Applied Mechanics and Materials
ISSN: 1662-7482, Vols. 201-202, pp 433-437
doi:10.4028/www.scientific.net/AMM.201-202.433
© 2012 Trans Tech Publications, Switzerland
Online: 2012-10-26
Regenerative Braking System Pressure Control Calculation
Based on ABS Hydraulic Model
Liang Chua, Jian Chenb, Liang Yaoc, Chen Chend and Jianwei Caie
Jilin University, Changchun, Jilin Province 130021, P.R. China
a
[email protected], [email protected], [email protected], [email protected],
e
[email protected]
Keywords: Regenerative braking system; ABS; Hydraulic model; Master cylinder; Wheel cylinder;
Accumulator; Valve
Abstract. The main objective of this work is to present a methodology for development of
regenerative braking system hydraulic model that can be used to estimate the master cylinder
pressure, master cylinder travel position, normal open valve fluid flow, normal open valve
cross-sectional area, normal close valve fluid flow, normal close valve cross-sectional area,
accumulator fluid flow and brake caliper fluid flow. According to the above hydraulic model
calculation, the cooperation between regenerative braking system generator and ABS hydraulic
braking control will be smooth and the arbitration strategy can be designed. Through the simple
hydraulic model, the entire brake circuit of ABS can be derived easily.
Introduction
Regenerative braking system based on ABS control can significantly improve vehicle stability and
oil consumption. According to the hydraulic model calculation in this work, the cooperation
between regenerative braking system generator and ABS hydraulic braking control [1-3] will be
smooth and the arbitration strategy [4] can be designed.
The similar function products have been produced in the world. But the domestic research and
development is still in the initial stage. The key technology includes the control logic, ECU, sensors,
hydraulic control unit development and evaluation of matching system. Hydraulic control unit is the
core implement components, its performance directly affects the control system’s performance.
One Wheel Hydraulic Circuit
First, a simplified hydraulic brake circuit is placed with ABS simple model. In addition, braking
system should be considered where no ABS intervenes. Fig. 1 shows the hydraulic circuit with one
wheel model. It consists of an inlet valve (NO), an outlet valve (NC), a wheel cylinder (Cal), a
master cylinder (MC), a spring accumulator (accu) and a pump with controlled flow rate (P).
Fig. 1
Simplified brake circuit model
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Advances in Engineering Design and Optimization III
q: Volumetric flow rate
p: Pressure
A: Cross-sectional area
V: Volume
cq: Flow coefficient
E: Modulus of elasticity
V0: Volume of master cylinder
∆p: Pressure difference
ρ: Fluid density
α: Flow coefficient
accu: Accumulator
β: Characteristic parameter
The hydraulic flow dynamic formulas can be derived as below:
2 ∆ p NO
q NO = A NO c q
ρ
V Cal
p MC =
E
V0
p
Coefficient
: Pressure deviation
x : Velocity
v :
Volumetric flow rate
(1)
2 ∆ p NC
q NC = A NC c q
 p
=  Cal
 α Cal
,
c:
(2)
ρ
1
 β Cal


(3)
(∑ q )
(4)
MC
Vaccu = c accu p accu
(5)
The balance equations are the following.
∑q
MC
= qP + AMC x − q NO
(6)
VCal = q NO − q NC
(7)
Vaccu = q NC − qP
(8)
∆PNO = PMC − PCal
(9)
∆PNC = pCal − p accu
(10)
And pMC, pCal and paccu differential equations:
p MC =
E
V0

 q P + A MC x − A NO c q


2 ( p MC − p Cal ) 


ρ

(11)
Applied Mechanics and Materials Vols. 201-202
pCal
p
= α Cal β Cal  Cal
 α Cal



1−
1
β Cal
435

2( p MC − pCal )
2( pCal − p accu ) 
 ANO cq

− ANC cq


ρ
ρ


(12)

2( pCal − p accu )
1 
 ANC cq

q
−
P

c accu 
ρ

p accu =
Therefore, ANO, ANC
(13)
and paccu can be expressed by the following equations.
~
pMC = f1 ( pMC , pCal , ANO , x, q P ) ⇒ ANO = f1 ( p MC , p MC , pCal , x, q P )
(14)
~
pCal = f 2 ( p MC , pCal , paccu , x, ANC ) ⇒ ANC = f 2 ( pMC , p MC , pCal , paccu , x, q P )
(15)
p accu = f 3 ( pCal , p accu , q P )
(16)
According to the equations (1) to (10), we can get paccu calculation form the following equations.
p accu =
1
1
V accu =
c accu
c accu
∫ (q
NC
− q P )dt ⇒ p accu


