Variable boost characteristic control strategy of hydraulic systems for brake-by-wire based on driving style | Scientific Reports

Scientific Reports volume 14, Article number: 29412 (2024) Cite this article

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This paper proposes a control strategy for the variable boost characteristics of electronic hydraulic brake (EHB) systems based on the driving style in response to the nonlinear challenges faced by the EHB systems in intelligent driving under complex personalized requirements. Initially, the working principle of the active braking of the EHB-booster was analyzed, and equivalent dynamic models and Karnopp friction models were established. Subsequently, by identifying the displacement and velocity parameters of the brake pedal, three types of variable boost characteristics-sporty, comfortable, and standard-were designed to satisfy the requirements of different driving styles. Then, to address the nonlinear disturbances caused by the variable boost characteristics, a variable-gain multiclosed-loop control strategy that considers nonlinear friction and inertia compensation was developed. Finally, the proposed control strategy was tuned and verified through the AMESim and Simulink cosimulation platform and vehicle tests. The results demonstrate that the strategy exhibits excellent control performance under various braking conditions that match driving styles, with steady-state control errors within 0.1 Mpa, providing a feasible solution for the complex nonlinear problems faced by personalized implementation in higher-order intelligent driving.

With the rapid development of intelligent vehicle technology, the driving experience and vehicle safety have become the focus of public attention. The electronic hydraulic brake (EHB) system, which is the core of the safety performance of intelligent driving vehicles, directly affects the lives of drivers and passengers. In the wide applications of electric and hybrid vehicles, the EHB system significantly improves the effectiveness of brake energy recovery through collaborative action with electric motor braking. Although EHB systems have significant advantages in terms of response speed and control accuracy, they are not without challenges. The nonlinear characteristics of the hydraulic system, the hysteresis effect of the transmission mechanism, and the coupling of the servomotor electromagnetic characteristics make it a serious challenge for the EHB system to achieve precise pressure control. Importantly, with the diversification of driving styles and the increase in personalized needs, the traditional “one-size-fits-all” braking system can no longer meet the expectations of all drivers1, and these needs further highlight the nonlinear problems of the EHB systems. The diversity of driving styles requires a braking system to adapt to different driving habits and preferences, thereby providing a more personalized driving experience. This personalized demand involves not only the adjustment of the braking response, but also the optimization of the braking feel, making the braking process more natural and comfortable.When the EHB braking system actively regulates the pressure of the master cylinder for braking, it confronts nonlinear issues such as the time-varying characteristics of the hydraulic system and the frictional hindrance of the transmission mechanism. The individualized braking force control requirements will significantly enhance the working scenarios and control complexity of the wire-controlled braking system, further causing a greater disparity in dynamic response between the EHB braking motor and hydraulic components, resulting in torque fluctuations during the braking mode switching process. Eventually, what is fed back to the driver is the instability of the feedback torque of the brake pedal, that is, the instability of the driving style2.

In view of the above problems, the academic and industrial circles have carried out a lot of development and research on the coordinated control of EHB, and achieved extensive and profound research results. Suzdaleva and colleagues developed a model based on the driving environment to determine driving behavior, which significantly outperformed traditional models in identifying driving behaviors and predicting data, primarily using Bayesian methods to recognize three different driving patterns related to fuel consumption3. Lv and colleagues proposed a collaborative optimization method for controller parameter optimization based on driving behavior recognition and cyber-physical systems, showing that the designed method is conducive to enhancing the overall performance of the controller and further validating its effectiveness through vehicle experiments4. Ma and colleagues explored the characteristics of driving behavior and fuel economy through extensive Monte Carlo methods and verified their correctness using Gaussian process regression models5. Qiu and colleagues’ research demonstrated that different driving behaviors have a considerable impact on the energy utilization and recovery effect during the regenerative braking process of electric vehicles, with aggressive driving behaviors yielding better energy recovery effects than moderate and mild driving behaviors6. Park and Meng, through the establishment of accurate mathematical models of the braking system and computer simulations to verify their accuracy, delved into how to adjust the force felt on the brake pedal to adapt to drivers with different driving styles7,8,9. Li and Sun, in order to achieve satisfactory control results, explored the fast response of the motor, using motor torque to compensate for the response hysteresis of hydraulic braking, meeting the requirements for coordinating dynamic response differences10,11. Todeschini and colleagues proposed an adaptive cascade control architecture for BBW systems, particularly suitable for racing applications. This system, with an inner loop controlling position and an outer loop controlling pressure, effectively addresses the challenges of BBW systems in racing applications12. The innovation of this control strategy lies in its adaptive mechanism, capable of handling nonlinear characteristics and external disturbances related to racing applications. Wang and colleagues utilized fuzzy reasoning technology to recognize the driver’s braking intentions and designed corresponding control strategies to enhance the level of intelligent braking. The innovation of this work lies in its recognition and response to the driver’s intentions, making braking control more aligned with the driver’s expectations13. Chen and Zhao proposed an active braking pressure precise control algorithm for an electric power-assisted braking system14, and a variable servo characteristic matching method based on driving style recognition, adjusting braking boost in real-time to adapt to different driving scenarios. The innovation of this method lies in its ability to dynamically adjust the braking system according to the driver’s behavior patterns, enhancing the adaptability and personalization of the braking system15. Zhang et al. proposed a new personalized MPC control strategy that conforms to the characteristic E design method. A data collection platform of driving behavior characteristics of typical vehicles under following conditions is constructed16.

