0164] Specifically, the Bayesian optimization algorithm is ensured to search within the search boundary to avoid saturation, oscillation, or numerical divergence of the actuator. The preliminary optimal solution set and corresponding fitness obtained by particle swarm optimization (PSO) are used as the initial sample set for Bayesian optimization, providing a reference starting point for subsequent local optimization.

[0165] S3-5-2. Construct and run a surrogate model using the Gaussian process regression method to obtain the predicted mean and variance;

[0166] Specifically, the surrogate model is the core of Bayesian optimization. It establishes a probabilistic mapping relationship between input and output through Gaussian Process Regression (GPR): the input is the combination of PID parameters, and the output is the comprehensive performance objective function value. The role of the surrogate model is to predict the system performance at new parameter points without rerunning complex simulations, and to provide the predicted mean (expected performance) and variance (prediction uncertainty), thus providing a basis for subsequent intelligent sampling.

[0167] S3-5-3. Based on the predicted mean and variance, construct a sampling function, and adaptively sample the initial sample set based on the sampling function to obtain candidate parameters;

[0168] Specifically, an acquisition function is constructed based on the predicted mean and variance of the surrogate model. This acquisition function can employ methods such as Expected Improvement (EI) or Upper Confidence Bound (UCB). The acquisition function comprehensively considers both the predicted mean (representing performance potential) and variance (representing exploratory value), dynamically selecting the next set of candidate parameter points in the parameter space to achieve a balance between exploration and utilization. The optimal point of the acquisition function is the parameter combination for the next simulation verification, outputting the candidate parameters.

[0169] S3-5-4. Apply the candidate parameters to the closed-loop control model and calculate the comprehensive performance objective function using the same method as S3-1 and S3-3.

[0170] S3-5-5: Add the comprehensive performance objective function obtained in S3-5-4 to the initial sample set, and repeat S3-5-1 to S3-5-4 until the preset number of iterations is reached or the improvement of the comprehensive performance objective function in several consecutive iterations is lower than the set threshold, and obtain the optimal parameters.

[0171] In Bayesian optimization, setting the "several iterations" too small may lead to spurious convergence, briefly trapping the system in a local equilibrium region instead of achieving the global optimum. Conversely, setting it too large can result in redundant computation, prolonging optimization time but offering limited performance improvement. To ensure convergence stability while maintaining computational efficiency and avoiding performance saturation due to excessive iterations, in this embodiment, if the improvement in the overall performance objective function after five consecutive iterations is less than a set threshold, the optimization process is considered converged, and the current optimal PID parameters are output as the optimal parameters.

[0172] S3-5-6. Apply the optimal parameters to the PID controller to generate the corresponding drive signal and send it to the linear steering execution system to generate the control strategy.

[0173] This embodiment combines PID control algorithm with PSO-BO hybrid optimization algorithm, achieving intelligent and efficient control parameter optimization process while ensuring the simplicity of the control system structure, significantly shortening the parameter optimization time. By combining global and local optimization, it effectively improves the global optimality and stability of the optimization results, significantly enhancing the dynamic response speed and steady-state accuracy of the linear steering actuator, and improving the system's robustness under complex conditions such as backlash, friction, and feedback coupling. Furthermore, this optimization framework has adaptive parameter update capabilities, enabling online correction and intelligent optimization of the control strategy under different operating conditions.

[0174] S4. Construct simulation environments under different operating conditions, simulate control strategies under different operating conditions, and obtain simulation results;

[0175] Since performance optimization in stage S3 was performed only in a single simulation environment, it cannot directly reflect the stability performance of the steer-by-wire system under complex actual operating conditions. In other words, it is difficult to demonstrate the true dynamic characteristics of the steer-by-wire system under different loads, friction, backlash, and external disturbances. Therefore, stage S4 sets up simulation environments under different operating conditions to perform multi-scenario simulations of the control strategy. This allows for a quantitative evaluation of the steer-by-wire system's response consistency and stability margin changes under parameter variations and external disturbances, thereby verifying the robust stability of the control strategy under complex nonlinear conditions and ensuring its reliability and universality in real-world operating environments.

[0176] Therefore, S4 includes:

[0177] S4-1. Select a representative set of working condition parameters and set different working conditions; the representative set of working condition parameters includes road adhesion coefficient, steering damping coefficient, load inertia, backlash size and command change rate, etc.

