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International Journal of Automotive Technology, Vol. 18, No. 4, pp. 707−718 (2017)
DOI 10.1007/s12239−017−0070−0
Copyright © 2017 KSAE/ 097−15
pISSN 1229−9138/ eISSN 1976−3832
707
NOVEL ELECTRONIC BRAKING SYSTEM DESIGN FOR EVS
BASED ON CONSTRAINED NONLINEAR HIERARCHICAL CONTROL
Ronghui Zhang
1, 2)
, Kening Li
3)*
, Fan Yu
3)
, Zhaocheng He
1, 2)
and Zhi Yu
1, 2)
Research Center of Intelligent Transportation System, School of Engineering, Sun Yat-sen University,
Guangdong 510275, China
Guangdong Key Laboratory of Intelligent Transportation Systems, Guangdong 510275, China
State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering,
Shanghai JiaoTong University, Shanghai 200240, China
(Received 4 July 2016; Revised 18 October 2016; Accepted 22 December 2016)
ABSTRACT−Both environment protection and energy saving have attracted more and more attention in the electric vehicles
(EVs) field. In fact, regarding control performance, electric motor has more advantages over conventional internal combustion
engine. To decouple the interaction force between vehicle and various coordinating and integrating active control subsystems
and estimate the real-time friction force for Advanced Emergency Braking System (AEBS), this paper’s primary intention is
uniform distribution of longitudinal tire-road friction force and control strategy for a Novel Anti-lock Braking System (Nov-
ABS) which is designed to estimate and track not only any tire-road friction force, but the maximum tire-road friction force,
based on the Anti-Lock Braking System (ABS). The longitudinal tire-road friction force is computed through real-time
measurement of breaking force and angular acceleration of wheels. The Magic Formula Tire Model can be expressed by the
reference model. The evolution of the tire-road friction is described by the constrained active-set SQP algorithm with regard
to wheel slip, and as a result, it is feasible to identify the key parameters of the Magic Formula Tire Model. Accordingly,
Inverse Quadratic Interpolation method is a proper way to estimate the desired wheel slip in regards to the reference of tire-
road friction force from the top layer. Then, this paper adapts the Nonlinear Sliding Mode Control method to construct
proposed Nov-ABS. According to the simulation results, the objective control strategy turns out to be feasible and satisfactory.
KEY WORDS : Electric vehicle, Constrained active-set SQP algorithm, Parameters identification, Nonlinear sliding mode
control, Hierarchical Control
1. INTRODUCTION
As the developments of economy and technology,
automobile industry has brought human being much
convenience. Car ownership is booming, especially in
developing areas. But, the emission and energy shortage
problems have become increasingly severe because the
cars with internal combustion engines are dominant.
Therefore, electrifying vehicles appears to be a solution to
the above problems. Environmental protection and energy
conservation have attracted more and more researchers’
eyes, in recent years. The main benefits of electric vehicles,
commercially, are the energy saving and cost competitive
advantages. In addition, EVs are actually a typical
mechatronic system just like precision machines controlled
by computers, robots and so on, because EVs using one or
more electric motors for propulsion rather than internal
combustion engines. Mechatronics technology, especially
the mechatronic control, is developing rapidly and
prompting the development of electric vehicles. Several
outstanding researches have been working on this aspect of
EVs (Attia et al., 2014; Hori, 2004; Kim et al., 2015a; Kim
and Huh, 2016; Zhang et al., 2013a; Noceda and Wright,
2006). Compared with conventional vehicles, EVs, with
advanced mechatronic technologies, have safer feature of
better driving performance as well as being cleaner and
saving energy. Compared with internal combustion engines
and hydraulic braking systems, the advanced electric
motors have the following most significant advantages:
First, they have 10 ~ 100 times faster torque response,
bringing them to the millisecond-level; second, there is
extremely precise feedback of the generated motor current/
torque (motor torque ∝ motor current); third, continually
variable speed, in essence (reference the Figure 1 which
illustrates the torque–speed characteristics of electric
motors); fourth, with small size and powerful output it can
be easily located in-wheel motors (Marino et al., 2013; Ma
et al., 2011; You et al., 2014).