The customization of driving experience emerges as a pivotal application scenario in advanced intelligent driving. Drivers and passengers can tailor the response characteristics of the electro-hydraulic brake (EHB) system to their personal habits and preferences, thus achieving a variety of driving or riding experiences17. This adaptability improves driving dynamics, making it more aligned with individual tastes and comfort levels18. Furthermore, mature personalized control strategies have the potential to optimize energy consumption in conjunction with driver habits. For example, for users with a preference for a comfortable driving style, these strategies can optimize braking and acceleration processes, thereby improving vehicle fuel economy or electric driving range. The variable gain control strategy also has inherent advantages for intelligent system integration and data-driven optimization prospects. It can coordinate control with intelligent cockpit systems, vehicle networking, and adaptive cruise control technologies to achieve a more nuanced human-computer interaction experience. Research in these areas will provide a broad implementation foundation for the application of the EHB system and facilitate the technical deployment and specific application of active braking in intelligent driving scenarios19.

However, the above studies still have certain shortcomings20. Although some studies have proposed control strategies based on driver behavior recognition, these strategies still have limitations in accurately adjusting brake boost in real time to adapt to different driving scenarios. For example, the adaptive cascade control architecture proposed by Todeschini et al. performs well in racing applications but needs further optimization in dealing with nonlinear characteristics and external disturbances related to racing applications; Similarly, some researches on multiloop control strategies using MPC and neural networks require large computing resources, which is a challenge for intelligent wire control in multi-vehicle matching and integration21. In this context, we propose a variable boost characteristic control strategy for a braking-by-wire hydraulic system based on driving style. By analyzing the active braking working principle of the EHB booster, equivalent dynamic and Karnopp friction models were established, and three types of boost characteristics were designed: sporty, comfortable and normal. This strategy not only considers nonlinear friction and inertia compensation but also achieves precise matching of different driving style requirements through a variable-gain multiclosed-loop control strategy. Compared with previous studies, the advantage of this study is that it adopts an innovative control strategy, that is, different PID gain parameters are used in different control closed loops, and personalized driving style needs are specifically considered, which can significantly improve the control accuracy and driving experience of the EHB system, while consuming less computing resources and providing stable performance22. Moreover, the variable gain control strategy, after undergoing stability testing in complex working conditions, demonstrates a higher safety factor. It is capable of providing a personalized control strategy with a built-in safety margin, tailored to specific scenarios and external conditions.Through the AMEsim and Simulink co-simulation platform and actual vehicle test, the effectiveness of the proposed control strategy is verified. The nonlinear characteristics of EHB systems during active braking are considered in a comprehensive way, and a practical and effective solution is provided, which is rare in the existing researchs.

The EHB system investigated in this study comprises a permanent magnet synchronous motor (PMSM), gears, a ball screw transmission mechanism, a brake pedal, a master cylinder, and a hydraulic control unit. The operational principle is shown in Fig. 1. (1) Upon depressing the brake pedal by the driver, the PMSM converts the servo motor force into a horizontal force exerted on the booster valve body through gears and a ball screw. Subsequently, the rubber feedback disc couples the driver’s brake pedal force with the horizontal force of the booster valve body to actuate the master cylinder plunger and generate pressure within it. Consequently, the master cylinder brake fluid flows through to pressurize it further into the brake caliper and generates braking torque on the wheels. (2) In an active braking mode, where driver participation is not required for braking action, based on high-level demand signals, the EHB system controls the servo motor to actuate the master cylinder plunger, thus achieving the active braking function.

Structural diagram of EHB-booster.

The permanent magnet synchronous motor serves as the power source of the EHB system, and the mathematical expressions of the voltage equations of the direct axis d and the quadrature axis q of the permanent magnet synchronous motor in the rotor reference frame are represented by Eq. (1)23.

The relationship between the electromagnetic torque of the motor and the current is represented by Eq. (2).

The relationship between the electromagnetic torque of the motor and the electrical angular acceleration is given by Eq. (3).

