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공학석사학위논문
스티어 바이 와이어 시스템 조향 반력
및 랙 위치 제어
Steering Feel and Rack Position Control of
Steer By Wire System
2019년 2월
서울대학교 대학원
기계항공공학부
김 민 준
i
Abstract
Steering Feel and Rack Position Control of
Steer by Wire System
Minjun Kim
School of Mechanical and Aerospace Engineering
The Graduate School
Seoul National University
Steer by Wire (SBW) system is next generation steering apparatus for autonomous
vehicle that it has no mechanical link between steering column and tire steering
gearbox, the inner space of vehicle can be extended and utilized as the living room.
SBW System is generally divided into two main parts, one is the steering reaction
force control system and the other one is the rack position control system.
Because of disconnection between column and gearbox, steering information like
steering angle should be transmitted by electrical signal, and road and tire
condition have no effect on steering system. So it needs to generate resistive torque
for the driver to make appropriate steering feel like conventional power steering
system which generates assist torque to the driver. The resistive torque can be
obtained by setting reference torque based on measured data composed of 4-
dimension which are steering angle, angular velocity and vehicle speed. It can be
designed using system parameters and dynamics and set by optimization of tuning
parameters. In terms of rack system, it is important that has to be controlled to
precise position. SBW gearbox is generally high friction system which the
nonlinearity is high that it is hard to control with linear system. And the road has
ii
various conditions so the force from tire changes continuously. This paper
proposes methodology about steering reaction and rack position control using
sliding mode control and the disturbance observer to compensate uncertainty
caused by road conditions. And it also suggested the system performance results
evaluated by hardware in the loop system(HILS).
Keywords: Steer by Wire, Steering Feel Target, Impedance Control, Sliding Mode
Control, Disturbance Observer, Hardware in the Loop(HILS)
Student Number: 2017-28425
iii
Contents
Abstract i
List of Tables v
List of Figures v
Nomenclature vii
Chapter 1 Introduction ....................................................................... 1
1.1 Research Background ............................................................... 1
1.2 Research Overview ................................................................... 2
Chapter 2 Steer-by-wire System Architecture ................................... 4
2.1 Steering Reaction Module ......................................................... 5
2.2 Rack System Module ................................................................ 7
2.3 Overall system architecture ....................................................... 8
Chapter 3 State Estimation .............................................................. 10
3.1 System Requirement ............................................................... 10
3.2 Kalman Filter .......................................................................... 11
Chapter 4 Steering Feel Target ........................................................ 13
4.1 Reference Torque ...................................................................... 13
4.2 Target Torque Generation .......................................................... 15
iv
Chapter 5 Control System ............................................................... 19
5.1 Steering Reaction Module ......................................................... 19
5.2 Rack System Module ................................................................ 22
Chapter 6 HILS Test Results ........................................................... 28
6.1 HILS System Configuration ...................................................... 28
6.2 Results of Steering Reaction Module ........................................ 31
6.3 Results of Rack System Module ............................................... 36
Chapter 7 Conclusions ................................................................... 42
Bibliography .......................................................................... 43
국문초록 ............................................................................... 45
v
List of Tables
Table 4.1 Steering feel targets .............................................................. 16.
Table 6.1 Steering reaction module test scenarios ................................ 31.
Table 6.2 Target performance for rack system ..................................... 36.
Table 6.3 Rack system module test scenarios ...................................... 37.