Active control systems (such as ABS, 4WS and ESP,
etc.) are widely used in traditional vehicles and is popular
because they can cope with complex operating conditions
and improve the security and comfort of vehicles (Kwon et
*Corresponding author. e-mail: lkn@sjtu.edu.cn
708 Ronghui Zhang et al.
al., 2015; Zhang et al., 2013b; Zheng et al., 2014).
Typically, integrated vehicle dynamics control has attracted
wide attention and has become a hot area of research in the
domain (Song, 2012; Xiao et al., 2011; Gordon et al., 2003;
Nagai et al., 2002; Yu et al., 2008; Vale et al., 2014; Li et
al., 2008). Nonetheless, most studies focus on the
calculation of tire friction or total yaw moment, rather than
on its efficient implementation, though they do, in fact,
enhance the performance of vehicles. Regardless of the tire
friction generation mechanism, only some relatively simple
methods (such as only allocating yaw moment to brake
forces in one single axle (Gordon et al., 2003; Zhang et al.,
2013b; Zheng et al., 2014; Ren et al., 2014) are being used
currently. Due to the lack of consideration for the tire–road
interaction, their strategy is possibly infeasible in practice.
For example, when needing a lot of tire force, simply
increasing brake force can make matters dangerous,
especially if the slip ratio of the tire has been sufficiently
large. There are some methods, such as nonlinear robust
control, nonlinear optimum distribution, et al. (Yim, 2015;
Hattori et al., 2002; Kim et al., 2014), which were used to
fix this but the full realization of the tire friction problem
indicates there is a urgent need for more research in this
area, because it is the key issue to enhancing handling
performance. Furthermore, the real-time tire-road friction
force is the key factor for the AEBS, a subsystem of
Advanced Driver Assistant System (ADAS) (Hassannejad
et al., 2015), which can be used to estimate the Warning
Index (WI) (Kusano and Gabler, 2012; Kim et al., 2015b;
Lee et al., 2012).
In the past few years, due to the lack of proper sensors
for internal combustion engine vehicles, precise value of
tire-road friction forces is not available but a rough
estimate has been made. However, the EVs can give a fine
and accurate value. Because EVs use an in-wheel motor,
the brake torque and angular acceleration of the wheel can
be acquired easily.
A kind of main/servo loop integrated control structure
has been presented previously, in several articles
(Mokhiamar and Abe, 2004; Shen and Yu, 2004; Hou et
al., 2015). The calculation of the desired stable forces of
tires is the main part of the mail loop and the desired stable
forces is produced in the servo loop. Previous articles have
stated the main loop design and tire force contribution. In
addition to the existing ABS, this paper is a comprehensive
supplement added for EVs, and describes a way to
parameters implement tire identification and control in
servo loop.
The structure of this document is as follows: section II
describes the tire model with in-wheel motor and the
structure of Nov-ABS controller; section III calculates the
expected longitudinal slip ratio; section IV implements
that; section V uses the numerical simulation results to
verify proposed method.
2. NOV-ABS AND CONTRLLER STRATEGY
In order to master the basic characteristics of braking
system, this paper amends the problem of wheel slip-
control due to only taking the longitudinal dynamics of the
EV into account, while ignoring the effect of load transfer
via a simplified dynamics model of a quarter-vehicle model
with in-wheel motor which is shown in Figure 2, The
dynamic equations of motion for this system please check
the following description.
In this paper, we only consider the longitudinal
dynamics of the vehicle. So, the problem of wheel slip
control is best explained by looking at a quarter-car model
as shown in Figure 3. The dynamic equations of motion of
the system are
(1)
du
mF
dt
=−
Figure 1. Torque-speed characteristics of electric motors
and internal combustion engines.
Figure 2. Control architecture of the Nov-ABS with In-wheel motor.
NOVEL ELECTRONIC BRAKING SYSTEM DESIGN FOR EVS BASED ON CONSTRAINED NONLINEAR 709
(2)
(3)
F=mg (4)
Where:
m is mass of quarter-car;
u is horizontal velocity of vehicle movement;
F is friction between tire and road;
J is the inertia of wheel;
ω is wheel angular velocity;
r is the radius of wheel;
T is braking torque;
F is braking force gained from in-wheel motor;
F is vertical power;
g is gravitational acceleration.
Note that u is estimated using the front and rear wheel
center speed (Zhao et al., 2015) and F is get from T in-
wheel motor, as shown in Figure 4.