[0178] S4-2. Construct a full closed-loop simulation model including a linear steering actuation system and a PID controller in the Simulink and CarSim co-simulation platform;

[0179] S4-3. Based on the control strategy, the linear steering system is simulated under different working conditions using a full closed-loop simulation model to obtain the simulation results of the linear steering system, i.e., the simulation results for each working condition. Each simulation result includes parameters such as the corresponding output signal (actual steering angle of the wheel), angle response (deviation between the actual displacement angle of the rack and the target displacement angle), torque transmission (torque transmitted between components), and speed change (angular velocity of the motor or rack).

[0180] A torque signal refers to the change in torque values ​​transmitted between different components (such as motors, racks, and reduction gears) in a linear steering system over time. These torque values ​​change over time to form a signal, which can be represented as a time-varying sequence.

[0181] S5. Based on the simulation results, calculate the stability under different working conditions, and generate stability evaluation results by combining the stability judgment criteria.

[0182] S5 includes:

[0183] S5-1. Calculate the integral of the deviation between the actual displacement angle and the target displacement angle of the rack under each working condition, and use it as the angle error integral for each working condition; where the angle error integral is used to reflect the accumulation of error, the smaller the value, the higher the tracking accuracy of the linear steering actuator.

[0184] S5-2. Calculate the standard deviation of the angular velocity of the motor or rack under each working condition, and use it as the speed variation fluctuation under each working condition; the smaller the speed variation fluctuation, the more stable the dynamic response of the linear steering actuator.

[0185] S5-3. Select the maximum and minimum torque signals for each working condition, and calculate the average value of the torque signals for each working condition;

[0186] S5-4. Based on the average value of each torque signal, each maximum torque signal, and each minimum torque signal, calculate the torque fluctuation index for each working condition;

[0187] Specifically, the difference between the maximum and minimum torque signals for each operating condition is calculated. The ratio of each difference to the average torque signal for the corresponding operating condition is then used as the torque fluctuation index. The smaller the torque fluctuation index, the smoother the force transmission of the linear steering system.

[0188] S5-5. The stability of the control strategy is obtained by weighted summation and mean calculation of the integral of the angle error, the speed change fluctuation and the torque fluctuation index for each working condition.

[0189] S5-6. Based on stability and stability judgment criteria, generate stability evaluation results for the control strategy.

[0190] Specifically, based on the stability assessment criteria, the stability of the current control strategy is evaluated to determine whether it meets the application requirements. If the stability does not meet the requirements, it is necessary to return to S3 for readjustment.

[0191] In this embodiment, due to the nature of the integral of angle error, the fluctuation of speed change, and the exponential of torque fluctuation, the smaller the corresponding stability, the better. This indicates a more excellent control strategy, meaning that the linear steering system has lower errors, fluctuations, and instabilities under all operating conditions. Therefore, the stability judgment criterion is:

[0192] If the stability is less than 0.2, it means the control strategy can be used directly, has excellent performance, and is beneficial to the stability of the linear steering execution system. Otherwise, it is necessary to return to S3 for re-optimization.

[0193] In summary, this invention comprehensively evaluates the stability and robustness of a linear steering actuation system by simulating different operating conditions in a Simulink and CarSim co-simulation platform. It also quantitatively assesses the stability of the control strategy by weighted summation of multiple performance indicators (such as angle error integral, speed variation fluctuation, and torque fluctuation index). With clear stability judgment criteria, the system can quickly determine whether the control strategy meets application requirements. If not, it returns to the optimization stage for adjustment through a feedback mechanism, thereby ensuring the stability and reliability of the control system under various complex operating conditions, improving system performance, accuracy, and safety, and ensuring its adaptability to practical application needs.

[0194] like Figure 3 As shown, a stability evaluation system for a linear steering actuation system includes:

[0195] The dynamics construction module is used to collect the operating parameters of the vehicle's linear steering system and construct the dynamic equations of the linear steering system through the nonlinear mechanical principles and frictional principles of mechanical transmission; the linear steering system includes a steering motor, a reduction mechanism, and an actuator;

[0196] The first strategy module is used to simulate the linear steering actuation system based on the dynamic equations and generate an initial control strategy using the CarSim-Simulink co-simulation method.

[0197] The second strategy module is used to optimize the PID controller based on the initial control strategy using the PSO-BO hybrid optimization algorithm to obtain the control strategy.

[0198] The simulation module is used to build simulation environments under different operating conditions, simulate control strategies under different operating conditions, and obtain simulation results.

[0199] The stability evaluation module is used to calculate the stability under different operating conditions based on the simulation results, and generate stability evaluation results by combining the stability judgment criteria.

[0200] The dynamics building module includes:

[0201] The data acquisition unit is used to collect the operating parameters of the vehicle's linear steering system.

