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In order to improve the braking performance and safety performance of electric vehicles driven by a hub motor, the cylinder pressure estimation and pressure control of its hydraulic braking system are studied. In this paper, a mathematical model is established for the solenoid valve, a key component of the hydraulic actuator, and the hydraulic and electrical characteristics of the solenoid valve are studied. A state equation is established for the solenoid valve, and the square root volume Kalman filter (SRCKF) algorithm is used to estimate the solenoid valve spool position. The brake fluid flow and brake wheel cylinder pressure are calculated based on the spool position. Finally, a solenoid valve spool position control algorithm based on sliding mode variable structure algorithm is designed, and the brake pressure in the brake wheel cylinder is controlled by adjusting the spool position. Matlab/Simulink-AMESim software simulation and hardware-in-the-loop were used to verify the algorithm. Simulation results show that the brake cylinder pressure can be estimated accurately, and the pressure control algorithm can accurately follow the control target value.

Electric vehicles driven by in-wheel motors are highly competitive in the market. An important method to improve the energy utilization rate of electric vehicles is braking energy recovery technology. This technology has always been a hot research area for electric vehicles. While studying the braking energy regenerative technology, the research team designed a new type of hydraulic control unit. Based on the HCU, a series of regenerative braking energy coordinated control research is carried out [

The target wheel cylinder pressure is calculated by the ABS control algorithm. Based on the target wheel cylinder pressure, the estimated value of the current pressure of the wheel cylinder, and the current solenoid valve working condition, the solenoid valve control command is calculated by the pressure control algorithm. The current actual pressure of the wheel cylinder and the target pressure are monitored in real time. The control command and working status of the solenoid valve are constantly adjusted by the pressure control algorithm so that the actual pressure of the wheel cylinder reaches the target pressure as soon as possible.

Qu introduced the pressure control method based on program logic (if-else) [

Due to the increasingly higher requirements for control accuracy and speed of the wheel cylinder pressure control system, the PID algorithm has gradually failed to meet the demand. Aiming at the various defects of PID control algorithms, such as poor real-time control system, poor robustness, easy to generate oscillations in the integration link, susceptibility to external disturbances, and sensitivity to changes in system parameters, various advanced and effective control theories [

The hydraulic pressure control unit (HCU) is the core unit of the hydraulic pressure control system. The solenoid valve is one of the main devices. The hydraulic pressure control of the wheel cylinder is closely related to the solenoid valve. At present, commonly used solenoid valves include on-off valves, high-speed on-off valves, and linear solenoid valves. Since the on-off valve only has two states of open and closed, it is very difficult to achieve continuous flow control. In [

The high-speed on-off valve has the same working principle as the traditional on-off valve. The on-off of the brake fluid is controlled by switching between the on and off states of the high-speed solenoid valve. The difference is that the operating frequency of the high-speed on-off valve is higher. In [

The proportional valve can continuously control the brake fluid flow. However, the cost of the proportional valve is relatively high, and it is not realistic to apply it to the automobile brake system. In [

After analysis of references, in order to improve the braking performance and safety performance of the wheel motor-driven electric vehicle, a composite braking system was designed. In compound brake systems, high-speed on-off valves are used to control the brake fluid flow. The mathematical model of the high-speed on-off valve was established, the hydraulic characteristics and the electrical characteristics of the high-speed on-off valve were studied. The state equation of the high-speed switching valve is established, and the square root volume Kalman filter (SRCKF) algorithm [

This paper is structured as follows: in Section

As shown in Figure

Architecture of proposed hydraulic control unit.

The structure of the solenoid valve can be referred from Dr. Fan’s thesis [

During braking, the valve spool is mainly subjected to spring force, friction force between push rod and pipe wall, electromagnetic force, and hydraulic power of brake fluid. The structure of the on-off solenoid valve is shown in Figure

The structure of the on-off solenoid valve.

The force analysis diagram of the solenoid valve is shown in Figure

Force analysis diagram of valve.

The model of electromagnetic force

According to Maxwell’ stress theory, the electromagnetic force acting on the spool can be expressed as

Coil magnetic field strength is mainly determined by two factors: one is the magnitude of current, and the other is the back electromotive force. Therefore, the loop control valve coil circuit model is

When the valve spool is opened by electromagnetic force, the velocity and direction of brake fluid will change. In this paper, the space between the spool and the oil inlet of the solenoid valve is taken as the research object, as shown in Figure

Schematic diagram of hydrodynamic force.

Dimensional parameters of the space consisting of the spool and seat are substituted into equation (

The flow rate of brake fluid through the valve seat is expressed as

According to Bernoulli equation in fluid mechanics,

Combining equations (

Combining equations (

When the solenoid valve is working, the spool will move up or down to change the wheel cylinder pressure. At this time, the transient flow force can be expressed as

The entire pressure estimation and pressure control system is shown in Figure

Overall structure diagram of the pressure estimation and pressure control system.

In the pressure control algorithm, a spool position controller based on the sliding mode algorithm is adopted to adjust the WCP. The input of pressure control algorithm is spool position

The calculation method of the brake wheel cylinder pressure is mainly based on the P-V characteristic curve of the brake fluid. The volume increase of the brake fluid volume in each control cycle plus the original brake fluid volume can be used to obtain the total volume in the wheel cylinder. Then, the P-V characteristic curve check table can be used to obtain the pressure value in the brake wheel cylinder.