In this study, a hysteresis-loop based current controller
(Kazmierkowski and Malesani, 1998) is proposed and
implemented to control the in-wheel motor, as illustrated in
Figure 3. By tracking the error between measured current
and reference current, the hysteresis-loop based current
controller works as a current-loop controller for in-wheel
motor via a three-phase inverter. In this way, the
electromagnetic torque of the motor can follow the
changing reference signal. For tire-road friction force is
directly proportional to electromagnetic torque, which is
expressed as:
(5)
And, electromagnetic torque T is proportional to
current i which is expressed as:
(6)
The generated electromagnetic torque T is converted
into braking force F by the in-wheel motor and
mechanism, which can be expressed as:
(7)
where ϕ is screw lead angle, Φ is the flux linkage, η, η is
efficiency factor, i stands for the value of phase current.
In other words, the tire-road friction force can be
computed by
(8)
In terms of , the longitudinal slip can be
computed by
(9)
Therefore, according to the real-time dynamic value of
, and the reference tire model, the following
equation can be acquired which means the Magic Formula
will be adapted and the non-linear relationship of the tire-
road friction force F and the homologous λ can be
described by this equation
(10)
where μ is the coefficient of friction
d
JrFT
dt
ω
=−
TFr=
cot
FT
r
ϕη⋅
=⋅
2Ti=Φ⋅
cot 2cot
T
FTi
rr r
ϕη ϕη
⋅⋅Φ⋅ ⋅
== ⋅= ⋅
2cot
ˆT
Jd Jd
Fi
rdt r rdt r
ωωϕη⋅Φ⋅ ⋅
=+=+ ⋅
ˆ
F
ˆ
λ
ˆur
u
ω
λ
−
=
ˆ
F
ˆ
λ
2cot =()iF F
r
ϕη μλ
⋅Φ⋅ ⋅ ⋅=⋅
Figure 3. Quarter-car model.
Figure 4. Control Block diagram of in-wheel motor.
710 Ronghui Zhang et al.
In addition, because the control objective of Nov-ABS is
to track any λ ( ) with respect to any
craved forces and moments from the upper control layer,
we can calculate the λ as regard to F (F) with
numerical method of nonlinear equations according to the
Equation (8). And finally we can get the following
equation:
(11)
3. CONSTRAINED SQP ALGORITHM FOR
REFERENCE TIRE MODEL PARAMETERS
IDENTIFICATION
The LuGre model is popular because its parameters have a
physical significance and its velocity-dependency is also
physically consistent. However, the quasi-static value of
the aim slip is necessary for the controller design of ABS.
So, the alleged Magic formula is the root of the reference
tire model in this paper. In terms of research on vehicle
dynamics, it is an extensively used semi-empirical tire
model which be used to calculate steady-state tire force and
moment characteristics. When given values of vertical load
and the longitudinal dynamics of the vehicle, the general
form of the formula can be expressed to the following
equation.
(12)
where μ the coefficient of longitudinal friction, λ the
longitudinal slip, B stiffness factor, C shape factor, D
peak value, E curvature factor.
In fact, the vehicle operating conditions are varied, for
example, a wide variety of road conditions. Therefore, the
Magic formula essential parameter (B, C, D and E)
should be online estimated.
In order to bring the error between the estimated value
and the true value of B, C, D and E to a minimum, a
performance index is introduced in this paper. With the
weighted sum of squares of the error of the estimated value
and the true value
of the tire-road friction force, the
original parameter recognition problem is transformed into
a constrained optimization problem, and can be expressed
to:
(13a)
(13b)
where
w weighting factor
The minimum and maximum constraint range for B, C,
D and E respectively are x and x.
With the implementation of the constrained SQP
algorithm, we can propose a scheme to get the minimum
value of PI. In this process, parameters are optimized by
using the active-set Sequential Quadratic Programming
(SQP) method, which is the most popular optimization
algorithms and can reach the region near an optimum point
relatively quickly with the boundary constraints.
Because the active set SQP approach is suitable for both
the small inequality constrained problems and the large
inequality constrained problems, it is considered to be the
best choice for reference tire model parameters
identification.
First, the upper and lower limits of the constraint
Equation (13b) can be converted into conventional
inequality constraints as follows
(14)
(15)
where I is the 4 × 4 identity matrix.