[0202] The steering mechanism unit is used to construct the electrical equations, electromagnetic torque equations, and motor layer rotational dynamics equations of the steering actuator motor based on operating parameters, electromagnetic principles, and Newton's second law, thereby generating a dynamic model of the steering actuator motor.

[0203] The speed reduction mechanism unit is used to construct a dynamic model of the speed reduction mechanism based on operating parameters and the kinematic and dynamic equivalence principles of gear transmission.

[0204] The rack displacement element is used to construct a rack linear displacement dynamic model based on operating parameters, the nonlinear mechanical principle of mechanical transmission, and the tribological principle.

[0205] The dynamics building unit is used to generate the dynamic equations of the linear steering system based on the dynamics model of the steering actuator motor, the dynamics model of the reduction mechanism, and the dynamics model of the rack linear displacement.

[0206] The second strategy module includes:

[0207] Closed-loop control unit, used to build a closed-loop control model of a linear steering actuation system in the Simulink environment based on dynamic equations and initial control strategy;

[0208] The performance index unit is used to run the closed-loop control model, obtain the simulation output results, calculate the initial performance index, normalize it, and generate the performance index.

[0209] The objective function unit is used to construct a comprehensive performance objective function based on performance metrics through weighted summation.

[0210] The initial optimization unit is used to perform a global parameter search based on the comprehensive performance objective function using the PSO optimization algorithm to generate a preliminary set of optimal solutions for the PID controller parameters.

[0211] The secondary optimization unit is used to take the initial optimal solution set as the search boundary and perform local optimization through the BO optimization algorithm to generate a control strategy.

[0212] The performance indicator unit includes:

[0213] The speed index subunit is used to run the closed-loop control model, generate simulation output results, and determine the time required for the output of the linear steering actuation system to reach the steady-state value, which is then used as a dynamic speed index.

[0214] The stability index subunit is used to calculate the proportion by which the maximum peak value of the output of the linear steering execution system exceeds the steady-state value based on the simulation output results, and to serve as a dynamic stability index.

[0215] The stable convergence subunit is used to calculate the time required for the output of the linear steering actuation system to enter the steady-state error band based on the simulation output results, and to use this as the stable convergence speed.

[0216] The tracking accuracy subunit is used to calculate the absolute value of the difference between the output of the linear steering actuation system and the target output based on the simulation output results, and use it as a tracking accuracy index.

[0217] The backlash influence subunit is used to calculate the proportion of time when the linear steering system experiences zero torque and changes in motor angular velocity based on the simulation output results, and to use this as the degree of backlash influence.

[0218] The normalization sub-unit is used to normalize the dynamic speed index, dynamic stability index, tracking accuracy index, stable convergence speed, and backlash influence to generate performance indicators.

[0219] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0220] Example 2:

[0221] Setting up condition 1 as a step steering input simulates the actual road conditions when a vehicle turns at an intersection. The step steering input can be used to describe the instantaneous characteristics of the system, thereby judging the dynamic performance of the control system. The front wheel steering angle range of a vehicle generally does not exceed 45°, therefore, 10°, 30°, and 45° front wheel steering angles are set as inputs. The vehicle speed is set to 40 km / h, the road surface adhesion coefficient is 0.85, the simulation time is 1 second, and this invention is used for processing.

[0222] like Figure 4 , Figure 5 and Figure 6 As shown, regardless of whether the input is a small or large angle, the optimization of the PID controller by the hybrid algorithm combining PSO and BO can achieve good angle tracking performance. The response time of the steering execution system to reach the desired target is within 100ms, and there is no overshoot, which is better than traditional PID control.

[0223] Example 3:

[0224] Because real-world driving conditions often involve complex road scenarios requiring repeated left and right turns to avoid multiple obstacles, the performance requirements for linear steering systems are high. Therefore, a sinusoidal steering scenario was selected as scenario 2. To cover different driving scenarios, a city road scenario was tested at a speed of 72 km / h, and a highway scenario was tested at a speed of 100 km / h, resulting in two scenarios.

[0225] Scenario 1: The vehicle speed is set to 72km / h and the road surface adhesion coefficient is 0.85.

[0226] Scenario 2: The vehicle speed is set to 100km / h and the road surface adhesion coefficient is 0.85.

[0227] During the verification process, the expected value of the front wheel steering angle was 5sin(0.6t), and the simulation time was 20s. The present invention was used for optimization under the conditions of scenario 1 and scenario 2.

[0228] Depend on Figure 7 , Figure 8 , Figure 9 and Figure 10 It can be seen that, under different vehicle speed conditions, the front wheel steering angle and front wheel steering angle error optimized by the present invention are both kept within ±0.12°, while the front wheel steering angle error under the traditional method is within ±0.19°. This indicates that the PSO–BO hybrid optimization algorithm of the present invention can have better steering angle tracking performance.