In those equations, \(u_d\) and \(u_q\) are the stator voltages in the d- and q-axes, respectively; \(R_S\) is the stator resistance; \(i_d\) and \(i_q\) represent the d- and q-axis currents;\(L_d\) and \(L_q\) are the d- and q-axis inductances; \(\omega _e\) is the motor’s electrical angular velocity, \(\omega _m\) is the mechanical speed of the motor shaft; \(p_n\) is the number of magnetic poles of the motor, \(\psi _f\) is the flux linkage generated by the permanent magnet; \(T_e\) is the electromagnetic torque of the motor, J is the moment of inertia of the motor, and \(T_L\) is the load torque of the motor; and \(T_f\) is the friction torque of the motor.

This study defines the direction in which the pedal input push rod is pressed in the positive direction for force and displacement. For the pedal-input push rod of the EHB braking system, the following dynamic equation is established:

In Eq. (4), \(m_i\) is the mass of the pedal input push rod, \(x_i\) is the displacement of the pedal input push rod and \(\dot{x}_i\) is its velocity; \(F_i\) is the force from the driver stepping on the brake pedal transformed to the pedal input push rod, \(F_{is}\) is the force between the pedal input push rod and the screw shaft, \(F_{ss}\) is the elastic force of the pedal return spring, \(F_{ir}\) is the force between the pedal input push rod and the main surface of the rubber feedback disc, and \(F_{iv}\) is the force between the pedal input push rod and the rear end face of the servo valve body. K is the stiffness coefficient between two rigid bodies, C is the damping coefficient between two rigid bodies, \(x_s\) and \(\dot{x}_s\) are the displacement and velocity of the screw shaft, respectively; where \(F_{ssp}\) is the preload force of the pedal return spring; \(K_{ss}\) is the stiffness coefficient of the pedal return spring; and \(C_{ss}\) is the damping coefficient of the spring. The pedal input push rod and the rubber feedback disk have a small gap, denoted \(\varDelta _1\). When the displacement difference between the push rod and the main surface of the feedback disc is less than this value, there is no interaction force between them. Therefore, we can express the force between the push rod and the feedback disc as follows:

In Eq. (5), \(K_{irs}\) is the stiffness coefficient of the main surface of the rubber feedback disc, \(C_{irs}\) is the damping coefficient of the main surface of the rubber feedback disc and \(x_{rm}\) is the displacement of the main surface of the rubber feedback disc, \(\dot{x}_{rm}\) is its velocity. A small gap \(\varDelta _2\) exists between the pedal input push rod and the servo valve body. When the displacement difference between the pedal input push rod and servo valve body is less than this value, they do not contact each other; therefore, the force between the pedal input push rod and servo valve body can be expressed as:

In Eq. (6), \(x_v\) and \(\dot{x}_v\) represent the displacement velocity of the servo valve body, respectively.

During the motion of an electronic hydraulic braking and transmission system, dynamic or static friction forces are generated and the value of the friction force is related to speed and pressure. This study selected the Karnopp friction model, which describes the zero point of speed24. In the dead zone of speed, the friction force and the resulting force of the other forces acting on the system are balanced. Therefore, the mathematical model is as follows:

In Eq. (7), \(T_f\) is the friction torque, \(T_e\) is the difference between the motor output torque and the load torque, \(T_s\) is the static friction torque when there is no load, D is the viscous friction coefficient, \(T_c\) is the Coulomb friction torque when the load is zero, G is the Coulomb friction coefficient, \(F_l\) is the load force, \(\omega _1\) is the motor angular velocity , and \(\varepsilon\) is the motor direction threshold.

To facilitate the measurement of the load of the electronic brake booster, a load spring with a stiffness of 100 N/mm was adopted, and its displacement was measured using a stroke sensor14. The final identification results are listed in Table 1.

Driving styles can be classified into aggressive, conservative, and standard types based on behavioral characteristics. Among these, the feeling of the brake pedal plays a crucial role in categorizing driving styles. This paper proposes three distinct characteristics of the brake boost: sport, comfort, and normal to align with the classification of driving styles and achieve precise braking control in conjunction with the motion state of a vehicle. Consequently, this design enabled adjustable boost characteristics in electronic braking systems.

Because the driver forms a stable habit of the brake pedal feeling provided by the vacuum booster, this study uses the boost curve of the vacuum booster as a benchmark to design and optimize the brake booster boost characteristic curve25. Figure 2 shows the complete boosting curve of the normal brake characteristics during brake and return strokes. This curve is set as the basic booster characteristic. The hysteresis between the brake and return strokes of the comfortable and sports brake pedals was approximately the same as that of the normal type. For simplicity and readability of the curves, the diagrams for the Comfortable and Sport brake boost characteristics show only the brake stroke curve.

Schematic of the pedal force characteristics of different driving styles.

Multi-closed-loop control strategy with variable boost characteristics.

When designing different brake boost characteristics, the design purpose of the comfort brake boost characteristic is to achieve a smoother braking process and make the driver feel that the pedal is ’light’. This characteristic is manifested in the boost characteristic curve as a larger jump-in value and a relatively larger boost ratio in the linear boost section. By contrast, the sporty type of brake pedal feel emphasizes the “intense” operation of the driver in the braking process. To ensure the stability and safety of the braking process, the sporty type of brake pedal feel is designed to be rather ’heavy’, and its boost characteristic curve has a lower jump value and boost ratio26.

Gleichzeitig, it is necessary to ensure that when the driver applies the same brake pedal depth and pedal force, the master cylinder pressure corresponding to the comfort boost characteristic curve is the largest, the pressure of the sporty boost characteristic curve is the smallest, and the pressure of the normal boost characteristic curve is at the middle level. This comparison helps us understand the impact of different brake pedal feeling modes on the braking system performance and provides a theoretical basis for the design and optimization of subsequent control strategies.

As shown in Fig. 3, the multi-closed-loop control strategy based on the variable-boost characteristics of the driving style includes the current, speed, and position loops of the motor. In the controller design process, the current loop is first designed, and then the speed and position loops are designed and debugged. Because the control accuracy of the variable boost characteristic is affected by nonlinear factors such as friction, damping, hysteresis, and hydraulic loss, a feedforward control with friction compensation and inertia compensation is added.

The current loop includes a PWM inverter, motor winding, and hydraulic load system. The difference between the target servo displacement \(x_{ref}^*\) matched by the driving style and the actual position displacement \(x_{act}\) of the mechanism is controlled using a PD controller. The proportional term \(k_p\) allows the servo valve body to reach the target position quickly, and the differential term \(k_d\) controls the output amplitude of the proportional term based on the rate of change in the position difference, thereby improving the response speed27. Therefore, the position-loop control law is \(i_1\):

In Eq. (8), \(x_{ref}^*\) and \(x_{act}\) are the target servo displacement and actual displacement, respectively, \(k_p\) and \(k_d\) are the proportional and differential gains, respectively.

According to the target servo displacement and the actual servo displacement, the target speed \(\dot{x}_{ref}^*\) and actual speed \(\dot{x}_{act}\) can be obtained. The speed control is designed with a feed forward friction compensation coefficient \(c_f\), which can improve the response speed of the servo valve body and eliminate the influence of some friction factors. However, owing to the large inertia of the system, it is not desired to produce oscillation or large overshoot after reaching the target position, so an inertia compensation coefficient \(c_i\) needs to be designed. Therefore, the speed loop current control law \(i_2\) is:

In addition, because the hydraulic system has different boost ratios under different boost characteristics, the PD controller of the position loop and proportional controller of the speed loop cannot eliminate the steady-state error that occurs after the servo displacement is controlled by the position and speed controls. To eliminate these residual errors, the integral term \(k_i\) must be introduced; therefore, the control law of the integral control is \(i_3\):

The variable gain control strategy involves a lot of parameters. Table 2 shows the reference values for each gain parameter in normal driving style. The parameter Settings of other driving styles can be obtained by adaptive adjustment on this basis.Finally, the current control law of the variable-boost characteristic multiclosed-loop control strategy is obtained as \(i_{ref}\):

Cosimulation: AMEsim as Slave and Simulink as Master [AME2SLCosim]. Created by Microsoft Visio (Version 2410), the URL is https://www.microsoftstore.com.cn/software/office/visio-professional-2021.

This paper describes the development of an EHB model and a multiloop control simulation model using AMEsim and MATLAB/Simulink. The purpose of these models is to facilitate the cosimulation, debugging, and validation of control strategies. The key parameters of the cosimulation are listed in Table 3.

The interfaces between AMEsim and Simulink enable simulations to be performed using a combination of AMEsim and Simulink models. The interfaces provide two main options: importing the AMEsim model into Simulink, or importing the Simulink model into AMEsim. Considering the advantages of Simulink in the control strategy design, this study uses the first method, as shown in Fig. 4, the picture on the left is the screenshot of the AMEsim model of this study, corresponding to the structural simulation model of EHB; the picture on the right is the screenshot of the Simulink model, corresponding to the control strategy model. The figure shows the construction results of the AMEsim and Simulink models and the co-simulation relationship.

The algorithm designed in this paper is compared with the classical PI controller. Since the PI controller is also a multiclosed-loop control algorithm with algorithm architecture similar to this paper, the simulation test condition is set as the sinusoidal pulse condition test matching the classical PI controller in the cosimulation experiment, which is convenient for comparison of control effects. After the control strategy verifies the control effect in the cosimulation stage, verification of the real vehicle test platform can be started. The reference value of each gain parameter can be obtained by performing multiple rounds of debugging, which can improve the test efficiency to a certain extent14,28. Figure 5 shows the control effect curve under sinusoidal pulse condition in the co-simulation experiment. where the bias and amplitude of the target sinusoidal pressure were set to 30 bar (3.0 MPa) and the frequency was maintained at 1 Hz.

Results of cosimulation experiments: sinusoidal pulse.

Results of cosimulation experiments: four wheels braking force.

Results of cosimulation experiments: three driving styles.

By analyzing the curves in Fig. 5, it can be observed that the braking pressure tracking effect under the control strategy designed in this study is good. The pressure control effect can still be maintained when the mechanism is braking in the direction of change, and the pressure tracking error is always controlled within 0.05 MPa. When controlled by the classical PI control strategy, the master cylinder actuator displacement is tracked by a relatively large hysteresis. Conversely, the control strategy in this study takes into account the friction factor of the mechanism and performs the feedback compensation so that the master cylinder actuator displacement can always closely follow the target value. In addition to the maximum error of 0.75 mm in the value-added time, the rest of the stage ensures a good control effect, with an error value of less than 1%. In addition, the coupling relationship between the torque and excitation axes of the PMSM is not considered under the simple PI control strategy, which results in the excitation axis current not being well controlled near the target value, which also leads to a poor torque axis current-following effect. In contrast, under the control of the control strategy in this paper, the current of the PMSM, the steady-state error is less than 0.4 A, and the tracking effect is always maintained with high accuracy.

Figure 6 illustrates the change curves of the braking force of the four wheels in the EHB braking system under sinusoidal working conditions, where FL FR RL RR correspond to the left and right wheels of the front axle and the left and right wheels of the rear axle, respectively. The AMEsim hydraulic model is set as the equal distribution of braking force between the front and rear axles. It can be observed from the curves that under sinusoidal working conditions, the trend of braking force change of the four wheels is the same, except that there is a slight difference in fluctuation between them during the change in direction of the brake push rod, and the change amplitude is within 2%, which indicates that the four-wheel synchronized braking effect is good.

The data in Fig. 7 were derived from the AMEsim hydraulic model as the actuator component of the cosimulation. The curves demonstrate the relationship between the brake master cylinder pressure and pedal force for the three boost characteristics, where green represents comfortable characteristics, blue represents normal characteristics, and red represents sports characteristics. These curves visualize the details of the different braking characteristics, verifying the design requirements. First, the three driving modes maintain the same cut-in force during the braking initiation phase, which ensures the consistency of the initial braking feeling. Second, during the boost jump-in phase, the comfortable mode corresponds to the largest boost jump-in value, the normal mode is slightly second, and the sporty mode is the smallest. Next, for the brake stroke, the comfortable mode has the largest boost ratio, whereas the sport mode has the smallest. This design of varying boost ratios allows the booster to provide different boost effects depending on the driving style, thereby realizing variable boost control. When the runout point is reached, the motor servo boost no longer increases in either mode, and the slopes of the three curves remain the same after the runout point. The maximum pedal force is 1995 N for the sport mode, 1665 N for the normal mode, and 1153 N for the comfortable mode; the difference in the maximum master cylinder braking force of the three characteristics is 3.15%. Finally, it is obvious from the curves that at the runout point, the pedal force required for the normal and sport modes is similar, whereas the comfortable mode requires the least pedal force. This braking performance enables the driver to achieve a more precise braking experience in different modes.

Physical diagram of the test vehicle-AutoBots-Pro-W4.

The test vehicle selected for this study was the distributed drive-by-wire chassis AutoBots-Pro-W4. Figure 8 shows a photograph of the test vehicle. We opted for this specific chassis due to its advanced CAN communication and Ethernet capabilities, coupled with a precise sensor system, which are essential for real-time communication control and for constructing a real vehicle verification platform. Most importantly, the test vehicle’s wire-actuated braking system aligns with the structural parameters of the braking system under study, making it an ideal candidate for our experiments. The AutoBots-Pro-W4 is equipped with brake pedal displacement sensors, master cylinder thrust and displacement sensors, brake lines and master cylinder pressure sensors, vehicle speed and wheel speed sensors, and motor position and current sensors, all of which are critical for our testing requirements. Its design and performance have been validated in similar research, establishing it as a reliable platform for our study. In this study, the MATLAB automation function of the TSmaster software (the interface is shown in the upper right corner of Fig. 8) was used to achieve real-time communication control through a dedicated CAN card and build a real vehicle verification platform to ensure the experimental plan.