Next, the definition of the Lagrangian for the
constrained problem (10a) is following:
(16)
where is the inequality constraints. And in this part,
the active set with any feasible x can be as expressed:
(17)
The optimization problem (11) can’t be handled by
Lagrangian methods because of the inequality-constraints
straightly. Then, active set SQP methods are adopted here,
which extend the inequality-constrained problem to
equality-constrained one. In particular, each iteration x
will generate a subset of constraints which also are a called
working set I in this method and it only fixes equality-
constrained sub-problems. Furthermore, in this process we
just impose the constraints in the working sets as equalities
and neglect all other constraints. Each iteration will update
this working set following the rules which based on
Lagrange multiplier estimates. Assuming that at the
iteration the quadratic programming is given as
following:
(18a)
(18b)
At working set I, the equality-constraints optimization
problem should be solved here
(19)
0λλ<≤
()
2cot ()=0
FF
iF
r
μλ
ϕη μλ
−⋅
⋅Φ⋅ ⋅
=⋅−⋅
{}
(, , , , )
sin[ arctan ( arctan( )) ]
BC DE
DC BEB B
μμλ
λλ λ
=
=−−
ˆ
F
[]
ˆ
ˆ
min ( , )
, , ,
PI w F F x
xBCDE
μλ
⎡⎤
=−
⎣⎦
=
∑
.. ≤≤st x x x
Ax b≥
[] [ ]
,, ,AIIbx x=− = −
(, ) () ( )Lx PI x x bϕϕα=− −
∑
ψ∈i
{}
() |Ax i Ax bψ=∈ ≥
(, )xϕ
1
min ( ) 2
qp PI p pWp=∇ +
.. ( ) 0st A p A x b+−≥
() ()
1
min 2
.. ( ) 0,
PI p p W p
st a p A x b i I
∇+
+−=∈
NOVEL ELECTRONIC BRAKING SYSTEM DESIGN FOR EVS BASED ON CONSTRAINED NONLINEAR 711
Specifying δ=p−p, we get
(20)
Where q(p) and q are independent of each other. Because
in the premise of not changing the problem solution, we
can get q(p) from the objective, it can be expressed as
follows that the QP sub-problem to be solved at the kth
iteration
(21a)
(21b)
Assume that the optimal δ selected from (21a) is not
zero current, we need determine how long to move in this
direction. For to the constraints, if is possible,
be set, or else, be set.
In order to get the maximum reduction in q, we hope the
subject is still feasible when α is as large as possible in [0,
1] range, then we get:
(22)
In the quadratic model, all SQP method is dependent on
a choice of W. When there is a way to approximate the
Lagrangian Hessian, a quasi-Newton approximation must
be used. For example, the BFGS updates formula by using
Hessian approximation B instead of W, we set
(23)
(24)
But, this method will converge quickly when is
positive-definite at the array of points x, on the contrary if
it is negative, it doesn’t work well by using the BFGS
update.
The scheme which the update is definitely always well-
defined the damped BFGS updating for SQP has been
designed (Nocedal and Wright, 2006; Zhang et al., 2015).
According to this scheme, the following equation is defined:
(25)
where the scalar θ is defined as
(26)
Update B as follows
(27)
It ensures that B is positive-definite.In accordance
with the above description, the flow diagram of the
constrained SQP algorithm is stated as follows:
And and is defined by Equations (8) and (9).
4. SLIDING MODE CONTROLLER
Because this controller will be used in many uncertain
conditions, such as a variety of road surface parameters and
the noise from sensors, then it should be strong enough to
adapt that. With regard to this reason, we introduce the
sliding mode method in our paper to control this nonlinear
system. At first, the definition of a time-varying sliding
mode surface is given as follows:
(28)
The Equations (1), (2) and (6) will deduce the following
equation:
(29)
Setting
(30)
has
(31)
Because the tire slip λ is the only one parameters that
may influence our estimates of the function f, thus, we
can draw the difference between the actual and the
() ()
1
() ()
2
qp PI Wqpδδδδ+=∇+ +
1
min
2
PI Wδδδ∇+
()
.. 0,st a i Iδ=∈
pδ+
ppδ=+
ppαδ=+
min 1, min bap
a
α
δ
⎛⎞
−
=⎜⎟
⎜⎟
⎝⎠
(,) (,)
sx x
yLxx Lxx
=−
=∇ −∇
Bss B y y
BB
sBs sy
=− +
L∇
(1 )ry Bsθθ=−−
1, 0.2
0.8 , 0.2
if s y s B s
sBs if s y s B s
sBs sy
θ
⎧≥
⎪
=⎨<
⎪−
⎩
Bss B rr
BB
sBs sr
=− +
ˆ
F
ˆ
λ
sλλ=−
(1 ) 2cot
ur
d
u
dt
rF ui
J
uuJ
ω
λ
λϕη
−
⎛⎞
⎜⎟
⎝⎠
=
−+− ⋅Φ⋅ ⋅ ⋅
=+
(1 )
rF u
J
fu
λ
−
+−
=
2cot i
fuJ
ϕη
λ⋅Φ⋅ ⋅ ⋅
=+
Figure 5. Flow chart of the calculation of desired
longitudinal slip ratio.