[0229] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0230] 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 technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A stability evaluation method for a linear steering execution system, characterized by, include: The operating parameters of the vehicle's linear steering system are collected, and the dynamic equations of the linear steering system are constructed through the nonlinear mechanical principles and tribological principles of mechanical transmission. The linear steering system includes a steering motor, a reduction mechanism, and an actuator. Based on the dynamic equations, the linear steering actuation system is simulated using the CarSim-Simulink co-simulation method to generate an initial control strategy; Based on the initial control strategy, initial performance indicators are calculated and normalized to generate performance indicators. The PID controller is then optimized using the PSO-BO hybrid optimization algorithm to obtain the control strategy. The initial performance indicators include dynamic speed indicators, dynamic stability indicators, tracking accuracy indicators, stable convergence speed, and backlash influence. Construct simulation environments under different operating conditions, simulate control strategies under different operating conditions, and obtain simulation results; Based on the simulation results, the stability under different working conditions is calculated, and the stability evaluation results are generated by combining the stability judgment criteria. The dynamic equations for constructing the linear steering actuation system include: Collect the operating parameters of the vehicle's linear steering system; Based on operating parameters, electromagnetic principles and Newton's second law, the electrical equations, electromagnetic torque equations and motor layer rotational dynamics equations of the steering actuator motor are constructed to generate a dynamic model of the steering actuator motor. Based on the operating parameters, and combined with the kinematic principles and dynamic equivalence principles of gear transmission, a dynamic model of the reduction mechanism is constructed. Based on operating parameters, the nonlinear mechanical principle of mechanical transmission, and the tribological principle, a rack linear displacement dynamic model is constructed. Based on the dynamics model of the steering actuator motor, the dynamics model of the reduction mechanism, and the dynamics model of the rack linear displacement, the dynamic equations of the linear steering system are generated. Tooth gap influence degree The corresponding formula is: ； ； in, This indicates the duration during which the linear steering system experiences zero torque and a change in motor angular velocity. Indicates the total simulation duration. Represents absolute value. Indicates an indicator function, This indicates the integration operation. Indicates the torque threshold. This represents the minimum speed threshold for determining if the motor's angular velocity is changing. Indicates at time Torque is transmitted downwards. Indicates at time The first derivative of the downward motor angle.

2. The stability evaluation method for a linear steering execution system according to claim 1, characterized by, The obtained control strategy includes: Based on the dynamic equations and initial control strategy, a closed-loop control model of a linear steering actuation system is established in the Simulink environment; Run the closed-loop control model, obtain the simulation output results, calculate the initial performance index and normalize it to generate the performance index; Based on performance metrics, a comprehensive performance objective function is constructed by weighted summation. Based on the comprehensive performance objective function, the PSO optimization algorithm is used to perform global parameter search and generate a preliminary set of optimal solutions for the PID controller parameters. Using the initial optimal solution set as the search boundary, the BO optimization algorithm is used for local optimization to generate a control strategy.

3. The stability evaluation method for a linear steering execution system according to claim 2, characterized by The generated performance metrics include: Run the closed-loop control model, generate simulation output results, and determine the time required for the output of the linear steering actuator to reach the steady-state value, which is then used as a dynamic speed indicator. Based on the simulation output results, the proportion by which the maximum peak value of the linear steering execution system exceeds the steady-state value is calculated and used as a dynamic stability index. Based on the simulation output results, the time required for the output of the linear steering actuation system to enter the steady-state error band is calculated and used as the stable convergence speed; Based on the simulation output results, the absolute value of the difference between the output of the linear steering execution system and the target output is calculated and used as an indicator of tracking accuracy. Based on the simulation output, the proportion of time when the torque is zero and the motor angular velocity changes in the linear steering system is calculated, and this proportion is used as the degree of backlash influence. The dynamic speed index, dynamic stability index, tracking accuracy index, stable convergence speed, and backlash influence are normalized to generate performance indicators.

4. The stability evaluation method for a linear steering execution system according to claim 1, characterized by The obtained simulation results include: Select a representative set of operating parameters and set different operating conditions; In the Simulink and CarSim co-simulation platform, a full closed-loop simulation model including a linear steering actuation system and a PID controller was constructed. Based on the control strategy, the simulation is carried out under different operating conditions using a full closed-loop simulation model to obtain the simulation results for each operating condition.