Control input pressure curves for three types of experimental conditions.

Considering the different pedaling forces and speeds in different driving styles, the actual vehicle test selected three types of working conditions: sinusoidal, ramp, and variable-speed pulses for test verification. The specific conditions of the test vehicles are listed in Table 4. Among them, the sine and ramp pulses both simulated seven conditions of 15–60% amplitude of the brake pedal, and the variable speed pulse condition simulated five conditions of different action times of rapid deceleration (60% brake pedal) and emergency braking (100% brake pedal), as shown in Fig. 9. It should be noted that, because the CAN message sending is set with a sending interval of 20 ms, the curve has jagged steps.

Figure 10 shows the change curves of the motor control current (red curve) and the actual motor current (blue curve) under the three braking conditions. The current vibration that appears periodically in the initial stage of braking is due to the jump-in value stage of the EHB booster during the boosted braking process. The motor control strategy designed in this study can stabilize the current within 100 ms. The statistical results of control errors are shown in Table 4, in the steady-state stage of the braking process, the current changes in the three working conditions follow well, and the steady-state error does not exceed 3%, indicating that the current loop control strategy designed for the variable-boost characteristics operates normally, and the dynamic performance of the EHB-booster is good.

Current curves corresponding to three types of experimental conditions.

Master cylinder pressure curves of three types of experimental conditions.

Figure 11 shows the change curves of the control input pressure (red curve) and master cylinder brake pressure (blue curve) under the three braking conditions. The curve in Fig. 11 shows that the strategy designed in this study performed well under the three types of boost conditions. It can maintain good pressure under various conditions. The average delay of the actual pressure compared to the target control pressure was within 50 ms, and the peak error was within 0.1 Mpa, as shown in Table 5. The braking commutation actions that occur periodically under the three test conditions do not show an obvious overshoot in the pressure curve, which further illustrates the accuracy of the cosimulation model built in this study and the effectiveness of the multiclosed-loop control strategy designed in this study.

In Figs. 10 and 11, it can be observed that under various experimental conditions designed based on the three types of braking boost characteristics, there are significant changes in the gradients and slopes of the curves between different conditions. From the A and B plots of both figures, it can be seen that as the percentage of the brake pedal increases gradually from 15 to 60%, whether it is a sinusoidal pulse or a ramp pulse, the change in the braking pressure is proportional to the change in the percentage of the pedal, showing a gradually increasing trend. Comparing the result curves of the co-simulation experiment as shown in Fig. 5, it can be seen that the trends of simulation and real vehicle tests are consistent. In the real vehicle tests for various conditions, there is a phase lag in the braking pressure to varying degrees. The sinusoidal pulse condition has a lag of within 15ms, and the ramp pulse has an average lag of within 40ms. With the increase in the braking cycle, the lag time increases slightly.The pressure increases from 1.2 MPa at 15% to 4.8 MPa at 60%, demonstrating good tracking performance throughout the test cycle. Particularly noteworthy is the variable speed pulse test with five conditions, where significant slope changes can be seen in the C plots of Figs. 10 and 11. During the test, the brake pedal is pressed to 60% and 100% pedal positions in 200 ms, 500 ms, and 1000 ms, respectively, and the rate of increase in braking pressure shows distinct differences. The 1000 ms condition has the smallest pressure change slope, the 200 ms condition has the largest, and the 500 ms condition is in between. These changes correspond to the comfortable, normal, and sport braking requirements of driving styles. At the same time, at the initial stage of braking pressure increase, the slopes of pressure increase for these conditions show little difference, which is the initial stage of the braking pedal boost characteristic. By comparing the real vehicle test data with the simulation results, we find that the trends of changes in control input pressure, master cylinder brake pressure, and motor control current are highly consistent. In comfort mode, the real vehicle test data show the highest jump value and a relatively higher jump ratio in the linear boost section; in sport mode, the real vehicle test data also show a lower jump value and a lower boost ratio, both matching the simulation results.

In summary, the real car test can be verified with the results of the cosimulation (Fig. 7) and the boost characteristic curve (Fig. 2), further verifying the effectiveness and robustness of the variable boost characteristic control strategy based on driving style, which provides a basis for more complex scenarios and working conditions. However, we also noticed some differences between real vehicle tests and simulation results, which may be due to the nonlinear characteristics of the braking system modeling and the imperfect match of test conditions. These differences provide valuable feedback and will guide us in further optimizing the simulation model to better reflect the actual situation.

In this study, a variable boost characteristic control strategy based on the driving style is proposed to address the nonlinear challenges faced by a wire-controlled hydraulic brake system (EHB) with the personalized needs of intelligent driving. Its effectiveness was verified through a cosimulation and real vehicle tests.

This study innovatively proposes a design of the feel of the brake pedal based on the driving style and designs three modes, sporty, comfortable, and normal, to match the requirements of different driving styles.

A multi-closed loop control strategy that adapts to the variable boost characteristics is adopted, in which the speed loop adopts proportional control based on friction and inertia compensation to reduce the influence of nonlinear factors. The position loop introduces variable gain PD control to improve the response rate, and the current loop introduces a variable gain integral term to eliminate the steady-state error and the following error under the condition of variable boost characteristics.

Through cosimulation and verification of the test of the real vehicle, the control strategy proposed in this study can effectively address the nonlinear problems faced by the variable-boost EHB system and perform precise control of the brake pressure under the premise of changes in driving style.

The control strategy of this study provides a new concept for the personalized control strategy of the EHB system, which can significantly improve the control accuracy and driving experience of the EHB system and contribute to the improvement of the control accuracy and applicability of active braking in intelligent driving.

However, we are aware of certain limitations due to the limitations of the experimental equipment and sites. Specifically, our real vehicle testing failed to cover key conditions such as corner braking, high speed braking, low adhesion road surface, and emergency braking on variable adhesion road surface. These conditions are critical to the safety and reliability of autonomous vehicles. In addition, in the advanced autonomous vehicle system, in addition to the electronic hydraulic braking (EHB) system, there are a variety of configurations such as electronic mechanical braking (EMB) and pneumatic EBS to correspond to complex application scenarios of multiple models such as passenger cars and commercial vehicles. There is no doubt that these complex road conditions and application scenarios and vehicle types will involve the need for more personalized driving styles, resulting in more complex nonlinear disturbances.

In view of these limitations, we suggest that future studies can be based on the control strategy proposed in this study to establish a dynamic model closer to the actual complex conditions, to more accurately simulate and predict the performance of the braking system under different conditions. At the same time, we recommend exploring data-driven and deep learning methods to more effectively identify and eliminate nonlinear interference terms and improve the robustness and adaptability of braking systems. In addition, given the need for personalized driving styles, future research could further explore how control strategies can be used to meet the needs of different drivers and how these strategies can be implemented in autonomous driving technologies.

Data are provided within the manuscript and the Supplementary Material Files.

Meng, B., Yang, F., Liu, J. & Wang, Y. A survey of brake-by-wire system for intelligent connected electric vehicles. IEEE Access 8, 225424–225436 (2020).

Article Google Scholar

Li, D. et al. Review of brake-by-wire system and control technology. Actuators (2022).

Suzdaleva, E. & Nagy, I. Two-layer pointer model of driving style depending on the driving environment. Transp. Res. Part B Methodol. 128, 254–270 (2019).

Article Google Scholar

Lv, C. et al. Driving-style-based codesign optimization of an automated electric vehicle: A cyber-physical system approach. IEEE Trans. Industr. Electron. 66, 2965–2975 (2018).

Article ADS Google Scholar

Ma, Y. & Wang, J. Personalized driving behaviors and fuel economy over realistic commute traffic: Modeling, correlation, and prediction. IEEE Trans. Veh. Technol. 71, 7084–7094 (2022).

Article Google Scholar

Chengqun, Q. et al. A novel regenerative braking energy recuperation system for electric vehicles based on driving style. Energy 283, 129055 (2023).

Article Google Scholar

Park, S., Bae, S. & Lee, J. M. Numerical evaluation of braking feel to design optimal brake-by-wire system. Int. J. Veh. Des. 37, 1–23 (2005).

Article Google Scholar

Meng, D., Zhang, L. & Yu, Z. A dynamic model for brake pedal feel analysis in passenger cars. Proc, Inst. Mech. Eng. Part D J. Automob. Eng. 230, 955–968 (2016).

Article CAS Google Scholar

Pan, H., Guo, X., Pei, X. & Dong, X. Modeling, simulation and experimental analysis of brake pedal feel for passenger car (SAE Technical Paper, Tech. Rep, 2017).

Book Google Scholar

Sun, F., Liu, W., He, H. & Guo, H. An integrated control strategy for the composite braking system of an electric vehicle with independently driven axles. Veh. Syst. Dyn. 54, 1031–1052 (2016).

Article ADS Google Scholar

Li, L. et al. Transient switching control strategy from regenerative braking to anti-lock braking with a semi-brake-by-wire system. Veh. Syst. Dyn. 54, 231–257 (2016).

Article ADS Google Scholar

Todeschini, F., Corno, M., Panzani, G., Fiorenti, S. & Savaresi, S. M. Adaptive cascade control of a brake-by-wire actuator for sport motorcycles. IEEE/ASME Trans. Mechatron. 20, 1310–1319 (2014).

Article Google Scholar

Yong, J.-W., Gao, F., Ding, N.-G. & He, Y.-P. Pressure-tracking control of a novel electro-hydraulic braking system considering friction compensation. J. Central South Univ. 24, 1909–1921 (2017).

Article Google Scholar

Zhao, J., Chen, Z., Zhu, B. & Wu, J. Precise active brake-pressure control for a novel electro-booster brake system. IEEE Trans. Industr. Electron. 67, 4774–4784 (2019).

Article ADS Google Scholar

Chen, Z., Zhu, B., Zhao, J. & Wu, J. Variable servo characteristic brake system matching and implementing method based on driving style identification. IEEE Trans. Transp. Electrif. 9, 45–59 (2022).

Article Google Scholar

Zhang, R., Zhao, W., Wang, C. & Tai, K. Research on personalized control strategy of ehb system for consistent braking feeling considering driving behaviors. Energy 293, 130568 (2024).

Article Google Scholar

Lyu, N., Xie, L., Wu, C., Fu, Q. & Deng, C. Driver’s cognitive workload and driving performance under traffic sign information exposure in complex environments: A case study of the highways in china. Int. J. Environ. Res. Public Health 14, 203 (2017).

Article PubMed PubMed Central Google Scholar

Tian, H. Research on personalized control strategy of electric booster braking system for intelligent electric vehicle. Master’s thesis, (Jilin University, 2020).

Guoshun, C. A. I., Haoji, L. I. U., Jiwei, F. E. N. G., Liwei, X. U. & Guodong, Y. I. N. Review on the research of motion planning and control for intelligent vehicles. J. Autom. Saf. Energy 12, 19 (2021).

Google Scholar

Zhang, Q. et al. Key technologies and research progress of brake-by-wire system for intelligent electric vehicles. J. Mech. Eng. 60, 339–365 (2024).

Google Scholar

Xiong, L., Li, C., Zhuo, G., Cheng, Y. & Wang, X. Development status of electromechanical brake configuration and control technology. Automot. Eng. 45, 2187–2199 (2023).

Google Scholar

Jamil, H. et al. Analysis on the driving and braking control logic algorithm for mobility energy efficiency in electric vehicle. Smart Grids Sustain. Energy 9, 12 (2024).

Article Google Scholar

Sozer, Y. & Torrey, D. A. Adaptive flux weakening control of permanent magnet synchronous motors. In Conference Record of 1998 IEEE Industry Applications Conference. Thirty-Third IAS Annual Meeting (Cat. No. 98CH36242), vol. 1, 475–482 (IEEE, 1998).

Olsson, H., Åström, K., Canudas de Wit, C., Gäfvert, M. & Lischinsky, P. Friction models and friction compensation. Eur. J. Control 4(3), 176–195 (1998).

Article Google Scholar

Walker, J., Rucoba, R., Barnes, D. & Kent, S. Brake Vacuum Booster Characterization (Tech. Rep., SAE Technical Paper, 2019).

Book Google Scholar

Chen, P. et al. Design and power-assisted braking control of a novel electromechanical brake booster. SAE Int. J. Passeng. Cars Electron. Electric. Syst. 11, 171–181 (2018).

Google Scholar

Xiong, L., Han, W., Yu, Z.-P. & Li, H.-C. Pressure precisely control of master cylinder on integrated-electrohydraulic brake system considering the critical nonlinear characteristics. J. Mech. Eng. 55, 117–126 (2019).

Article Google Scholar

Chen, Q. et al. A multi-closed loop pressure control in electro-hydraulic brake system for electric vehicle. Int. J. Electr. Hybrid Veh. 15, 272–291 (2023).

Article Google Scholar

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This research was supported by the National Natural Science Foundation of China (Grant No.51975428).

Wuhan University of Science and Technology, School of Automobile and Traffic Engineering, Wuhan, 430065, China

Zhen Shi, Yunbing Yan & Sen Zhang

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Z.S. contributed to the conceptualization, methodology, sofware, visualization and design of the study and was involved in the drafting and revision of the manuscript. Y.Y. contributed to the conceptualization and design of the study and was involved in the drafting and revision of the manuscript. S.Z. assisted in the completion of the experiments and was involved in the drafting and revision of the manuscript. All authors have revised the paper.

Correspondence to Zhen Shi.

The authors declare no competing interests.

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Shi, Z., Yan, Y. & Zhang, S. Variable boost characteristic control strategy of hydraulic systems for brake-by-wire based on driving style. Sci Rep 14, 29412 (2024). https://doi.org/10.1038/s41598-024-80788-2

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Received: 31 July 2024

Accepted: 21 November 2024

Published: 27 November 2024

DOI: https://doi.org/10.1038/s41598-024-80788-2

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