Temperature Compensation Algorithm for Hydraulic System Pressure Control

Huien Gao, Liang Chu, Jianhua Guo, and Dianbo Zhang

(1.State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China; 2.Jilin Provincial Institute of Standards, Changchun 130022, China)

Abstract: In this paper the control mechanism of solenoid valve is analyzed, which shows the solenoid valve control is actually the control of coil current. The response characteristic of coil current is related to coil inductance and resistance. The coil resistance is influenced greatly by the ambient temperature and the self-heating of coil, which affects the control precision of coil current. First, considering the heat dissipation mode of coil, the coil temperature model is established from the perspective of heat conduction, and a temperature compensation algorithm for hydraulic system pressure control is put forward. Then the hardware-in-the-loop testbed is set up by using the dSPACE platform, carrying out wheel cylinder pressurization tests with inlet valve fully opened at -40 ℃ and 20 ℃, and testing the actual pressure of wheel cylinder with the target pressures at -40 ℃ and 6 000 kPa/s (pressurization rate). The results show that the pressure control temperature compensation algorithm proposed in this paper accurately corrects the influence of resistance temperature drift on the response accuracy of wheel cylinder pressure. After the correction, the pressure difference is less than 500 kPa, which can meet the control accuracy requirements of solenoid valve, enriching the linear control characteristic of solenoid valve.

Key words: braking energy recovery; heat conduction; temperature compensation; linear pressure control; rapid control prototype

For braking energy recovery of automobile, the key coordinated distribution of electro-hydraulic braking force is the accurate response of hydraulic braking force[1-7]. As the main actuator of hydraulic control unit, the solenoid valve’s control precision determines the response characteristic of wheel cylinder pressure, which is very important to the brake safety of the whole vehicle. For the linear solenoid valve of hydraulic control unit, patents[8-9]calculate the coil current according to the pressure difference of valve port and obtain PWM control signals, finally correcting the coil current in real time by comparing the measured control signal with the allowable deviation range of the system. For the solenoid valve of ABS/ESP hydraulic unit, patent[10]analyzes the working principle, the relationship between current and coil flux, etc., finally obtaining the calibration method of drive current of solenoid valve. Ref. [11] carries out an experimental study for the component mechanism and control characteristic of ESC hydraulic control unit and controls the high-speed on-off valve and hydraulic pump motor based on a number table method, obtaining a good pressure control effect. For the control of wheel slip rate, patent[12]proposes a hydraulic brake control method, which takes the estimated pressure of wheel cylinder, pressure of main cylinder and target pressure of wheel cylinder as the main reference parameters, and controls the action time of solenoid valve by using the hydraulic model in the reverse direction.

Most researchers have only studied the linear control characteristic of solenoid valve, only a few researchers consider the influence of coil temperature on the linear control of solenoid valve. This paper studies the control mechanism of solenoid valve, and points out that the key to solenoid valve control is the control of coil current and that the response characteristic of coil current is related to the coil inductance and coil resistance. Through studying the coil temperature characteristic of solenoid valve, we corrected the control signal of solenoid valve and put forward a coil current temperature compensation algorithm of solenoid valve, which improves the current control accuracy of solenoid valve and realizes precise control of wheel cylinder pressure.

1 Working Principle and Control Mechanism of Solenoid Valve

The braking system configuration used in this paper is the electronic braking system developed by a research team. The braking system configuration is shown in Fig.1[13]. In the active pressurization process, the braking system closes the two normally open valves of anterior and posterior axes to control the pressurization of wheel cylinder by linear adjustment of high pressure accumulator and inlet valves #1 and #2.

Fig.1 Braking system configuration

1.1 Force analysis of solenoid valve

The inlet and outlet valves in the hydraulic braking system and the two-way valves at the front end of wheel cylinder are linear valves. Taking the inlet valve as an example, the force on solenoid valve in the working process is analyzed as belows. The structure of inlet valve is shown in Fig.2 and the force analysis is shown in Fig.3.

Through analysis, the force equation of the valve is obtained as

(1)

wheremis the mass of spool;xis the displacement of spool;Fv(damping force) andFf(frictional force) are less thanFm(electromagnetic force),Fh(hydraulic force) andFs(spring force), so their influences on spool movement are ignored.

According to Ref.[14], the magnitude ofFm(electromagnetic force) is related to the coil current of solenoid valve andx(spool displacement), so its calculation formula is shown as

(2)

whereNis turns of the coil;Iis the coil current;δis the length of air gap;A0is the sectional area of working air gap;μ0is the permeability of vacuum;lis the minimum primary working air gap.

Fig.2 Structure of inlet valve

Fig.3 Force analysis of spool

According to Ref.[15], the magnitude ofFh(hydraulic force) is related to Δp(pressure difference of valve port) andx(spool displacement), so its calculation formula is presented as

(3)

whereCdis the flow coefficient;Cvis the velocity coefficient;Ris the radius of spool end;αis the direction angle; 2θis the opening of spool plane;ρis the liquid density;Lis the damping length.

Eq.(1) can be rewritten as

(4)

wherexsis the pre-tightening displacement of spring;Ksis the spring stiffness.

Spool displacement-pressure difference-coil current relation obtained through the mathematical model simulation above when the spool is in a force balance state, as shown in Fig.4.

Fig.4 Spool displacement-pressure difference-coil current relation in static state

1.2 Analysis of control mechanism of solenoid valve

Through the above analysis, it is known that the control of inlet valve can be equivalent to the control of the current in the valve, however, it is difficult to control the current. A component with the characteristics of inductance (L) and resistance (R) is used as the inlet valve coil. It can be found that the relationship between the current and voltage at both ends of the inlet valve coil[16]

(5)

It can be seen from Eq.(5) that the voltage at both ends of the inlet valve coil has a linear relationship with the current under the influence of the coil inductance. Because the hydraulic braking system should be coordinated with the motor brake, a more precise control of the wheel cylinder pressure is required. However, the control of wheel cylinder pressurization mainly depends on the control of the inlet valve. The pressurization mode of wheel cylinder has different requirements for different braking conditions (the range of pressurization rate is large), so for the inlet valve, a large range of speed control should be achieved. Through the above analysis, it is known that the control of pressurization valve depends mainly on the control of spool force of inlet valve. Among themFvandFfcan be ignored;FhandFscannot be actively controlled when the spool is working; onlyFmcan be controlled. The characteristic of inlet valve can be controlled after the current in the control valve is obtained according to Eq.(2). The current delay in the coil caused by the influence of inductance is called response constant. There are many factors that can influence the valve response constant, so the characteristic of the valve is directly obtained from the test.

Fig.5 shows the duty ratio of the PWM signal corresponding to the current of solenoid valve. Fig.6 shows the wheel cylinder pressure, which the inlet valve can hold under the corresponding current.

Fig.5 Duty ratio of the PWM signal and corresponding current of solenoid valve with time

Fig.6 Wheel cylinder pressure which the inlet valve can hold under the corresponding current

2 Temperature Compensation Algorithm for Solenoid Valve

2.1 Temperature characteristic

The above model simulation results are obtained by simulations and tests for the actual hydraulic system at room temperature and ignores the influence of temperature on the current response characteristic. However, the hydraulic braking system is installed in the engine room of the car, so the working temperature depends on the external temperature. The lowest temperature in winter can reach -40 ℃ and the highest temperature in summer can reach 70 ℃ (depends on the differences of latitude and hatch greenhouse effect in summer), so the influence of temperature on braking system should be considered. The coil temperature characteristic of the inlet valve is the main influencial factor of the hydraulic control system. The measured coil resistances are 4.3 Ω (25 ℃), 3.07 Ω (-40 ℃), 6.25 Ω (120 ℃), respectively. If the coil is controlled at 4.3 Ω (25 ℃) under 1 A, a temperature change of 110 K could be generated after a few minutes. Therefore, the control signal of solenoid valve is adjusted by studying the coil temperature model. At the same time, the hydraulic system is tested at a low temperature to realize the precise control of pressure by comparing the change in characteristic of brake fluid under the low temperature condition.

2.2 Temperature model

Because the coil of solenoid valve is in contact with the hydraulic unit and is sealed by a control unit shell, the heat dissipation of coil is mainly realized by heat conduction with the hydraulic unit. Though the coefficient of heat conduction, the reciprocals of specific heat capacity of coil and hydraulic unit, heat power of coil, the following equation can be obtained:

(6)

whereTμis the coil temperature;kμis the coefficient of heat conduction between the coil and hydraulic unit;THAis the contact temperature between the coil and hydraulic unit;cμis the reciprocal of the specific heat capacity of the coil (unit: K/J);cμ=0.25 K/J;Pμ(t) is the heat power of the coil.

Because the coil is in contact with the hydraulic unit, the temperature of the coil can be expressed as

(7)

whereΘμis the temperature difference between the coil and hydraulic unit caused by change in the hydraulic unit temperature;θμis the temperature difference between the coil and hydraulic unit caused by changes in the coil temperature.

The volume of hydraulic unit is large, and its temperature changes slowly. The change in hydraulic unit temperature is expressed by the diffusion coefficient (D) as

(THA(t2)-THA(t1))2=D2(t2-t1)

(8)

Through the Green equation (the relationship between the heat source and thermal field) PT1 first order filtration, Eq.(7) can be expressed as

(9)

The calculation formula of hydraulic unit temperature can be obtained according to Eq.(9) by the weighted average method.

(10)

The time interval between coil measurement is the same. Undert1

(11)

Att2,Θ(t) can be calculated as

(12)

Among them, the temperature of hydraulic unit can be obtained by a temperature sensor of the car, so the coil temperature should not be measured directly. However, when the hydraulic system operates initially, the coil temperature is the same as the hydraulic unit temperature (ambient temperature). Therefore, at the initial time, the coil temperature can be replaced by the hydraulic unit temperature. The temperature difference between the coil and hydraulic unit can be obtained according to Eqs. (10) (12).

(13)

According to the measuring data, the mean square deviation of the temperature of hydraulic unit can be expressed as

(14)

The temperature value of the hydraulic unit att2can be calculated according to Eq.(11).

(15)

If the coil temperature cannot be measured or there is no measuring data, the coil temperature can be expressed as

(16)

The key parameter of solenoid coil control is the coil resistance, whose change is caused by the temperature. And the resistance is

(17)

whereRtis the coil resistance att;Ttis the coil temperature att;T0is the initial temperature of the coil;R0is the initial resistance of the coil.

According to different changes in resistance, the Duty value of the PWM signals at both ends of the coil can be adjusted to adjust the currentItarin the coil.

(18)

3 Temperature Characteristic of Fluid

The temperature characteristic of solenoid valve is analyzed above, and the temperature model of solenoid valve is established. The hydraulic system is tested at a low temperature below. Considering the change of brake fluid characteristic at low temperatures, the fluid temperature characteristic is analyzed.

When the fluid flows, mutual friction between internal fluids will happen. This phenomenon is called fluid viscosity; the ration of the frictional force on the internal unit area to the fluid velocity perpendicular to the flow direction of the fluid when the fluid flows is called dynamic viscosity. The kinematic viscosity (m2/s) is the ratio of the dynamic viscosity to the material density at the same temperature. It is known according to the Newton formula:

τ=ηdv/dx=ηD

(19)

whereτis the tangential stress;ηis the kinematic viscosity;Dis the shear rate.

The velocity of the fluid is different at different positions and the friction between the fluids with different velocities affects the movement of each other. This phenomenon is called resistance to motion[17]. In order to maintain the flow of the fluid, a reacting force must be applied, which is called shear stress (τ(N/m2)). The shear stress and shear rate are two characteristic parameters for the analysis of fluid characteristic.

Therefore, the influence factors of fluid viscosity are temperature, pressure, shear rate, etc. However, in a hydraulic control mode, the pressure and shear rate remain unchanged basically, so the most important factor affecting the fluid viscosity is the temperature. The viscosity property of brake fluid is shown in Tab. 1[18].

Tab.1 Viscosity characteristic of brake fluid

From Tab.1, it is obvious that the viscosity characteristic of fluid varies greatly at different temperatures, especially the viscosity of fluid at low temperature is larger. Therefore, for the study of hydraulic system, we should adjust the control mode under low temperature conditions. In this paper, the characteristic of the hydraulic system at low temperature is compared with that at room temperature and the temperature control model of the coil in the valve is adjusted to make the system adapted to the influence of temperature change.

4 Bench Test

In this paper, a hardware-in-the-loop testbed is built by using the rapid control prototyping hardware and software technology of dSPACE Company. Micro-Autobox is used as a ECU controller to run the vehicle model and brake control algorithm developed based on Matlab/Simulink environment. The host and Micro-Autobox is communicated with each other through TCP/IP communication protocol. Micro-Autobox receives the real-time sensor signal sent by I/O interface, runs the pressure control algorithm and sends the control signal of controller to RapidPro drive controller to drive the hydraulic braking system hardware, realizing the change of wheel cylinder pressure. The schematic diagram of bench test is shown in Fig.7.

Fig.7 Schematic diagram of bench test

In order to verify the pressure control temperature compensation algorithm, the bench test was carried out in a constant temperature environment. Considering that the higher kinematic viscosity of brake fluid at low temperature affects the pressurization rate of wheel cylinder, wheel cylinder pressurization tests are carried out with inlet valve fully opened at -40 ℃ and 20 ℃ for comparison and the test results are shown in Fig.8. According to NEDC, US06 and UDDS, cycle conditions commonly used in current regulations, the maximum pressurization rates are 5 230 kPa/s, 4 350 kPa/s and 2 570 kPa/s, respectively. At the time of braking in normal working conditions, the maximum pressurization rate is no more than 6 000 kPa/s, so the pressurization test at low temperature is carried out at 6 000 kPa/s. The test results are shown in Fig.9.

Fig.8 shows the pressurization contrast data of the pressurization valve when it is fully opened at high and low temperature, from which we can see that the starting time of wheel cylinder pressurization at -40 ℃ is the same as that at 20 ℃, but the pressurization rate at -40 ℃ is lower than that at 20 ℃ due to higher viscosity of brake fluid at low temperature.

Fig.8 High and low temperature contrast curves with inlet valve fully opened

Fig.9 Linear pressurization contrast curves of inlet valve

Fig.9 shows the linear pressurization contrast data of the pressurization valve at low temperature, from which we can see that before the correction, the starting time of pressurization is 0.5 s later than the target starting time at -40 ℃ and the pressure difference is larger, which greatly affects the braking safety. After correction, the pressure difference is less (within 500 kPa) and the pressure can better follow the target pressurization curve, which meets the control accuracy requirements of solenoid valve. Therefore, the pressure model proposed in this paper has an obvious effect on the temperature compensation for the hydraulic system.

5 Conclusions

Through the analysis of the working principle and control mechanism of the solenoid valve, it is concluded that the key to the linear control of the solenoid valve is to control the coil current. Then, through the analysis of current response characteristics, it is shown that the coil current is greatly influenced by the coil inductance and resistance, of which the ambient temperature and self-heating of coil greatly affect the resistance and reduces the control precision of current.

In this paper, the solenoid valve coil temperature model is established with the basis on the temperature characteristics of solenoid valve, and the temperature compensation algorithm for hydraulic system is put forward. Through the bench test, it is proved that the model can better correct the influence of coil resistance temperature drift and can follow the target pressurization rate at -40 ℃.