2001-01-0595 A Model-Based Brake Pressure Estimation ... - Delphi

SAE TECHNICAL
PAPER SERIES 2001-01-0595
A Model-Based Brake Pressure Estimation
Strategy for Traction Control System
Qingyuan Li, Keith W. Beyer and Quan Zheng
Delphi Automotive Systems
Reprinted From: Brake Technology, ABS/TCS, and Controlled Suspensions
(SP–1576)
SAE 2001 World Congress
Detroit, Michigan
March 5-8, 2001
400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-5760

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2001-01-0595
A Model-Based Brake Pressure Estimation Strategy for
Traction Control System
Copyright © 2001 Society of Automotive Engineers, Inc.
ABSTRACT
This paper presents a brake pressure estimation algorithm
for Delphi Traction Control Systems (TCS). A control
oriented lumped parameter model of a brake control
system is developed using Matlab/Simulink. The model is
derived based on a typical brake system and is generic to
other types of brake control hardware systems. For
application purposes, the model is simplified to capture
the dominant dynamic brake pressure response. Vehicle
experimental data collected under various scenarios are
used to validate the algorithm. Simulation results show
that the algorithm gives accurate pressure estimation. In
addition, the calibration procedure is greatly simplified
INTRODUCTION
Traction control plays an important role in improving
vehicle stability during vehicle acceleration. This is
achieved by controlling brake pressure and engine torque
together to reduce the wheel spin. During TCS brake
pressure information is used to determine the torque
reduction required by the engine. It is also used to prevent
over heating of the base brake system during controlled
brake events. Thus, brake pressure is valuable information
needed to improve the safety of the vehicle. However, few
vehicles install brake pressure sensors since it increases
the cost and requires additional diagnostic algorithms [1].
Therefore, an estimation algorithm is required to provide
the brake pressure information.
The current pressure estimation algorithm relies on
numerous of vehicle tests to determine the calibration
values. In an effort to improve the accuracy of brake
pressure estimation, reduce complexity of calibration and
save the calibration time, the model-based brake pressure
estimation strategy was developed. In this paper, a control
oriented lumped parameter model of a brake control
system is developed based on one channel hydraulic
brake system. For production implementation purposes,
Qingyuan Li, Keith W. Beyer and Quan Zheng
Delphi Automotive Systems
the higher order dynamics of the algorithm are ignored in
this physical model, and it is simplified to capture the
dominant dynamic brake pressure response. In order to
verify the simplified model, vehicle experimental data
collected under various conditions was used.
This paper outlines and describes the derivation of the
algorithm and presents the simulation results to show that
the algorithm gives accurate pressure estimation.
MODEL FOR TCS BRAKE PRESSURE
CONTROL SYSTEM
There are two types of disc brake calipers in current base
brake products. One is the fixed-caliper disc brake, where
two pistons are used to press the brake pad against the
disc from opposite directions, and the other is the floatingcaliper
disc brake, where only a single piston is used to
press the brake pads against the disc [2].
Figure 1 shows the model schematic of the brake
pressure control system for one simplified channel when it
is in traction control mode. The figure shows a motor, a
pump, an accumulator, an orifice, a pressure relief valve,
two solenoid valves labeled as a pressure apply valve and
pressure release valve, brake caliper and pad. The
pressure apply and release valves are represented by an
orifice and the corresponding control command. The
motor drives the pump. The accumulator and orifice
smooth the pressure transients. A pressure relief valve
provides safety to the system. In traction control mode,
the pressure generated by the pump is always higher than
the setting of the pressure relief valve, so the relief valve is
at work all the time. Therefore, the pressure labeled as s P
in Figure 1 can be assumed a constant, which is equal to
the setting of the relief valve. The pressure apply valve is
normally open, and the pressure release valve normally
closed. When the control command is in “APPLY” mode,
the fluid from the pump flows through the apply valve’s