1   p Cal
=
−
c accu   α Cal


1
 β Cal
p

− MC + A MC
E

V0


x



(17)
According to the equations (11) to (13), ANO and ANC can be deduced as below equations with
label d.
ANO =
E
E
d
q P + AMC x d − pMC
V0
V0
E
cq
V0
(
d
d
2 pMC
− pCal
ρ
d
d
β Cal p Cal
+
p MC
A NC =
β Cal p
d
Cal
E
cq
V0
)

E  d
 p Cal
V0 




2  d
 p Cal
ρ 




(18)
1


 β Cal
d

+ β Cal p Cal
q p + A MC x d 



1


d

 β Cal
E   p Cal
d
d 


p MC +
− A MC x  

V 0   α Cal 



+
E

c accu

V0



d
 p Cal

 α Cal
(
)
(19)
Another problem arises from the pump flow. How should these be chosen? The value of ANO
and ANC should be positive values. Negative values are not reasonable. Therefore, pq should match
the following conditions according to the equations (18) and (19).
q P1 >
d
p MC
− A MC x d
E
V0
(20)
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Advances in Engineering Design and Optimization III
1
β Cal p
d
Cal
qP2 >
p
d
MC
E d
p Cal
−
V0
E
d
β Cal p Cal
V0
d
 p Cal

α
 Cal
 β Cal



− A MC x d
(21)
If we choose the pump flow is now greater than these values, we guarantee positive valve
openings and it is also an adjustment principle for the pump flow.
Based on equations (11), (12), (13), (18) and (19), it is assumed that:
d
p MC = p MC
,
(22)
d
p Cal = pCal
,
(23)
We can get the following derivation.
(
)
(
)
a12
d
p MC − PMC
a11
(
)
(
)
a22
d
pCal − PCal
a 21
d
d
d
0 = a11 p MC − p MC
+ a12 p MC − PMC
⇒ p MC = p MC
−
d
d
d
0 = a 21 pCal − pCal
+ a 22 pCal − PCal
⇒ pCal = pCal
−
(
)
(24)
(
)
(25)
The result is one of the parameters a11, a12, a21, a22 adjustable stable error dynamics of the control
d
d
d
d
error pMC − PMC
and pCal − PCal
. In the control (18), (19), (24) and (25) by p MC
and pCal
, we
obtain a given dynamics of the control error. This control was implemented using a C-code
s-function in MATLAB/Simulink and applied to the well-implemented model.
Simulation Results
According to the simple model based on MATLAB/Simulink simulation, we can get the
relationship between pMC_target, pMC_actual, pCal_target, pCal_actual, paccu, ANO, ANC, qNC, qNO and qP as fig. 2.
Applied Mechanics and Materials Vols. 201-202
Fig. 2
437
Simulation results
Conclusions
Simulation results show that the simulated model pressure has a good consistency with the actual
pressure. Then the hydraulic calculation method described in this paper is a control concept for the
hydraulic control of the regenerative braking system. Based upon this concept, the hydraulic
pressure estimation and brake pressure control will get a good precision. In order to realize the
controller, a PID method can be implemented in the system and the control logic will be more
robust.
Acknowledgement
The research was supported in part by Project 2010DFB70360 of Program of International S&T
Cooperation and Project 2010CB736101 of National Program on Key Basic Research Project (973
Program).
References
[1] A. Kusano and T. Kuno, A. Co., Ltd.: US Patent 6,709,072. (2004).
[2] L. Petruccelli, M. Velardocchia and A. Sorniotti: SAE Technical Paper Series, No.
2003-01-3336.
[3] A. Fortina, M. Velardocchia and A. Sorniotti: SAE Technical Paper Series, No. 2003-01-3335.
[4] W. Choi, H. Park and S. Lee: SAE Technical Paper Series, No. 2004-01-0258.
Advances in Engineering Design and Optimization III
10.4028/www.scientific.net/AMM.201-202
Regenerative Braking System Pressure Control Calculation Based on ABS Hydraulic Model
10.4028/www.scientific.net/AMM.201-202.433