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Development of a control method for an electromagnetic semi-active suspension reclaiming energy with varying charge voltage in steps

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Abstract

A system of electromagnetic semi-active suspension reclaiming energy (ESASRE), with an novel control varying charge voltage in steps (CVCVIS) based optimal integrated controller, is newly proposed to improve ride comfort and energy reclaiming. The proposed CVCVIS is built by changing the number of battery packs. The dynamic model of the semiactive suspension reclaiming energy is established first, which fully accounts for the non-linear characteristics of the damping actuator reclaiming energy (DARE). The parameters of DARE are decided by a compromise between ride comfort and manufacturing cost, with consideration of installation convenience. A integrated control system for ESASRE includes a controller for calculating the real-time ideal control force based on optimal linear quadratic Gaussian (LQG) control and the other for calculating the number of charging batteries to obtain the real-time actual control force using the proposed quasilinear relation function. Performance comparisons are implemented using three suspension types: ESASRE, the passive suspension, and the ideal active suspension. The performance index of ESASRE is 19.8% lower than that of the passive suspension, and 3.82% higher than that of the active suspension. With ESASRE, the power flowing into the battery pack accounts for 77.72% of the total vibration energy absorbed by DARE.

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Abbreviations

a2:

acceleration of sprung mass, m/s2

c b :

damping of passive suspension, N·s/m

c s :

structural friction damping of ESASRE, N·s/m

c vvd :

variable viscous damping, N·s/m

E :

eigenvector of system

e dz−1 :

dead zone voltage when ?v equals 1 m/s, V

e i (i=a, b, c):

ith phase back EMF of PMSM, V

F :

actual control force, N

F ida :

ideal active control force, N

F idsa :

ideal semi-active control force, N

F mn :

mean value of F, N

f0:

lower cut off frequency, Hz

f(θ i ) (i=a, b, c):

ith phase position function about the rotor angle displacement, rad

G q (n 0):

road irregularity coefficient, m2/m−1

i ab , i ca , i bc :

a−b, c−a and b−c phases current respectively, A

i i (i=a, b, c):

ith phase current of PMSM, A

J :

suspension quadratic performance index

k 1 :

tire stiffness, N/m

k 2 :

suspension stiffness, N/m

k F−∆v :

the slope of the F relative to ∆v, N/(m/s)

L :

phase self inductance, H

M :

phase mutual inductance, H

m 1 :

unsprung mass, kg

m 2 :

sprung mass, kg

n 0 :

reference spatial frequency, m−1

P all :

all power absorbed by cs and DARE, kW

P b :

power flowing into battery pack, kW

P ls :

power consumed by three phase resistances and c s , kW

p p :

number of paralleled pole pairs of stator phases

p s :

lead of ball screw mechanism, m

q :

displacement input of suspension system, m

Q i :

ith diode in Figure 2

R :

phase resistance, Ω

S :

solution of Ricatti equation

S i :

ith controlled switch in Figure 2

T :

total time of vehicle running, s

T m :

electromagnetic torque of PMSM, N·m

t :

time variable, s

u :

vehicle speed, m/s

u 0 :

voltage of a single battery, V

u ba :

real-time charge voltage, V

−u os :

offset voltage to ceil(·) function, V

v flr :

floor value of ∆v, m/s

w :

road white-noise signal

x 1 :

vertical displacement of unsprung mass, m

x 2 :

vertical displacement of sprung mass, m

Y :

feedback gain matrix of LQG controller

∆v :

relative speed of ESASRE, m/s

δ 1, δ;2 :

weight of (x 1−q)2 and weight of (x 2−x 1)2

θ :

angular displacement of PMSM, rad

Φ :

flux linkage of PMSM, Wb

η :

number of charge batteries

a, b, c :

three phases of PMSM

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Authors and Affiliations

  1. School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang, 213013, China

    S. A. Chen, X. Li & L. J. Zhao

  2. Department of Mechanical Engineering, Chonnam National University, Gwangju, 500-757, Korea

    S. A. Chen, Y. X. Wang & Y. B. Kim

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  1. S. A. Chen
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  2. X. Li
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  3. L. J. Zhao
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  4. Y. X. Wang
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  5. Y. B. Kim
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Correspondence to Y. B. Kim.

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Chen, S.A., Li, X., Zhao, L.J. et al. Development of a control method for an electromagnetic semi-active suspension reclaiming energy with varying charge voltage in steps. Int.J Automot. Technol. 16, 765–773 (2015). https://doi.org/10.1007/s12239-015-0077-3

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  • DOI: https://doi.org/10.1007/s12239-015-0077-3

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