712 Ronghui Zhang et al.
predicted value of as follows:
(32)
Hence, finding a positive function F as following:
(33)
The best approximation of a continuous control law will
lead to . Combined with the Equations (28), (30) and
(31), we can get:
(34)
Then the estimation of T is
(35)
We get the system track by defining the
sliding surface , thus, we draw
(36)
To avoid dithering, where sign function sgn(s) is
replaced with the saturation function defined as
Because
letting from Equation (32)
and
,
we get:
(37)
The sliding condition is fulfilled because η is a positive
constant. This means that the sliding surface defined above
can be realized through the designed control law.
5. SIMULATIONS RESULTS AND ANALYSIS
In order to verify the validity of the proposed controllers,
we conducted a co-simulation with Carsim, Matlab/
Simulink and the simulation bench from this part (Ma et
al., 2011). The controller of Nov_ABS is designed using
Matlab/Simulink and the vehicle model is proposed using
the Carsim, which is used worldwide by over 110 OEMs
and Tier 1 suppliers and over 200 universities and
government research labs. And the simulation bench, as
shown in Figure 6, is used as the validation tool which is
the test bench of the HIL for the next work. For the reason
that the wheel dynamic is very fast dynamics, the sampling
time of simulation for parameters identification is 10 ms
and 100 ms for the controller of ABS, which should be
work more than 10 times per sec.
To start with, a torsional system is applied to our test
platform. Please reference the Figure 6. In this torsional
system, a long torsional shaft is used to connect the drive
side and the load side of the flywheels; meanwhile, gears
transmit the drive torque from the drive servomotor to the
axis by the gear ratio 1 : 2. The load servomotor is used as
the dynamometer in this lab. ± 3.84 Nm is the largest
ˆ
f
ˆˆ
()
u
ef f u
λλ=−=− −
ˆ
ff F−≤
0=
s
2cot 0
i
sf uJ
ϕη λ
⋅Φ⋅ ⋅ ⋅
=+ − =
ˆ()
2cot
uJ
ifλϕη
=− −
⋅Φ⋅ ⋅
0λλ−≡
0=s
ˆ()iiksgns=−
( ),
() ,
sgn s if s
sat s sifs
ϑ
ϑ
ϑϑ
⎧≥
⎪
=⎨<
⎪
⎩
ˆ
01λλ≤− ≤
u
F
u
=−
()
2cot
uJ
kF
r
η
ϕη
=+⋅
⋅Φ⋅ ⋅ ⋅
1=( )
2
2cot
= s ˆ
2cot
ˆ
ˆ
ˆ
= s ( )
2cot
s
() (
2cot
ds ss s
dt
i
fuJ
i
fuJ
ii
ff uJ
r
FuJ
uJ
Fsigns
r
λλ
ϕη
ϕη
ϕη
ηϕη
=−
⎡⋅Φ⋅⋅⋅⎤
⎛⎞
+
⎢⎥
⎜⎟
⎝⎠
⎢⎥
⎢⎥
⎛⎞
⋅Φ⋅ ⋅ ⋅
⎢⎥
−+
⎜⎟
⎢⎥
⎝⎠
⎣⎦
⎡⎤
−
−+
⎢⎥
⎣⎦
⋅Φ⋅ ⋅ ⋅
−⋅
≤
+⋅
⋅Φ⋅ ⋅ ⋅
[]
)
= s ( )sign s sηη
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎣⎦
≤−
Figure 6. Simulation bench.
