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Modeling and Control of A High Speed On/Off Valve Actuator

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Abstract

Accurate electromagnetic force control in a high speed on/off valve actuator (HSVA) can improve the performance of a vehicle braking system, and an accurate theoretical model is the key to smoothly controlling the high speed on/off valve. Therefore, a nonlinear model of an HSVA is proposed in this paper. Three subsystems are modeled as a spring/mass/damper system, a nonlinear resistor/inductor system and a multiwall heat transfer system, respectively. Then, a sliding-model controller combined with a sliding-model observer is designed to adjust the electromagnetic force for an accurate HSVA state control, taking the effect of the coil heating into account. The feasibility of the three submodels and the sliding-model controller are verified by comparing the simulation results with the experimental results obtained on a test bench. Our study shows that the three subsystems are coupled to one another through resistance, displacement, and temperature. When the excitation voltage exceeds 9 V, the coil temperature can reach more than 150 degrees Celsius within 300 s, and the electromagnetic force decreases by approximately 30 %. However, by applying the above control strategy, the electromagnetic force can also be stable, fluctuating within 5 % even if the temperature of the coil rises to the thermal equilibrium temperature.

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Abbreviations

A e :

section area of the air gap

B :

magnetic flux density

c :

coulomb friction term

c 1 :

specific heat capacity of the copper wire

c 2 :

specific heat capacity of the nylon frame

c 3 :

specific heat capacity of the shell

d r :

differential thickness

e :

is the estimation error

F M :

electromagnetic force

F S :

spring force

F pre :

preload of the return spring

H :

magnetic field

i :

current through the coil

i d :

desired current

i m :

measured current

J e :

eddy current density

k :

return spring

k pi :

proportional gain

k ii :

integral gain

L :

inductance of the coil

m 1 :

mass of the copper wire

m 2 :

mass of the nylon frame

m 3 :

mass of the shell

N :

number of turns on solenoid coil

n x, n y, n z :

direction cosines of the exterior normal to the boundary

P R :

copper loss

Pe :

iron loss

Q :

heat conduction rate

q :

heat flow

q hc :

heat flux of heat conduction

q t :

heat flux of thermal convection

q V :

heat generation ratio

R :

resistance of the coil

r 1 :

inner radius of a heat transfer layer

r 2 :

outer radius of a heat transfer layer

T :

temperature

U s :

supply voltage

U R :

voltage of the equivalent resistance

U L :

voltage of the equivalent inductor

η :

viscous damping term

x :

armature/spool displacement

xd :

desired armature position

λ :

thermal conductivity

λ x, λ y, λ :

heat conductivity coefficients in the x-, y- and z-directions

ε f :

black body coefficient

σ :

electrical conductivity

Ψ :

flux linkage

α w :

temperature coefficient of resistance

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Acknowledgement

This work was supported by the National Natural Science Foundation of China (grant number 51475197 and 51422505). The authors would like to thank Tianjin Trinova Automobile Technology Co. Ltd. for providing technical and experimental support for this research.

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Authors and Affiliations

  1. China Productivity Center for Machinery, China Academy of Machinery Science and Technology, Beijing, 100044, China

    Jigen Fang, Xifeng Wang & Jinjun Wu

  2. State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, 100084, China

    Liang Li & Xiang Gao

  3. School of Mechanical Engineering, Yanshan University, Hebei, 066004, China

    Shuai Yang & Yue Tian

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  1. Jigen Fang
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  2. Xifeng Wang
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  5. Liang Li
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Correspondence to Liang Li.

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Fang, J., Wang, X., Wu, J. et al. Modeling and Control of A High Speed On/Off Valve Actuator. Int.J Automot. Technol. 20, 1221–1236 (2019). https://doi.org/10.1007/s12239-019-0114-8

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  • DOI: https://doi.org/10.1007/s12239-019-0114-8

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