orifice with flow area a 1 , and enters the caliper’s chamber
to build up pressure P c so as to move the brake pad. At
the same time, the release valve is closed. When the
control command is in “RELEASE” mode, the fluid from
the caliper chamber flows through the release valve’s
orifice with flow area a 2 , and goes back to the tank. In
this mode, the apply valve is closed. A third state is the
“HOLD” mode, which is when both apply and release
valves are closed. The brake pad is modeled by a mass,
spring and damper system.
Pressure Relief Valve
M
P s
a 1
Apply
command
Q 1
Release
command
Q 2
a 2
V 0
P c
Caliper
Piston x p
Figure 1 Model schematic of one simplified channel
hydraulic-mechanical schematic of the brake pressure
control system
To summarize, the symbols used in Figure 1 are defined
as follows:
P s hydraulic line pressure
P c caliper chamber pressure
x p caliper piston displacement
V o initial chamber volume
Q 1 flow rate from apply valve
Q 2 flow rate from release valve
a 1 orifice area for apply valve
a 2 orifice area for release valve
K p
B p
a p caliper piston area
M p mass of the piston
B p damping coefficient
K p effective spring constant
MATHAMATICAL MODEL
From Figure 1, the mathematical model of TCS brake
pressure control system is described by the following
equations [3][4].
M ⋅ x + B ⋅ x + K ⋅ x = P ⋅ a − F
(1)
p
⋅⋅
p
Q −Q
p
⋅
p
V
+
p
p
+ V
β
c
dPc
⋅
dt
⋅
c o
1 2 = a p ⋅ xp
(2)
V a ⋅ x
c
Q
Q
1
= (3)
p
p
2 ⋅(
Ps
− Pc
)
= Cd
⋅ a1
⋅
(4)
ρ
= C
⋅ a
⋅
2⋅
Pc
ρ
2 d 2
(5)
where ρ is the fluid density, C d is the orifice flow
discharge coefficient, β is fluid bulk modulus, V c is the
feeding chamber volume, and F ko is the spring preload.
MODEL SIMPIFICATION
Assuming that the brake pressure is calculated only when
the brake pad is in full contact with the brake disc. Then,
⋅⋅
x ≈ 0 , ≈ 0
p
⋅
x . The fluid compliance effect is also
p
assumed negligible for the small volume V c , that is,
V
c
+
β
V
o
≈ 0
simplified to
K x = P ⋅ a − F
p
p
c
. Equations (1) and (2) are therefore,
⋅ (6)
p
ko
p
ko

⋅
− = p ⋅ p x a Q
Q 2
1 (7)
A compliance curve equation for the brake is given as
follows:
V a⋅
P
c
= (8)
b
c
where a and b are constants.
Combining the above equations, we get
x
p
a ⋅ P
a
p
b
c
= (9)
The flow chart of the new model-based TCS brake
pressure estimation algorithm is shown in Figure 2. In this
algorithm, the apply valve flow rate and the release valve
flow rate are calculated separately. Based on the flow
continuity equation, the TCS brake pressure estimation
value is calculated. In order to simplify the algorithm for
production implementation, the higher order dynamics of
the algorithm are ignored; this is also found to be a valid
assumption based on model analysis and model validation
results.
N
A
TCS Active
Control model =
Apply mode
Control mode =
Release mode
Flow Rate = 0.0
Brake Pressure = 0.0
A
Y
N
N
Y
Y
VALIDATION OF THE BRAKE PRESSURE
ESTIMATION ALGORITHM
In order to evaluate the brake pressure estimation
algorithm presented in this paper, the algorithm is
programmed using MATLAB/SIMULINK. Vehicle data is
used as inputs to the simulation model. The SIMULINK
diagram is shown in Figure 3.
The algorithm is validated for four pressure profiles:
(i) Changes in pressure;
(ii) High pressure;
(iii) Modulated pressure;
(iv) One channel activation;
The simulation results for these four cases are shown in
Figures 4 – 7.
Figure 4 shows the simulation and the vehicle test results
when the pressure increases and decreases quickly.
Figure 5 shows the simulation and the vehicle test results
when the pressure increases to a large amount of
pressure on one wheel and a smaller pressure on the
other wheel.
Figure 6 shows the simulation and the vehicle test results
when the pressure is applied and released several times.
Figure 7 shows the simulation and the vehicle test results
while only one channel is applying pressure.
Calculate Flow Rate
Calculate Flow Rate
Figure 2 Flow chart of TCS brake pressure estimation algorithm
Calculate Brake Pressure