5. The stability evaluation method for a linear steering execution system according to claim 1, characterized by The generated stability evaluation results include: Calculate the integral of the deviation between the actual displacement angle and the target displacement angle of the rack under each working condition, and use it as the integral of the angle error for each working condition; Calculate the standard deviation of the angular velocity of the motor or rack under each working condition, and use it as the velocity variation fluctuation under each working condition; Select the maximum and minimum torque signals for each working condition, and calculate the average torque signal value for each working condition; Based on the average value of each torque signal, each maximum torque signal, and each minimum torque signal, the torque fluctuation index for each operating condition is calculated. The stability of the control strategy is obtained by weighted summation and mean calculation of the integral of angle error, speed change fluctuation and torque fluctuation index under each working condition; Based on stability and stability judgment criteria, stability evaluation results of the control strategy are generated.

6. A stability evaluation system for a linear steering actuation system, used to implement the stability evaluation method for a linear steering actuation system according to any one of claims 1 to 5, characterized in that, include: The dynamics construction module is used to collect the operating parameters of the vehicle's linear steering system and construct the dynamic equations of the linear steering system through the nonlinear mechanical principles and frictional principles of mechanical transmission; the linear steering system includes a steering motor, a reduction mechanism, and an actuator; The first strategy module is used to simulate the linear steering actuation system based on the dynamic equations and generate an initial control strategy using the CarSim-Simulink co-simulation method. The second strategy module is used to optimize the PID controller based on the initial control strategy using the PSO-BO hybrid optimization algorithm to obtain the control strategy. The simulation module is used to build simulation environments under different operating conditions, simulate control strategies under different operating conditions, and obtain simulation results. The stability evaluation module is used to calculate the stability under different operating conditions based on the simulation results, and generate stability evaluation results by combining the stability judgment criteria.

7. A stability evaluation system for a linear steering actuation system according to claim 6, characterized in that, The dynamics building module includes: The data acquisition unit is used to collect the operating parameters of the vehicle's linear steering system. The steering mechanism unit is used to construct the electrical equations, electromagnetic torque equations, and motor layer rotational dynamics equations of the steering actuator motor based on operating parameters, electromagnetic principles, and Newton's second law, thereby generating a dynamic model of the steering actuator motor. The speed reduction mechanism unit is used to construct a dynamic model of the speed reduction mechanism based on operating parameters and the kinematic and dynamic equivalence principles of gear transmission. The rack displacement element is used to construct a rack linear displacement dynamic model based on operating parameters, the nonlinear mechanical principle of mechanical transmission, and the tribological principle. The dynamics building unit is used to generate the dynamic equations of the linear steering system based on the dynamics model of the steering actuator motor, the dynamics model of the reduction mechanism, and the dynamics model of the rack linear displacement.

8. A stability evaluation system for a linear steering actuation system according to claim 6, characterized in that, The second strategy module includes: Closed-loop control unit, used to build a closed-loop control model of a linear steering actuation system in the Simulink environment based on dynamic equations and initial control strategy; The performance index unit is used to run the closed-loop control model, obtain the simulation output results, calculate the initial performance index, normalize it, and generate the performance index. The objective function unit is used to construct a comprehensive performance objective function based on performance metrics through weighted summation. The initial optimization unit is used to perform a global parameter search based on the comprehensive performance objective function using the PSO optimization algorithm to generate a preliminary set of optimal solutions for the PID controller parameters. The secondary optimization unit is used to take the initial optimal solution set as the search boundary and perform local optimization through the BO optimization algorithm to generate a control strategy.

9. A stability evaluation system for a linear steering actuation system according to claim 8, characterized in that, The performance indicator unit includes: The speed index subunit is used to run the closed-loop control model, generate simulation output results, and determine the time required for the output of the linear steering actuation system to reach the steady-state value, which is then used as a dynamic speed index. The stability index subunit is used to calculate the proportion by which the maximum peak value of the output of the linear steering execution system exceeds the steady-state value based on the simulation output results, and to serve as a dynamic stability index. The stable convergence subunit is used to calculate the time required for the output of the linear steering actuation system to enter the steady-state error band based on the simulation output results, and to use this as the stable convergence speed. The tracking accuracy subunit is used to calculate the absolute value of the difference between the output of the linear steering actuation system and the target output based on the simulation output results, and use it as a tracking accuracy index. The backlash influence subunit is used to calculate the proportion of time when the linear steering system experiences zero torque and changes in motor angular velocity based on the simulation output results, and to use this as the degree of backlash influence. The normalization sub-unit is used to normalize the dynamic speed index, dynamic stability index, tracking accuracy index, stable convergence speed, and backlash influence to generate performance indicators.

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