The brake fluid volume increment is determined by the opening of the valve. The volume increase of the brake fluid is as follows:

The calculation method of the wheel cylinder pressure in the pressurization stage is shown in Figure

Schematic diagram of a method to calculate cylinder pressure.

Combining equations (

For equation (

Schematic diagram of SRCKF.

As can be seen from Figure

Combining equations (

Combining equations (

During the phase, the brake fluid increment can be expressed as

Then, the flow rate is integrated, and the volume increase of the brake fluid during the decompression phase can be obtained:

Finally, by adding the original brake fluid volume and the current volume increment, the cylinder pressure in the brake wheel cylinder during the decompression stage can be obtained by using the PV characteristic curve look-up table method:

The pressure control of the valve is also divided into a pressure increasing phase and a pressure reducing phase. The two phases are controlled differently. During the decompression phase, the valve port is completely opened to achieve the purpose of rapid decompression. The control method in the pressure increasing phase is relatively more complicated than that in the pressure reducing phase. The pressure control strategy in the pressure increasing phase is shown in Figure

The analysis in Section

As shown in Figure

Schematic diagram of cylinder pressure control strategy.

Similarly, the target value of the wheel-cylinder pressure and the target value of the spool distance are converted by the PID algorithm:

Relying on the PID algorithm, the control of the brake wheel cylinder pressure is converted to the control of the valve spool displacement. Then, the sliding mode variable structure control algorithm is used to solve the nonlinear problem between the wheel cylinder pressure and the valve spool displacement.

The sliding-mode surface is chosen as

By differentiating

Exponential reaching law is chosen:

According to equations (

According to equations (

The relationship between the target value of brake wheel cylinder pressure and the target value of solenoid valve coil current is as follows:

The brake wheel cylinder pressure estimation and control algorithms mentioned in this paper are verified by software cosimulation. Software cosimulation is shown in Figure

Schematic diagram of software cosimulation.

The execution period of pressure estimation algorithm and pressure control algorithm is 10 ms. The pressure estimation algorithm requires the solenoid valve opening time parameter, which is calculated by the pressure control algorithm. The pressure control algorithm section requires the wheel cylinder pressure target value and the pressure estimate difference. The coil current, voltage parameters, and master cylinder pressure are used as input parameters to the pressure estimation algorithm model and the control algorithm model, respectively.

Parameters of the valve model are listed in Table

Parameters of the valve model.

Variable | Symbol | Value |
---|---|---|

Mass of the valve spool | ||

Number of valve coil windings | 300 | |

The area of the magnetic pole | ||

Preload force of spring | ||

Stiffness coefficient of the return spring | ||

Width of secondary air gap | ||

Radius of the spool | ||

Electric resistance of the solenoid coil | ||

Mass density of brake fluid | ||

Inlet section area of valve | ||

Cone angle of valve seat |

The key to the accuracy of the pressure value lies in the spool displacement estimation. Therefore, the spool displacement estimation algorithm needs to be verified. In the simulation verification, the spool stroke of the solenoid valve is forced to make a cosine curve. The purpose of this is to verify the spool estimation algorithm based on SRCKF. During this process, the MCP is set to make a step change every 37.5 ms to see whether SRCKF is robust to MCP changes. The simulation curve is shown in Figures

The curve of estimated spool position value and real value.

The relative error between estimated spool position value and real value.

The curve of MCP and WCP.

The curve of estimated coil current value and real value.

As shown in Figure

Firstly, the wheel cylinder pressure estimation algorithm is verified. Figure

Schematic diagram of solenoid valve control instruction.

Curve of estimated pressure value.

Curve of error value.

The simulation verification results of the wheel cylinder pressure control algorithm are shown in Figures

Curve of estimated and actual cylinder pressure.

Curve of error value.

Curve of valve spool position.

In this paper, the pressure estimation and wheel cylinder pressure control algorithm designed in this paper are verified by software simulation. Then, the hardware-in-loop experiment is used to further verify the algorithm. The bench is shown in Figure

Architecture diagram of HIL.

As shown in Figure

Curve of data detail.

Curve of coil current.

Figure

Curve of stepped pressurization.

Curve of coil current.

In order to compare the pressure control effects of the proposed pressure control method and the on-off threshold control method, a slope WCP increase test was implemented. This method has been introduced in many references [

The curve of WCP pressure used by on-off threshold control.

The curve of coil current used by on-off threshold control.

Figure

The curve of WCP pressure used by the proposed control method.

The curve of coil current used by the proposed control method.

Firstly, this paper studies the working mechanism and characteristics of the solenoid valve of HCU. Then, according to the PV characteristics, the pressure estimation algorithm and pressure control method of brake wheel cylinder are designed. Finally, the pressure estimation and pressure control algorithm are verified by HIL, and the following conclusions are obtained:

The valve is an on-off switching solenoid valve. Electromagnetic force and hydraulic force together affect the position of the valve spool. The change in the position of the valve spool will affect the brake fluid flow into the brake wheel cylinder. Based on this, the state equation is established. Then, the position of the valve spool is calculated by the square root volume Kalman filter algorithm.

The electromagnetic force can be effectively adjusted by changing the coil current of the valve. The sliding mode variable structure algorithm is used to adjust the position of the valve spool, so as to change the brake fluid flow into the wheel cylinder. Finally, the purpose of accurately adjusting the brake wheel cylinder pressure was achieved.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.