Table 1. Parameters on different road surface.
Notation Value Unit
m mass of quarter-car 372.5 kg
u vehicle velocity 100 km/h
g acceleration of gravity 9.8 m/s
J wheel inertia 16 kg·m
r wheel radius 0.28 m
B lower bond of stiffness factor 8 -
C lower bond of shape factor 1 -
D lower bond of peak value 0.1 -
E lower bond of curvature factor 0.1 -
B upper bond of stiffness factor 18 -
C upper bond of shape factor 1.7 -
D upper bond of peak value 1.5 -
E upper bond of curvature factor 0.9 -
NOVEL ELECTRONIC BRAKING SYSTEM DESIGN FOR EVS BASED ON CONSTRAINED NONLINEAR 713
output torque of the two brushless DC servomotors. An
optical encoder is used to detect the angular position and
the speed of the two motors and this optical encoder must
be with a resolution of 8000 pulses per revolution.
Table 1 gives some Magic Formula’s empirical
parameters on different road surfaces and Figure 7 gives
these roads’ μ-λ curves.
Based on the previous description, the constrained range
of B, C, D and E can be acquired correspondingly. In
addition, the Table 2 shows the parameters chosen in this
simulations lab (Li et al., 2012).
In next section, we have implemented the simulations in
wide variety of circumstances to better validate the
effectiveness of our proposed identification scheme.
Figures 8 ~ 11 give the identification results. Different
range of sampling points and is a part of the
diversification of the test environment, which is from the
experimental data using at the test platform as shown in
Figure 5. Besides, the true value of B, C , D and E is
used to draw the true value of μ and the identified value of
B, C, D and E is used to draw the identified value of μ.
The identified value of μ will be within the scope of
when in the scope of [0,
0.01], as illustrated in Figure 8. According to Figure 9, we
can get that the value of 0.02 is the maximum for the error
between true and identified value of μ. When the scope of
sampling points is changed from
to , which is shown in Figure 10, the
identification result of that important points also has the
remarkable enhancement and these important points
contain a lot of useful information of the non-linear
characteristics of tire-road friction. From Figures 10 and
11, we can obtain that the value of 0.02 is the maximum for
the deviation of true and identified value of μ in the scope
ˆ
F
ˆ
λ
[]
0, 0.08λ∈
ˆ(1,2,, )jNλ=
ˆ(1,2,, )jNλ=
[]
0, 0.01
[]
0.125, 0.135
Figure 7. μ-λ curve of different road surface.
Table 2. Parameters used in simulations.
Road BC D E
Snow 17.430 1.4500 0.20 0.6500
Cobblestone, wet 14.027 1.4500 0.40 0.6000
Asphalt, wet 15.635 1.6000 0.80 0.4500
Cobblestone, dry 10.695 1.4000 0.85 0.6450
Concrete, dry 13.427 1.6402 0.97 0.5372
Asphalt, dry 13.427 1.5500 1.10 0.5327
Figure 8. True and identified value of μ ().
[]
0,0.01λ∈
Figure 9. Error of true and identified value of μ
().
[]
0,0.01λ∈
Figure 10. True and identified value of μ ().
[]
0.125,0.135λ∈
714 Ronghui Zhang et al.
of . What’s more, as shown in Figure 11,
when the range is the maximum deviation is
close to 0.03 and this deviation percentage is less than 5 %.
In summary, the identification results are consistent with
our expectations in these ranges according to the above
experimental data and analysis.
At last, the lower-level controller design is the core of
our work in this article. Here, we simulate the braking
process to access the performance of the Nov-ABS. We
give the simulation results for three cases (Case A, B and
C), as shown in Figures 12 ~ 19:
Case A: The vehicle is exposed to a constant reference
friction force F, with setting the input to 2555.4N at 0
second and the input to 3651 at 1.0 second on the same
road with asphalt, dry surface. Found at the Figures 12 ~
15, which demonstrated the vehicles dynamic response.
After a period of time delay, shown in Figure 12, the
estimated friction force is almost consistent with the
reference value F. The estimated value and the tracking
results of λ regarding F are given in Figure 13. Figure
13 gives the different value of F corresponding to the
different value of λ with the same road condition. It is
well known that the Nov_ABS can evaluate and explore
λ. The absolute value of vehicle acceleration rises from
[]
0.06, 0.25λ∈
[]
0, 0.4λ∈
Figure 11. Error of true and identified value of μ
().
[]
0.125,0.135λ∈
Figure 12. Reference and true value of friction force (Same
road, different F).
Figure 13. Reference and true value of λ (Same road,
different F).
Figure 14. Vehicle acceleration (Same road, different F).
Figure 15. Vehicle and wheel speed (Same road, different
F).
NOVEL ELECTRONIC BRAKING SYSTEM DESIGN FOR EVS BASED ON CONSTRAINED NONLINEAR 715
about 6.68 km/s to 9.5925 km/s along with the F
changes, as indicated in Figure 14. Figure 15 presents the
simulation result of the wheel and vehicle speed and we
can get that the speed of wheel and vehicle goes with the
changes of λ. Based on above description, although
maybe the tracking result is not perfect, but at least it is
good.
Case B: The vehicle is exposed to a constant reference
friction force F, with setting the input to 2555.4N during
the braking process. Figures 16 ~ 19 give the simulation
results when the road conditions change from wet asphalt
to dry asphalt at the second 1.0.
With the same F, according to Figures 16 and 18, we
can conclude that there is a little change in the whole
process about the true value of friction force and vehicle
acceleration. Figure 19 also proven this conclusion. What’s
more, let us focus on the Figure 16, when the road
conditions changes, we can get that there is a reduction
about the reference value of λ and the value decreased
from about 0.05545 to 0.03697 at 1.0 second although F
invariable. With the results of simulation experiment, we
can get that the tracking value of λ and the reference λ
are consistent, which is in line with our desired effect.
Case C: The vehicle is exposed to a continuous
changing reference friction force F, shown in Figure 20.
The simulation results are shown in Figures 20 ~ 23.
With changing F, according to Figures 20 and 22, we
can conclude that there is a continuous change in the whole
process about the true value of friction force and vehicle
acceleration. Figure 23 also proves this conclusion. What’s
more, let us focus on the Figure 21, when the road
conditions changes, we can get that there is a reduction
about the reference value of λ and the value increased
from about 0 to 0.03697 at 0.5 second and from 1.67
second to 5 second, the λ changed according to the
Figure 16. Reference and true value of friction force
(Different road, same F).
Figure 17. Reference and true value of λ (Different road,
same F).
Figure 18. Vehicle acceleration (Different road, same F).
Figure 19. Vehicle and wheel speed (Different road, same
F).
Figure 20. Reference and true value of friction force
(Same road, different F).
716 Ronghui Zhang et al.
sinusoidal changing F. With the results of simulation
experiment, we can get that the tracking value of λ and
the reference λ are consistent, which is in line with our
desired effect.
As described in Case A, Case B and Case C, with
changing road surface, the proposed control strategy is still
an acceptable adaptation. The proposed control strategy
can provide an agreeable adaptation to the variable
condition of road surface according to the results of Case
A, Case B and Case C.
6. CONCLUSION AND FUTURE WORK
Vehicle integrated control is an active area of research, and
our main/servo loop control strategy is its typical case. The
key point of this work is a component of the servo loop
which using in-wheel motor at Nov_ABS to achieve tire
friction control self-adapting to the road surface as
conditions change, which is targeted not only to estimate
and track any tire-road friction force, but the maximum
tire-road friction force, based on ABS. We proposed a two-
step solution: the first step is online recognition of Magic
Formula parameters with SQP method and acquirement of
Nov_ABS objective with numerical method accordingly;
the second step is dynamic implementation of Nov_ABS
by using a nonlinear sliding mode control method.
The research is dedicated to the study of distributed
micro-electric vehicles with in-wheel motors having
comprehensively integrated control. This work includes the
integration of the proposed Nov_ABS and the main loop
controller and also the introduction of optimal & robust
control to the main loop to seize parameter incertitude.
ACKNOWLEDGEMENT−This work was partially supported
by the Science and Technology Planning Project of Guangdong
Province under Grant No. 2014B010118002, and the National
Natural Science Foundation of China under Grant No. 51375298
and No. 51208500. The first author would like to express
appreciation to Dr. Kening Li and Pro. Fan Yu for valuable
discussions that improved the quality and presentation of the
paper.
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