List of Figures
Figure 2.1 Overall configuration of steer by wire system ......................... 4
Figure 2.2 Configuration of steering reaction module .............................. 5
Figure 2.3 DC motor electrical and dynamic model ................................. 6
Figure 2.4 Configuration of rack system module ..................................... 7
Figure 2.5 Overall system architecture ..................................................... 9
Figure 4.1 Reference torque 4-D map ..................................................... 13
Figure 4.2 Steering feel in the weave and transition test ........................ 14
Figure 4.3 Steering feel modeling ........................................................... 15
Figure 4.4 Steering feel optimization result ............................................ 18
Figure 5.1 Steering reaction module overall control architecture ........... 19
Figure 5.2 Rack system module architecture .......................................... 22
Figure 5.3 Rack system control system structure ................................... 23
Figure 5.4 DOB block diagram ............................................................... 26
Figure 6.1 Overall HILS system configuration ....................................... 28
Figure 6.2 Controller configuration ........................................................ 29
Figure 6.3 Hydraulic actuator configurations ......................................... 30
Figure 6.4 Kalman filtering performance ............................................... 32
vi
Figure 6.5 Weave test target .................................................................... 32
Figure 6.6 Results of weave test at 60 kph ............................................. 33
Figure 6.7 Results of weave test at 80 kph ............................................. 34
Figure 6.8 Results of transition test ........................................................ 35
Figure 6.9 Step input characteristic ........................................................ 36
Figure 6.10 Results of weave test at 60 kph ............................................. 38
Figure 6.11 Results of weave test at 80 kph ............................................. 39
Figure 6.12 Results of step test ................................................................. 41
vii
Nomenclature
Tsw Steering wheel torque
Jsw Steering wheel inertia
Bsw Steering wheel damping
FRsw Steering wheel friction
θsw Steering wheel angle
𝐽col Steering column inertia
θcol Steering column angle
FRcol Steering column friction
Ktbar Torsion bar stiffness
Rbelt Steering belt reduction ratio
Tmot Motor torque
R𝑎 Motor resistance
La Motor inductance
ia Motor current
v𝑏 Motor counter EMF
e𝑎 Motor voltage
Jmot Motor inertia
Bmot Motor damping
θmot Motor angle
Kmot Motor current coefficient
Fmot_rp Force from rack and pinion motor
Fmot_belt Force from ball screw motor
Mrack Rack mass
Brack Rack damping
Krack Rack stiffness
FRrack Rack friction
Fvehicle Force from vehicle
viii
Tmot_rp Torque from rack and pinion motor
Tmot_belt Torque from ball screw motor
rworm Reduction ratio of worm gear
Sc−factor Gear ratio of rack and pinion
ηefficiency Gear transmission efficiency
rpulley Belt-pulley ratio
rball_lead Length of ball screw lead
Tref Reference steering torque
1
Chapter 1
Introduction
1.1 Research Background
A steering system of modern vehicle, electrical power steering(EPS) system
has been applied for fuel efficiency, convenience and integrated control.
Nowadays, automobiles are expanding into living space as well as transportation
and autonomous technology has been developing gradually. From this viewpoint,
there is an increasing need to develop Steer by Wire (SBW) system that has less
restriction for inner space than conventional steering system. The conventional
type consists of a steering column, steering gearbox and universal joint to connect
them. It is inevitable that space constraints arise in the design of the vehicle due
to such a mechanical configuration. However, the universal joint in the SBW
system is unnecessary and it is replaced by electrical signal from steering wheel to
steer the tire. Therefore, since the mechanical constraints are eliminated, the
space utilization can be increased.
The SBW system can be divided into two main subsystems. One is steering
reaction module and the other is rack system module. A steering reaction module
offers resistive torque to driver from reference driver torque designed by engineer
2
and it makes drivers feel like conventional steering system. In terms of rack
system, the rack position control performance requires high accuracy for position
errors. However, the rack system has high friction which is high nonlinearity.
So, it has difficulties to control by linear model such as state feedback or LQR
control etc. There has to be compensated methodology to cover nonlinearity, so
the sliding mode controller and disturbance observer are adopted in this paper.
1.2 Research Overview
Steering reference torque to make steer feel can be generated using test data and
tuned by steering model. The input signals to control steering reaction module are
steering angle, angular velocity, vehicle speed and torque from sensor. Angular
velocity can be estimated using Kalman filtering method. Steering angle, vehicle
speed and steering torque are can be obtained by each sensors. The sliding mode
control method has been used to track the reference torque that the error in sliding
surface is difference between model angular velocity and sensor angular velocity.
Rack system has high friction that it needs to apply nonlinear control. