Electric vehicle time-varying optimal slip ratio prediction and control method based on time delay characteristics

Abstract

The present application relates to the technical field of vehicle electronic control, in particular to a time-varying optimal slip rate prediction and control method for electric vehicles based on time delay characteristics. The time-varying optimal slip rate prediction method in the present application takes the utilization adhesion coefficient, real-time slip rate and time delay factor of the current section as input, combines the known parameters of the reference section, and accurately calculates the time-varying optimal slip rate with the help of the correlation function. The motor braking torque calculation method based on the time-varying optimal slip rate takes the predicted time-varying optimal slip rate as the control target, first establishes a state space equation with the slip rate and its first derivative as state variables and the motor braking torque as the control variable, and discretizes it into a model suitable for digital control, then constructs a cost function that minimizes the slip rate tracking error and torque jump at the same time, obtains the optimal motor braking torque sequence by optimization, and finally outputs the first control variable in the sequence to realize accurate braking of the vehicle.

Description

A Time-Varying Optimal Slip Ratio Prediction and Control Method for Electric Vehicles Based on Time Delay Characteristics Technical Field

[0001] This invention relates to the field of vehicle electronic control technology, specifically to a time-varying optimal slip ratio prediction and control method for electric vehicles based on time delay characteristics. Background Technology

[0002] In the control strategies of vehicle anti-lock braking systems (ABS) and traction control systems (TCS), accurately obtaining and tracking the optimal slip ratio under current road conditions is crucial for improving braking performance, shortening braking distance, and ensuring driving stability. Currently, the determination of the optimal slip ratio mainly relies on the tire slip ratio-coefficient of adhesion relationship curve. This curve is typically described using classical static models, such as the Burckhardt model and the Magic Formula model, and its general form can be expressed as follows: (t)= ( (t)), where (t) represents the adhesion coefficient at time t. (t) represents the slip ratio at time t. (·) represents the corresponding function. Based on this type of static model, the existing methods for calculating the optimal slip ratio mainly include curve fitting and peak search: by collecting a series of corresponding data of slip ratio and adhesion coefficient during braking, a static curve is fitted, and then the slip ratio corresponding to the peak point of the curve is determined by differentiation or optimization algorithm, that is, the static optimal slip ratio.

[0003] However, tires exhibit significant dynamic time lag characteristics during real-world braking. Due to the viscoelasticity of tire rubber materials, the flexibility of the tire carcass structure, and the physical inertia of the force transmission between the tire tread and the road surface, the tire's mechanical response does not instantaneously follow changes in the slip ratio, but rather exhibits a certain dynamic lag. This means that during actual dynamic braking, there is a difference between the instantaneous coefficient of adhesion exhibited by the tire and the coefficient of adhesion calculated based on the current slip ratio using a static model. This time lag phenomenon means that the "optimal slip ratio" determined by the static model only represents a steady-state theoretical value and cannot accurately reflect the actual optimal operating point of the braking system during dynamic transient processes.

[0004] Under dynamic braking conditions, especially when the slip ratio changes rapidly, the optimal slip ratio calculated based on the static model will deviate from the instantaneous optimal slip ratio that the tire can currently provide maximum adhesion. If the controller uses this uncertain value as a target for tracking control, the system will not truly operate at its dynamic optimal condition, thus losing some braking potential. Because the target value being tracked (the static optimal slip ratio) itself does not reflect the dynamic characteristics of the system, the design of controllers (such as PID, sliding mode control, etc.) is difficult to achieve accurate and rapid tracking of the dynamic optimal point. This may lead to reduced braking efficiency, increased braking distance, or, on surfaces with sudden changes in the coefficient of friction, increased susceptibility to wheel lock-up or drive slippage.

[0005] It is evident that the existing methods for calculating the optimal slip ratio based on static models suffer from technical defects, such as low calculation accuracy and difficulty in matching the actual optimal working conditions of dynamic braking processes, because they do not consider the inherent dynamic time delay characteristics of tires. Summary of the Invention

[0006] To address the technical problem of low accuracy in calculating the optimal slip ratio due to neglecting the inherent dynamic time lag characteristics of tires, this invention provides a time-varying optimal slip ratio prediction method based on dynamic time lag characteristics. Based on the optimal slip ratio calculated using this method, this invention also provides a method, system, and electric vehicle for calculating motor braking torque.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A time-varying optimal slip ratio prediction method based on dynamic time delay characteristics includes:

[0009] Based on the vehicle's adhesion coefficient μ at the current time and on the current road segment i Real-time slip ratio λ i and the time delay factor ε characterizing dynamic time delay properties dyn Calculate the time-varying optimal slip ratio λ for the current road segment. bi ;

[0010]

[0011]

[0012]

[0013] In the formula, λ b0 μ represents the optimal slip ratio of the reference section. b0represents the maximum adhesion coefficient of the reference road segment, which is any road segment with a known static slip ratio-adhesion coefficient curve; arctan(·) represents the arctangent function; p(·) represents a function containing the first derivative; express The first derivative of ; h(·) represents the compensation function.

[0014] As a further improvement to the above scheme: λ bi The corresponding predicted time-varying maximum adhesion coefficient is:

[0015]

[0016] In the formula, μ bi This represents the predicted time-varying maximum adhesion coefficient for the current road segment.

[0017] As a further improvement to the above scheme: ε dyn These are either fixed values ​​pre-calibrated through experiments or dynamic values ​​updated in real time based on the tire's operating conditions.

[0018] As a further improvement to the above scheme: when ε in the current road segment dyn When is a dynamic value, its update is as follows:

[0019]

[0020]

[0021]

[0022]

[0023] In the formula, ε dyn (t) represents the time delay factor of the current road segment at time t; μ dyn (t) represents the dynamic output of the adhesion coefficient at time t in the current road segment; r s (t) represents the polar radius of the static model corresponding to the current road segment at time t; θ(t) represents the polar angle θ at time t; τ is the time delay constant; μ(t) represents the utilization adhesion coefficient of the current road segment at time t; λ(t) represents the real-time slip ratio of the current road segment at time t; A, B, C, D, E, A0, B0, C0, D0, and E0 are the corresponding equation coefficients.

[0024] This invention also provides a method for calculating motor braking torque based on time-varying optimal slip ratio, comprising:

[0025] The time-varying optimal slip ratio λ is calculated using the time-varying optimal slip ratio prediction method based on dynamic time delay characteristics described above. bi As the target for controlling the slip ratio of the current road section;

[0026] Based on the wheel angular velocity and moment of inertia, a state-space equation is established with slip ratio and its first derivative as state variables and motor braking torque as control variables, and it is discretized into a state-space model: x(t+1)=Ax(t)+Bu(t), where x(t+1) and x(t) represent the state variables at time t+1 and time t, respectively, u(t) represents the control variable at time t, and A and B are the corresponding system matrices;

[0027] A cost function is constructed for the finite prediction time domain and control time domain, and its optimization objective is to make the predicted slip rate trajectory track the slip rate control objective.

[0028] The future state of the vehicle is predicted based on the state-space model, and the optimal motor braking torque control sequence is calculated by solving the minimum cost function.

[0029] The first control variable in the optimal motor braking torque control sequence is converted into motor braking torque, which is then used to control the vehicle to perform braking.

[0030] As a further improvement to the above scheme, the state-space equation is:

[0031]

[0032] In the formula, The first derivative of the slip ratio λ ω is the second derivative of the slip ratio λ; r The angular velocity of the rear wheel. ω is the second derivative of the rear wheel angular velocity; f The angular velocity of the front wheel; The first derivative of the front wheel angular velocity, T is the second derivative of the front wheel angular velocity; r I is the braking torque of the motor acting on the rear wheel; I is the wheel's moment of inertia.

[0033] As a further improvement to the above scheme, the cost function is:

[0034]

[0035] In the formula, J i The cost function value; q i r i These are the weight coefficients for the corresponding terms; p t m tThese are the prediction time domain and the control time domain, respectively; y i [t+j|t] is the predicted slip ratio at time t for time t+j; y ir [t+j] is the control reference value of the slip ratio at time t+j; Δu[t+j] is the incremental value of the motor braking torque at time t+j.

[0036] As a further improvement to the above scheme: the final output is the motor braking torque T at time t. tq for:

[0037]

[0038] In the formula, u[t-1] is the value of the motor braking torque at time t-1; i0 represents the transmission ratio of the motor; η represents the mechanical efficiency of the motor; R1 represents the optimal slip ratio of the current road segment; q1 represents the weighting coefficient of the state tracking error; A 11 A 21 These represent specific elements in system matrix A; B 11 B 21 These represent specific elements in the system matrix B; r1 represents the weighting coefficient of the control variable increment.

[0039] This invention further provides a vehicle slip ratio optimization control system, applied to vehicles with electric motor braking systems, comprising:

[0040] The data acquisition module is used to acquire the vehicle's wheel speed and motor braking torque in real time, and process them to obtain the real-time slip ratio and adhesion coefficient at the current moment.

[0041] The time-varying optimal slip ratio prediction module is connected to the data acquisition module to receive real-time slip ratio and utilize the adhesion coefficient; it has pre-stored the static slip ratio-adhesion coefficient curve of the benchmark road section, as well as its optimal slip ratio and maximum adhesion coefficient, and executes a time-varying optimal slip ratio prediction method based on dynamic time delay characteristics as described above based on the time delay factor to calculate the time-varying optimal slip ratio of the current road surface.

[0042] The nonlinear model predictive control module is communicatively connected to the time-varying optimal slip ratio prediction module. It is used to execute a motor braking torque calculation method based on the time-varying optimal slip ratio as the slip ratio control target of the current road segment, as described above, to calculate the motor braking torque control command.

[0043] The drive execution module, which communicates with the nonlinear model predictive control module, is used to convert motor braking torque control commands into drive signals and output them to the vehicle's motor braking system to perform braking control.

[0044] This invention provides another electric vehicle, including a body, wheels, an electric motor braking system and a vehicle controller, characterized in that it also includes the aforementioned vehicle slip ratio optimization control system;

[0045] The vehicle slip ratio optimization control system communicates with the electric motor braking system and the vehicle controller to calculate the optimal slip ratio and corresponding electric motor braking torque based on the real-time driving status, and to perform anti-lock braking control of the vehicle through the electric motor braking system.

[0046] Compared with the prior art, the beneficial effects of the present invention are:

[0047] 1. This invention uses the current road segment's utilization adhesion coefficient and real-time slip rate as real-time inputs, combined with the time lag factor characterizing the tire's dynamic time lag characteristics, and utilizes the optimal slip rate and maximum adhesion coefficient of a benchmark road segment (a road segment with a known static slip rate-adhesion coefficient curve). Parameter correlation is established through the arctangent function related to polar coordinate transformation, and finally, through multi-parameter coupling calculation, the time-varying optimal slip rate of the current road segment is output. This achieves a quantitative consideration of the tire's dynamic time lag characteristics, requiring only a single point of real-time parameter to complete the prediction, thus balancing the real-time performance and accuracy of the prediction.

[0048] 2. The time-varying optimal slip ratio prediction method in this invention fully integrates the dynamic time-delay characteristics of the tire. By quantifying the asynchronous influence of control and output through the time-delay factor, it solves the problem that static models cannot reflect the dynamic response of the tire, significantly improving the matching degree between the predicted value and the actual working condition. On the other hand, it adopts the "baseline curve mapping + single-point parameter calculation" mode, which does not rely on a large amount of historical data or curve fitting. It can be solved using only the adhesion coefficient and real-time slip ratio at the current moment, significantly reducing the amount of data processing, improving the real-time performance of the prediction, and avoiding the lag of traditional methods. Furthermore, by introducing the first derivative of the polar angle for nonlinear compensation, combined with the fitting parameters, it accurately describes the dynamic geometric characteristics of the slip ratio-adhesion coefficient curve, ensuring the prediction accuracy. Finally, it adapts to different road surface types. Through parameter mapping of the baseline road segment (the road segment with a known static curve), it can quickly adapt to various untested road surfaces such as dry asphalt, wet asphalt, and ice and snow, solving the technical problems of poor robustness of traditional cause-based methods and the inability of response-based methods to predict in advance, providing accurate and forward-looking target references for subsequent braking control.

[0049] 3. The motor braking torque calculation method in this invention uses the time-varying optimal slip ratio as the slip ratio control target, ensuring that braking control always revolves around maximizing the road adhesion coefficient, thereby improving braking efficiency from the source and solving the problem that traditional methods have fixed control targets and cannot adapt to dynamic road surfaces. Simultaneously, a state-space equation is established with slip ratio and its first derivative as state variables and motor braking torque as the control variable, fully characterizing the dynamic characteristics of the braking system and avoiding the one-sidedness of control caused by considering only the slip ratio as a single variable. Furthermore, discretization transforms the continuous system into a model adapted to a digital controller, balancing control accuracy and real-time execution efficiency, which aligns with the rapid response characteristics of the motor braking system. Next, a cost function containing slip ratio tracking error and control variable increments is constructed, ensuring accurate tracking of the slip ratio target value while constraining sudden changes in motor braking torque, avoiding braking shocks and improving driving comfort. Finally, by solving the optimal torque control sequence and outputting the first control quantity, real-time updates of control commands are ensured, adapting to the dynamic changes of the time-varying optimal slip ratio, effectively preventing wheel lock-up or insufficient braking, and significantly improving braking safety and stability. Attached Figure Description

[0050] Figure 1 is a flowchart of the data acquisition-time-varying optimal slip ratio-prediction of optimal motor braking torque in this invention.

[0051] Figure 2 is a schematic diagram of the polar coordinate transformation principle in this invention.

[0052] Figure 3 is a schematic diagram of the principle of obtaining the time-varying optimal slip ratio in this invention.

[0053] Figure 4 is a fitting curve of slip ratio and adhesion coefficient in this invention.

[0054] Figure 5 shows the polar angle-polar radius fitting curve in this invention.

[0055] Figure 6 is a curve of slip ratio and adhesion coefficient in this invention.

[0056] Figure 7 is a graph showing the ratio of zero-point angle to polar coordinates in this invention.

[0057] Figure 8 is a graph showing the change of slip ratio over time in the first working condition of the embodiment.

[0058] Figure 9 is a graph showing the change of adhesion coefficient over time in working condition one of the embodiments.

[0059] Figure 10 is a graph showing the speed and braking distance versus time in the first working condition of the embodiment.

[0060] Figure 11 is a graph showing the changes in motor braking torque and acceleration over time in the first working condition of the embodiment.

[0061] Figure 12 is a graph showing the change of slip ratio over time in working condition 2 of the embodiment.

[0062] Figure 13 is a graph showing the change in adhesion coefficient in working condition 2 of the embodiment.

[0063] Figure 14 is a speed change curve in the second working condition of the embodiment.

[0064] Figure 15 is a graph showing the change in motor braking torque in the second working condition of the embodiment. Detailed Implementation

[0065] 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. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0066] As shown in Figure 1, this invention revolves around "data acquisition - model calculation - prediction output - control execution": The data acquisition unit acquires information such as wheel speed and motor output torque in real time, and outputs real-time data such as slip ratio and slip ratio change rate after processing; The variable-speed spiral tire model calls the stored slip ratio-adhesion coefficient curve, and generates a time-varying curve and corresponding mapping coefficients through polar coordinate mapping and time delay characteristics fusion; The time-varying optimal slip ratio predictor receives the above curve, mapping coefficients and real-time information, and outputs the time-varying optimal slip ratio through reference curve mapping and dynamic parameter calculation; The nonlinear model predictive controller uses this prediction value as a reference, combines it with the vehicle dynamics model to construct the state space equation, imports real-time angular velocity, angular acceleration and other data, solves the motor output torque control quantity by minimizing the cost function, and finally transmits the control quantity to the electric vehicle to achieve precise braking control based on the time-varying optimal slip ratio, taking into account both the tire time delay dynamic characteristics and control real-time performance throughout the entire process.

[0067] The core of the variable-speed spiral tire model is to solve the problem of accurately predicting the time-varying optimal slip ratio in braking control by integrating coordinate transformation and dynamic characteristics. This model first breaks through the limitations of the conventional Cartesian coordinate system, mapping the nonlinear stage of the slip ratio-adhesion coefficient curve to polar coordinates. A variable-speed spiral is constructed using the polar radius (distance from the pole to the real-time point) and polar angle (angle between the polar axis and the line connecting the real-time point), making the curves highly similar across different road surfaces, laying the foundation for a unified description and subsequent mapping. Then, the dynamic time-delay characteristics of the tire are incorporated. A commonly used first-order inertial time-delay model is adopted to fit the static slip ratio-adhesion coefficient curve to a fourth-order polynomial. The dynamic adhesion coefficient expression containing an explicit time-delay factor is obtained through differential and integral solving. The model is transformed into an explicit dynamic model in polar coordinates in one step, avoiding the shortcomings of implicit equations in rectangular coordinates that cannot reflect dynamic characteristics. At the same time, based on the parameter library of Burckhardt's mature tire model, it is transformed into a polar coordinate reference curve. By defining the mapping coefficient, the proportional relationship between the current road surface curve and the reference curve is established. Combined with the time lag factor, polar angle derivative and compensation function, the real-time calculation formula of the time-varying optimal slip ratio is finally derived. The predicted value can be used as the control target of the nonlinear model predictive controller, providing an accurate reference for the anti-lock braking system of electric vehicles and achieving efficient braking performance.

[0068] I. Variable speed spiral vehicle tire model

[0069] 1. Polar coordinate model transformation

[0070] In the control of anti-lock braking systems (ABS), braking performance is improved by controlling the slip ratio. Unlike the conventional rectangular coordinate system, the model based on a variable-speed spiral proposed in this invention maps the slip ratio-adhesion coefficient curve to polar coordinates, forming a variable-speed spiral. The conversion principle of the slip ratio-adhesion coefficient curve in polar coordinates is shown in Figure 2. Figure 2 illustrates the core principle of this invention in transforming the conventional rectangular coordinate relationship between slip ratio λ and adhesion coefficient μ into polar coordinates (polar radius r and polar angle θ). Here, the polar radius r represents the distance from the pole to the real-time data point, and the polar angle θ is the angle between the polar axis and the line connecting the data point. Through this conversion, the nonlinear curves of slip ratio-adhesion coefficient under different road conditions exhibit high similarity in polar coordinates, laying the foundation for establishing a unified curve description model and benchmark curve mapping, and overcoming the limitations of large differences and difficulty in unified analysis of different road surface curves under the rectangular coordinate system.

[0071] The nonlinear phase of the slip ratio-adhesion coefficient curve is transformed into a helical model, while the linear portion is excluded due to its geometric characteristics. Slip ratio λ and adhesion coefficient μ are the core parameters of braking control. In the nonlinear region, a Cartesian coordinate system is conventionally used to describe their relationship, providing a more accurate representation of the relationships between the curves.

[0072]

[0073] In the formula, μ is the adhesion coefficient, calculated from the longitudinal and vertical forces of the wheel, or indirectly measured by a sensor. λ is the slip ratio, calculated in real time from the wheel speed and vehicle speed. f(·) is the function expression in rectangular coordinates, which will be further specified using polynomial fitting.

[0074] By utilizing the geometric properties of polar coordinates, the two-dimensional rectangular coordinates (λ, μ) are transformed into polar radius r and polar angle θ, making the nonlinear curves of different road surfaces highly similar, which facilitates subsequent mapping calculations. The transformed variable-speed helical curve form is as follows:

[0075]

[0076] In the formula, r is the polar radius, representing the distance from the pole to the real-time point; θ is the polar angle, representing the angle between the polar axis and the line connecting the pole and the real-time point; g(·) is the function expression in polar coordinates.

[0077] 2. Time-delay tire model

[0078] Figure 3 illustrates the time lag phenomenon related to the optimal slip ratio. Figure 3 presents the logic for obtaining the time-varying optimal slip ratio, the core of which is distinguishing the optimal slip ratio under static and dynamic characteristics. The figure includes the static slip ratio-adhesion coefficient curve, the time-varying curve, the static optimal slip ratio (steady-state theoretical value), the time-varying optimal slip ratio (dynamic actual value), and key elements such as real-time data points and the line connecting the static point and the zero point. By integrating the tire's dynamic time lag characteristics, the time-varying curve can reflect the actual response of the tire during braking transients. The final output parameter of the time-varying optimal slip ratio solves the problem that the static model cannot match dynamic braking conditions, providing a target reference for precise braking control.

[0079] The most commonly used and closest model to tire dynamics in engineering is the first-order inertial time-delay model, whose core assumption is that the rate of change of the dynamic response is proportional to the difference between the static reference value and the current dynamic value. Its differential form is as follows:

[0080]

[0081] In the formula, u(t) is the input quantity at time t, such as the state quantity under static conditions; y(t) is the output quantity at time t, such as the state quantity under dynamic conditions; τ is the time delay constant, which is obtained through bench testing or actual vehicle calibration. τ is different under different tire and road surface conditions.

[0082] Under the static model, the static characteristics of the slip ratio-adhesion coefficient curve conform to nonlinear laws. This curve can be accurately fitted using a fourth-order polynomial, balancing accuracy and computational complexity. The fourth-order polynomial is expressed as follows:

[0083]

[0084] In the formula, a, b, c, d, and e are the coefficients of the polynomial, which are obtained by fitting the adhesion coefficient data under different slip ratios through actual vehicle tests using the least squares method.

[0085] The first-order inertial time-delay differential equation is solved by integration, and the static polynomial fitting result is substituted into the equation, introducing an explicit time-delay factor. (t,τ) establishes the relationship between dynamic output and static input, and obtains the dynamic adhesion coefficient calculation formula including the time delay factor, thus quantifying the influence of time delay on the adhesion coefficient.

[0086] The following explicit solution is obtained by solving using differential and integral methods:

[0087]

[0088] In the formula, μ dyn (t) represents the dynamic output of the adhesion coefficient at time t; (t,τ) is the explicit time delay factor at time t; τ is the time delay constant; exp represents the exponential function with the natural constant as the base.

[0089] When τ approaches 0, it indicates no lag, and the dynamic value instantly equals the static value. When τ approaches infinity, it indicates extreme lag, and the dynamic value always approaches 0.

[0090] Mapping from rectangular coordinates to rectangular coordinates yields:

[0091]

[0092] This equation is in an implicit form and cannot reflect the dynamic characteristics in polar coordinates. Therefore, the dynamic adhesion coefficient formula in rectangular coordinates is transformed into polar coordinates, using the polar radius r. dyn To describe the dynamic characteristics, the polar angle θ is still calculated from real-time μ and λ, ultimately yielding an explicit dynamic model in polar coordinates. This addresses the issue that the dynamic equations in Cartesian coordinates are implicit and cannot reflect the dynamic characteristics of polar coordinates, thus maintaining the consistency of the coordinate system. Therefore, the time-delay tire model in polar coordinates based on implicit equations is represented as follows:

[0093]

[0094] In the formula, r dyn(t) represents the extreme diameter under dynamic characteristics at time t; A, B, C, D, and E are all coefficients of the time-delay tire model, which are obtained by fitting dynamic test data in polar coordinates based on r and θ data under different time delay constants τ.

[0095] Static radius r s It is not only related to the polar angle θ, but also affected by the rate of change of the polar angle. By adding a first-order derivative term and a cubic polynomial compensation function h(θ), the actual static curve is fitted. By simplifying the calculation of the static polar radius and introducing the polar angle derivative and compensation function, the fitting accuracy is improved. Therefore, the static formula can be simplified to:

[0096]

[0097] In the formula, r s (t) represents the polar radius of the static model at time t; A0, B0, and C0 are the corresponding coefficients; θ(t) represents the time function of the polar angle θ; Let θ(t) denote the first derivative of θ(t); h(θ(t)) denotes the compensation function with respect to the polar angle θ.

[0098] The stored curves were solved to obtain the fitted curves in polar coordinates, as shown in Figures 4 and 5.

[0099] Figure 4 shows the fitting of the slip rate-adhesion coefficient curve in polar coordinates. After converting the relevant curves of different road surfaces into polar coordinates, a smooth curve is obtained by fitting a specific function, which presents the basic shape and distribution characteristics of each road surface curve in polar coordinates.

[0100] Figure 5 shows the fitting curves of polar angle and polar radius, reflecting the corresponding change law of polar radius when polar angle changes after polar coordinate transformation. The fitting curves can fit the actual data trend well, providing support for the subsequent establishment of a unified curve description model.

[0101] Based on the analysis of Figures 4 and 5, the static curve fitting can be obtained as follows:

[0102]

[0103] In the formula, A0, B0, C0, D0, and E0 are the corresponding equation coefficients.

[0104] The results were obtained by fitting static experimental data.

[0105]

[0106] The time delay factor is essentially a correction coefficient for the dynamic characteristics relative to the static characteristics. It is directly defined by the ratio of the dynamic radius to the static radius, establishing a proportional relationship between the dynamic and static radii, thus simplifying the quantitative expression of the time delay characteristics. The simplified representation is as follows:

[0107]

[0108] In the formula, ε dyn (t) represents the time delay factor of the current road segment at time t.

[0109] II. Time-varying optimal slip ratio predictor based on variable-speed spiral vehicle tire model

[0110] 1. Mapping in polar coordinates

[0111] The Burckhardt model is a commonly used slip-coefficient-adhesion model in the industry, which already includes calibration parameters for different road surfaces. Utilizing existing mature tire model parameter libraries, it is converted into polar coordinates to provide a baseline curve for polar coordinate mapping. The Burckhardt curve expression is:

[0112]

[0113] In the formula, , , These are the coefficients of the formula, and their values ​​are shown in Table 1.

[0114] Table 1 Burckhardt model parameters

[0115]

[0116] The transformed Burckhardt curves in polar coordinates are shown in Figures 6 and 7. Figure 6 shows that the curves exhibit a high degree of similarity, and the original curves can be replaced with the same equation. Figure 7 replaces the approximately nonlinear portion with polar coordinates, using curve one as a reference to observe the proportions. It is found that during the nonlinear phase, because the curves exhibit extremely similar proportional relationships, they can be considered as other curves mapped from the reference curve. This equation can be expressed as:

[0117]

[0118] In the formula, g i (θ) is the polar coordinate equation of the current curve; p i This is the mapping coefficient from the baseline curve (the slip ratio-adhesion coefficient curve corresponding to the baseline road segment) to the current curve; g store(θ) is the polar coordinate equation of the corresponding storage curve.

[0119] In polar coordinates, curves on different road surfaces have similar heights and can be considered as mappings of a reference curve, with a mapping coefficient p. i The polar radius is determined by the ratio of the polar radius of the current real-time point to the polar angle of the corresponding reference curve. Based on this, the proportional relationship between the current road surface curve and the reference curve is established, enabling "rapid solution of the current curve using the reference curve as a template".

[0120] The mapping coefficients can be obtained from polar coordinate transformation:

[0121]

[0122] Where: g store (θ i ) represents the polar radius length corresponding to the polar angle at the current moment; μ i λ represents the adhesion coefficient at the current moment. i θ represents the real-time slip rate at the current moment. i This is the real-time polar angle corresponding to the current moment.

[0123] Similarly, when the optimal slip ratio point of the mapping coefficient and the baseline curve is obtained, the optimal slip ratio of the current curve can be represented as follows:

[0124]

[0125] In the formula, p bi The mapping coefficient corresponding to the optimal slip ratio; θ bi λ is the polar angle corresponding to the optimal slip ratio. b0 The optimal slip ratio for the baseline curve; μ b0 λ is the maximum adhesion coefficient of the reference curve. bi μ represents the time-varying optimal slip ratio for the current curve. bi This represents the predicted maximum adhesion coefficient for the current curve.

[0126] In the above formula, p bi =p i The expression for the time-varying optimal slip ratio and the estimated value of the predicted maximum adhesion coefficient can be obtained as follows:

[0127]

[0128] When the storage curve has time delay characteristics, the resulting expression for the storage curve is as follows:

[0129]

[0130] In the formula, gbs (θ) is the polar coordinate equation representing the time-delay characteristics; p(θ) is the principal part function containing the first derivative. From this, the time-varying optimal slip ratio and the predicted maximum pavement coefficient of the current road segment can be obtained as follows:

[0131]

[0132] The solved time-varying optimal slip ratio is used as the control target reference value for the nonlinear model predictive controller, thereby allowing the calculated motor drive torque to be output to the motor for control. It is evident that the time delay factor has little impact on the tire model in polar coordinates; only the curve containing the first derivative of the slip ratio needs to be used to determine and calculate the corresponding time-varying optimal slip ratio.

[0133] III. Nonlinear Model Predictive Controller Based on Time-Varying Optimal Slip Ratio

[0134] The core of this nonlinear model predictive controller based on time-varying optimal slip ratio is to use the time-varying optimal slip ratio output by the variable-speed spiral tire model as the control reference target to achieve precise closed-loop control of electric vehicle braking. Based on the longitudinal dynamics of a semi-rear-wheel-drive electric vehicle, the controller analyzes the relationship between front and rear wheel forces, slip ratio, and wheel speed to construct a state-space equation with slip ratio and its first derivative as state variables and motor braking torque as control variables. This equation is then discretized into a discretized model for adaptive model predictive control. Subsequently, a finite prediction and control time domain is defined, and a cost function incorporating slip ratio tracking error and control variable increments is constructed, with the optimization objective of "making the predicted slip ratio trajectory accurately track the time-varying optimal slip ratio." By importing real-time angular velocity and angular acceleration data acquired by a data acquisition unit, the optimal motor braking torque control sequence is obtained by minimizing the cost function. Finally, the first control variable is extracted and converted into motor output torque by combining parameters such as transmission ratio and mechanical efficiency, and then transmitted to the motor braking system for braking. The entire process fully integrates the tire's time-delay dynamic characteristics with nonlinear control logic, balancing real-time control and accuracy, effectively improving the braking performance of electric vehicles.

[0135] In the modeling and control of this invention, a half-vehicle model is used for longitudinal dynamics analysis. It is assumed that the vehicle is a rear-wheel drive configuration: the front wheels are driven wheels and are used to characterize the vehicle speed; the rear wheels are driving wheels and braking wheels, and are controlled by the braking torque of the motor.

[0136] To simplify the analysis and maintain the symmetry of the control logic, this invention uses a half-vehicle model for dynamic modeling and control design. The vehicle is symmetrical from left to right, so one side (e.g., the left side) is selected as the analysis object, while the control logic for the other side is the same.

[0137] 1. Dynamic Model

[0138] For a semi-rear-wheel-drive electric vehicle, considering only longitudinal braking dynamics, the rotational inertia and force analysis are performed separately for the drive wheels and driven wheels. The front wheels are driven wheels (without active torque), and the rear wheels are drive wheels (affected by the motor's braking torque). The relationship between wheel torque, angular velocity, and longitudinal force is established to provide a force basis for subsequent longitudinal dynamics analysis.

[0139] Force analysis of the front and rear wheels:

[0140]

[0141] In the formula, I is the moment of inertia of the wheel; , These are the wheel angular velocities of the front and rear wheels, respectively, measured in real time by wheel speed sensors; T r This represents the torque acting on the rear wheel; r in this part is the wheel radius; F xf F xr These represent the longitudinal forces acting on the front and rear wheels, derived from force analysis, and indirectly reflect the road surface adhesion.

[0142] Considering load transfer during braking (acceleration causing center of gravity shift), and based on parameters such as vehicle weight, wheelbase, and center of gravity height, the vertical force of the rear wheels is derived. Then, the coefficient of adhesion is defined by combining the ratio of longitudinal force to vertical force. By correlating the vertical force and longitudinal force, the coefficient of adhesion is quantified. Therefore, the vertical force of the rear wheels and the coefficient of adhesion can be expressed as:

[0143]

[0144] In the formula, F zr The vertical force acting on the rear wheel is denoted by ρ; G is the vehicle's weight; l1 is the front wheelbase; m is the vehicle's mass; h is the height of the center of gravity. For vehicle acceleration; L is the total wheelbase; μ r The coefficient of adhesion for the rear wheels.

[0145] A longitudinal force balance analysis of the entire vehicle is performed. By combining the torque-force relationship between the front and rear wheels and eliminating longitudinal force variables, a dynamic equation containing only wheel speed and torque is obtained. A closed-loop correlation is established between the motor braking torque, wheel speed, and vehicle acceleration. Based on this, an overall vehicle analysis yields the following:

[0146]

[0147] The slip ratio formula is as follows:

[0148]

[0149] In the formula, λ is the slip ratio; v is the vehicle speed; ω r This is the angular velocity of the rear wheel.

[0150] Because this model is a rear-wheel-drive electric vehicle, the front wheels can be considered as driven wheels to reflect vehicle speed:

[0151]

[0152] In the formula, ω f This represents the angular velocity of the front wheel.

[0153] Based on the classic definition of slip ratio and considering the characteristics of rear-wheel drive vehicles, the simplified slip ratio formula is as follows:

[0154]

[0155] Differentiating both sides of the above equation yields the following transformation:

[0156]

[0157]

[0158]

[0159]

[0160]

[0161]

[0162] Taking the derivative of the slip ratio formula twice consecutively, we get:

[0163]

[0164]

[0165]

[0166]

[0167] In the formula, The first derivative of the slip ratio λ ω is the second derivative of the slip ratio λ; r The angular velocity of the rear wheel. ω is the second derivative of the rear wheel angular velocity; f The angular velocity of the front wheel; The first derivative of the front wheel angular velocity, The second derivative of the front wheel angular velocity.

[0168] By selecting slip ratio and its first derivative as state variables, rear wheel torque as control variable, and slip ratio as output variable, the state-space equations can be obtained. This transforms the nonlinear dynamics into a standard "state-input-output" control form, adapting it to a model predictive control framework.

[0169] The state-space equations are expressed as follows:

[0170]

[0171] 2. Nonlinear Model Predictive Control

[0172] make ,Will Choose the input control variable as u=T r The output variable is y=x1. The state-space equation can be written as:

[0173]

[0174] In the formula: , , , , , The state-space equations, using the first derivative which introduces the slip ratio, can represent the dynamic characteristics contained within the curve.

[0175] Discretizing the above equation, we get x(t+1) = Ax(t) + Bu(t), where x(t+1) and x(t) represent the state variables at time t+1 and time t, respectively, u(t) represents the control variable at time t, and A and B are the corresponding system matrices; specifically represented as follows:

[0176]

[0177] In the formula, b1 = a1·T s b2 = a2·T s b3 = a3·T s b4 = a4·T s b5 = a5·T s b6 = a6·T s ;

[0178] x1[t+1|t] and x2[t+1|t] are the predicted values ​​of state variables x1 and x2 at time t for time t+1, respectively; yt[t+1|t] is the predicted value of the output variable at time t for time t+1; x1[t] and x2[t] are the values ​​of state variables x1 and x2 at time t, respectively; u[t-1] is the value of the control variable at time t-1; Δu[t] is the increment value of the control variable at time t.

[0179] Assuming u[t+1|t] = u[t], the predicted value at time t+1 can be obtained as follows:

[0180]

[0181] In the formula: ; ; ; ; ; ; ; ; , Let y[t+2|t] be the predicted value of state variables x1 and x2 at time t to time t+2, and let y[t+2|t] be the predicted value of output variables at time t to time t+2.

[0182] The above formula can be rearranged as follows:

[0183]

[0184] In the formula: ; ; ; ; ; ; ;

[0185] .

[0186] Set the prediction time domain to p t The control time domain is set to m t The cost function equation is obtained as follows:

[0187]

[0188] In the formula, J i The cost function value; q i r i These are the weight coefficients for the corresponding terms; y i [t+j|t] is the predicted slip ratio at time t for time t+j; yir [t+j] is the control reference value of the slip ratio at time t+j; Δu[t+j] is the incremental value of the motor braking torque at time t+j.

[0189] To minimize the cost function, the optimal control value is obtained.

[0190]

[0191] In the formula: ΔU[t] is the set of control variables obtained by solving; Δu[t+m t +j] is t+m t The increment of the control variable at time +j.

[0192] The driving torque T of the motor is also represented by the braking torque on the wheels. r as follows:

[0193]

[0194] In the formula: η represents the braking torque of the motor; i0 represents the transmission ratio of the motor; η represents the mechanical efficiency of the motor.

[0195] Choosing a time domain and control time domain both to be 2, and using the first term with the minimum cost function as the control variable adjustment value, the optimized motor output torque can be expressed as:

[0196]

[0197]

[0198] In the formula, R1 is the reference value of the state variable x1, and is the calculated time-varying optimal slip ratio.

[0199] The calculated output motor braking torque is transmitted to the motor for control.

[0200] IV. Vehicle Slip Rate Optimization Control System

[0201] The vehicle slip ratio optimization control system is specifically designed for electric motor brake vehicles. Its core consists of four functional modules working together: The data acquisition module collects raw data such as front and rear wheel angular velocities and motor output torque in real time through wheel speed sensors and motor braking torque sensors. After processing, it outputs real-time slip ratio, slip ratio change rate, and adhesion coefficient. The time-varying optimal slip ratio prediction module pre-stores a Burckhardt baseline curve parameter library, polar coordinate mapping algorithm, and time delay factor calculation model. After receiving real-time parameters, it fuses them with the baseline curve proportional mapping and dynamic time delay characteristics to output the time-varying optimal slip ratio and the estimated maximum adhesion coefficient for the current road surface. The nonlinear model predictive control module incorporates a semi-rear-wheel-drive vehicle longitudinal dynamics model, discretized state-space equations, and cost function optimization algorithms. Using the time-varying optimal slip ratio as a reference target, it solves for the optimal motor braking torque control quantity. The drive execution module consists of a transmission system and a motor braking execution unit, responsible for converting torque commands into drive signals to control motor braking. The system operates continuously with the logic of "real-time perception - dynamic prediction - precise control - closed-loop feedback": First, data is collected by sensors and preprocessed to obtain key parameters. Then, the time-varying optimal slip ratio is obtained through polar coordinate mapping, mapping coefficient calculation and time delay factor fusion. Subsequently, the control module constructs the state space equation and solves the optimal torque through convex optimization. Finally, the execution module performs braking and repeats the process in subsequent sampling cycles to form closed-loop control to adapt to the dynamic adhesion coefficient changes of different road surfaces.

[0202] V. Electric Vehicles

[0203] Electric vehicles, in addition to traditional basic hardware such as the vehicle frame, front and rear wheels (including wheel speed sensors), electric motor braking system, and vehicle control unit (VCU), have added a vehicle slip ratio optimization control system. This system includes a data acquisition module, a time-varying optimal slip ratio prediction module, a nonlinear model predictive control module, and a drive execution module. It is further supported by auxiliary components such as a power management system, a center of gravity height sensor, and a road surface adhesion feedback unit to ensure coordinated operation. Its operation adapts to different road surface braking requirements throughout the entire process. After vehicle startup, the slip ratio optimization control system automatically initializes, loading the pre-stored Burckhardt baseline curve parameter library, the time delay constant τ calibration value, and vehicle design parameters, completing communication handshakes with the vehicle controller and electric motor braking system. During driving, the data acquisition module continuously collects wheel speed and electric motor braking torque data and receives vehicle acceleration data. The system dynamically calculates the slip ratio λ and feeds back parameters such as the adhesion coefficient μ_i to the prediction module. When the driver triggers a braking command, the prediction module outputs the time-varying optimal slip ratio λbi within 10ms based on real-time data and the time lag factor ε_dyn. The control module quickly solves for the optimal motor braking torque and outputs a command. The motor braking system precisely adjusts the torque to track λbi, avoiding wheel lock-up or insufficient braking. When driving on roads with varying adhesion coefficients, the system dynamically updates the mapping coefficient pi and the time lag factor εdyn, correcting λbi and braking torque in real time. At low speeds, it switches to mechanical braking assist mode to compensate for errors. The entire system fully leverages the advantages of fast motor braking response and high precision through closed-loop logic, achieving efficient and safe braking on different road surfaces while balancing braking performance and driving stability.

[0204] VI. Simulation Verification

[0205] The simulation was set up with two different road surfaces with varying adhesion coefficients. The initial speed was 50 km / h. In scenario one, the road surface was set as a transitional surface with a high adhesion coefficient ranging from 1 to 0.6, and in scenario two, the road surface was set as a transitional surface with a low adhesion coefficient ranging from 0.6 to 1 .... The model parameters of the electric vehicle are shown in Table 2.

[0206] Table 2 Electric Vehicle Model Parameters

[0207]

[0208] Under condition one, the experimental results are shown in Figures 8 to 11. Figure 8 shows the change of slip ratio over time in condition one. The curve clearly shows the dynamic change process between the real-time slip ratio and the predicted time-varying optimal slip ratio. The real-time slip ratio can track the time-varying optimal slip ratio well, reflecting the accuracy of the prediction method and the effectiveness of the control. Figure 9 shows the change of adhesion coefficient over time in condition one, including three curves: road adhesion coefficient, utilized adhesion coefficient, and estimated adhesion coefficient. The three curves have basically the same trend, and the estimated adhesion coefficient can accurately match the actual road adhesion coefficient, verifying the reliability of the adhesion coefficient estimation method. Figure 10 shows the changes of speed and braking distance over time in condition one. The linear speeds of the front and rear wheels gradually decrease over time, while the braking distance continuously increases over time, intuitively reflecting the speed decay and braking distance changes of the vehicle during braking. Figure 11 shows the changes in motor braking torque and vehicle acceleration over time in operating condition 1. The motor braking torque is dynamically adjusted according to braking demand, and the vehicle acceleration changes accordingly. The overall trend conforms to the correlation between torque and acceleration during braking, reflecting the precise adjustment of torque by the control strategy.

[0209] Analysis of Figures 8-11 and experimental data shows that the slip ratio prediction errors are RMSE: 0.004218 and MAPE: 2.92%. The adhesion coefficient estimation errors are RMSE: 0.038814 and MAPE: 2.91%. When the real-time slip ratio is 0.015, the optimal slip ratio around 0.14 can be predicted, with a prediction range of approximately 89.3%, demonstrating good prediction performance. Similarly, the adhesion coefficient also exhibits strong predictive performance. The overall braking time is 6.21 seconds, and the maximum braking acceleration reaches 3.096. It also exhibits good tracking performance on road surfaces with continuously varying adhesion coefficients in the middle.

[0210] Under operating condition two, the experimental results are shown in Figures 12-15. Figure 12 shows the slip ratio versus time curve in operating condition two. The real-time slip ratio closely tracks the predicted time-varying optimal slip ratio, and their dynamic trends are consistent, demonstrating the good performance of the time-varying optimal slip ratio prediction method and control strategy under this operating condition. Figure 13 shows the change of the adhesion coefficient in operating condition two. The trends of the road adhesion coefficient, the utilized adhesion coefficient, and the estimated adhesion coefficient are synchronized. The estimated adhesion coefficient can accurately reflect the actual road adhesion coefficient condition, further verifying the effectiveness of the estimation method. Figure 14 shows the changes of speed and braking distance versus time in operating condition one. The linear speeds of the front and rear wheels decrease steadily during braking, while the braking distance gradually increases over time, clearly showing the vehicle's braking deceleration process and distance accumulation under this operating condition. Figure 15 shows the change of motor braking torque versus time in operating condition two. The braking torque output is dynamically adjusted according to the vehicle's braking state and the changes in the road adhesion coefficient. The curve trend reflects the real-time optimization and adjustment of the motor braking torque by the control strategy to adapt to different braking requirements.

[0211] Analysis of Figures 12-15 and experimental data shows that the slip ratio prediction errors are RMSE: 0.002046 and MAPE: 1.77%. The adhesion coefficient estimation errors are RMSE: 0.018743 and MAPE: 2.20%. When the real-time slip ratio is 0.017, the optimal slip ratio near 0.09 can be predicted, with a prediction range of approximately 81.1%, demonstrating good prediction performance. Similarly, the adhesion coefficient also exhibits strong predictive performance. The overall braking time is 5.75 seconds, and the maximum braking acceleration reaches 3.039. It also exhibits good tracking performance on road surfaces with continuously varying adhesion coefficients in the middle.

[0212] The test results show that the vehicle exhibits good predictive and control performance on both road surfaces with varying adhesion coefficients from low to high and from high to low. However, mechanical braking is required at low speeds due to the high tire noise, which leads to larger errors in the results. Since braking performance is evaluated within the operating range of 0.05 to 0.95 times the initial speed, low-speed control is not considered.

[0213] The technical solution of this invention is based on the general characteristics of torque control methods, and its core partitioning and prediction logic do not depend on the sign of the slip ratio. Under driving conditions, the slip ratio is negative, but the curve still exhibits peak characteristics. Subsequent control circuits will calculate the optimal motor drive torque accordingly to achieve anti-slip control. Therefore, the prediction and control methods have consistent applicability in both braking and driving scenarios.

[0214] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A time-varying optimal slip ratio prediction method based on dynamic time delay characteristics, characterized in that, This includes: based on the vehicle's adhesion coefficient μ at the current moment on the current road segment. i Real-time slip ratio λ i and the time delay factor ε characterizing dynamic time delay properties dyn Calculate the time-varying optimal slip ratio λ for the current road segment. bi ; ； ； In the formula, λ b0 μ represents the optimal slip ratio of the reference section. b0 represents the maximum adhesion coefficient of the reference road segment, which is any road segment with a known static slip ratio-adhesion coefficient curve; arctan(·) represents the arctangent function; p(·) represents a function containing the first derivative; express The first derivative of ; h(·) represents the compensation function.

2. The time-varying optimal slip ratio prediction method based on dynamic time delay characteristics according to claim 1, characterized in that, λ bi The corresponding predicted time-varying maximum adhesion coefficient is: In the formula, μ bi This represents the predicted time-varying maximum adhesion coefficient for the current road segment.

3. The time-varying optimal slip ratio prediction method based on dynamic time delay characteristics according to claim 1 or 2, characterized in that, ε dyn These are either fixed values ​​pre-calibrated through experiments or dynamic values ​​updated in real time based on the tire's operating conditions.

4. The time-varying optimal slip ratio prediction method based on dynamic time delay characteristics according to claim 3, characterized in that, When ε in the current road segment dyn When is a dynamic value, its update is as follows: ； ； ； In the formula, ε dyn (t) represents the time delay factor of the current road segment at time t; r dyn (t) represents the polar radius under dynamic characteristics at time t; r s (t) represents the polar radius of the static model corresponding to the current road segment at time t; θ(t) represents the polar angle θ at time t; τ is the time delay constant; μ(t) represents the adhesion coefficient of the current road segment at time t; λ(t) represents the real-time slip ratio of the current road segment at time t; A0, B0, C0, D0, and E0 are the corresponding equation coefficients, and A, B, C, D, and E are the coefficients of the time-delay tire model.

5. A method for calculating the braking torque of a motor based on a time-varying optimal slip ratio, characterized in that, include: The time-varying optimal slip ratio λ is calculated using the time-varying optimal slip ratio prediction method based on dynamic time delay characteristics as described in any one of claims 1-4. bi As the slip ratio control target for the current road segment, a state-space equation is established based on the wheel angular velocity and moment of inertia, with slip ratio and its first derivative as state variables and motor braking torque as control variables. This equation is then discretized into a state-space model: x(t+1)=Ax(t)+Bu(t), where x(t+1) and x(t) represent the state variables at time t+1 and time t, respectively, u(t) represents the control variable at time t, and A and B are the corresponding system matrices. A cost function is constructed for the finite prediction time domain and control time domain, with the optimization objective being to make the predicted slip ratio trajectory track the slip ratio control target. The future state of the vehicle is predicted based on the state-space model, and the optimal motor braking torque control sequence is calculated by solving the minimum cost function. The first control variable in the optimal motor braking torque control sequence is converted into motor braking torque, which is used to control the vehicle to perform braking.

6. The method for calculating motor braking torque based on time-varying optimal slip ratio according to claim 5, characterized in that, The state-space equations are: In the formula, The first derivative of the slip ratio λ ω is the second derivative of the slip ratio λ; r The angular velocity of the rear wheel. ω is the second derivative of the rear wheel angular velocity; f The angular velocity of the front wheel; The first derivative of the front wheel angular velocity, T is the second derivative of the front wheel angular velocity; r I is the braking torque of the motor acting on the rear wheel; m is the wheel moment of inertia; r is the vehicle mass; and r is the wheel radius.

7. The method for calculating motor braking torque based on time-varying optimal slip ratio according to claim 6, characterized in that, The cost function is: In the formula, J i The cost function value; q i r i These are the weight coefficients for the corresponding terms; p t m t These are the prediction time domain and the control time domain, respectively; y i [t+j|t] is the predicted slip ratio at time t for time t+j; y ir [t+j] is the control reference value of the slip ratio at time t+j; Δu[t+j] is the incremental value of the motor braking torque at time t+j.

8. The method for calculating motor braking torque based on time-varying optimal slip ratio according to claim 7, characterized in that, The final output is the motor braking torque T at time t. tq for: In the formula, u[t-1] is the value of the motor braking torque at time t-1; i0 represents the transmission ratio of the motor. η represents the mechanical efficiency of the motor; R1 represents the optimal slip ratio for the current road segment; q1 represents the weighting coefficient of the state tracking error; A 11 A 21 These represent specific elements in system matrix A; B 11 B 21 These represent specific elements in the system matrix B; r1 represents the weighting coefficient of the control variable increment.

9. A vehicle slip ratio optimization control system, characterized in that, The system is applied to vehicles with electric motor braking systems and includes: a data acquisition module for real-time acquisition of the vehicle's wheel speed and electric motor braking torque, and processing to obtain the real-time slip ratio and coefficient of adhesion at the current moment; a time-varying optimal slip ratio prediction module, communicatively connected to the data acquisition module, for receiving the real-time slip ratio and coefficient of adhesion; pre-stored static slip ratio-coefficient of adhesion curves of a reference road segment, as well as its optimal slip ratio and maximum coefficient of adhesion, and based on a time-delay factor, executing a time-varying optimal slip ratio prediction method based on dynamic time-delay characteristics as described in any one of claims 1-4 to calculate the time-varying optimal slip ratio of the current road surface; a nonlinear model predictive control module, communicatively connected to the time-varying optimal slip ratio prediction module, for using the time-varying optimal slip ratio as the slip ratio control target of the current road segment, executing a time-varying optimal slip ratio-based electric motor braking torque calculation method as described in any one of claims 5-8 to calculate the electric motor braking torque control command; and a drive execution module, communicatively connected to the nonlinear model predictive control module, for converting the electric motor braking torque control command into a drive signal and outputting it to the vehicle's electric motor braking system to execute braking control.

10. An electric vehicle, comprising a body, wheels, an electric motor braking system, and a vehicle controller, characterized in that, It also includes a vehicle slip ratio optimization control system as described in claim 9; the vehicle slip ratio optimization control system is communicatively connected to the motor braking system and the vehicle controller, and is used to calculate the optimal slip ratio and the corresponding motor braking torque according to the real-time driving status, and to perform anti-lock braking control of the vehicle through the motor braking system.

Images