TCS Brake Pressure Estimate Model
1
s
Xp
Displacement
Vs. Pressure
Ps
Pc
Apply Command
Apply
Valve
Release Command Release
Valve
Figure 3 SIMULINK diagram of one channel brake pressure estimation model for TCS
From the results, it is apparent that the new model-based
TCS brake pressure estimation gives fairly accurate brake
pressure estimation. Since this algorithm is based on a
physical model, it can predict brake pressure accurately
over all testing conditions. And a big advantage of the
proposed algorithm is the reduction of calibration time.
CONCLUSION
In this paper, a model-based brake pressure estimation
algorithm for TCS is presented. The algorithm is simplified
based on model analysis to enable production
implementation. The pressure estimation algorithm is
validated using vehicle data. The simulation results show
that the new algorithm can predict brake pressure
accurately for traction control systems, and is robust for
all testing cases.
In addition, there are fewer calibration variables that need
to be determined from testing than in the current
algorithm. This means significant savings in calibration
time and cost. This algorithm more accurately estimates
the pressure at the driven wheel allowing the brake control
systems to depend more heavily on this estimation. The
improved algorithm can reduce brake wear and improve
driver comfort during an active brake control event.
ACKNOWLEDGMENTS
The authors acknowledge gratefully the technical support
of Bryan T. Fulmer, Joseph A. Elliott of Delphi Technical
Q1
Q2
1/ap
Xp_dot
Center Brighton and James R. Bond of Delphi Technical
Center Dayton. Specially, for the discussion with Bryan T.
Fulmer
REFERENCES
1. Paul, J., Klinkner, W., Muller, A., “Electronic stability
program - the new active safety system of mercedesbenz”
SAE 97-06 957128.
2. “Automotive Brake Systems,” Robert Bosch GmbH,
1995.
3. Merritt, H.E., “Hydraulic Control Systems” John Wiley
and Sons, Inc., 1967.
4. Doebelin, E.O., “System Dynamics Modeling,
Analysis, Simulation, Design” Marcel Dekker, Inc.,
1998.
CONTACT
Qingyuan Li and Keith W. Beyer are systems engineers
in Chassis Systems, and Quan Zheng is a Controls
engineer in Forward Energy and Energy Management
Systems at Delphi Automotive Systems, Technical Center
Brighton, 12501 E. Grand River, Brighton, MI 48116. Their
contacting emails are as follows:
qingyuan.li@delphiauto.com.
keith.w.beyer@delphiauto.com.
quan.zheng@delphiauto.com

Pressure(PSI)
Pressure(PSI)
Pressure(PSI)
Pressure(PSI)
150
100
50
0
-50
-100
Model Estimated Pressure LR
Measured Pressure LR
-150
0 1 2 3 4
Time(Second)
5 6 7 8 9
300
250
200
150
100
50
0
Model Estimated Pressure RR
Measured Pressure RR
-50
0 1 2 3 4
Time(Second)
5 6 7 8 9
Figure 4 Comparison of brake pressure estimation for quick changes in pressure
200
150
100
50
0
-50
-100
Model Estimated Pressure LR
Measured Pressure LR
-150
0 1 2 3 4 5
Time(Second)
6 7 8 9 10
350
300
250
200
150
100
50
0
Model Estimated Pressure RR
Measured Pressure RR
-50
0 1 2 3 4 5
Time(Second)
6 7 8 9 10
Figure 5 Comparison of brake pressure estimation for high pressure events

Pressure(PSI)
Pressure(PSI)
Pressure(PSI)
150
100
50
0
-50
-100
Model Estimated Pressure LR
Measured Pressure LR
-150
0 1 2 3 4 5
Time(Second)
6 7 8 9 10
120
100
80
60
40
20
0
Model Estimated Pressure RR
Measured Pressure RR
-20
0 1 2 3 4 5
Time(Second)
6 7 8 9 10
Figure 6 Comparison of brake pressure estimation during pressure modulation
Pressure(PSI)
200
150
100
50
0
-50
-100
Model Estimated Pressure LR
Measured Pressure LR
-150
0 1 2 3 4
Time(Second)
5 6 7 8
300
250
200
150
100
50
0
Model Estimated Pressure RR
Measured Pressure RR
-50
0 1 2 3 4
Time(Second)
5 6 7 8
Figure 7 Comparison of brake pressure estimation for pressure activation on one channel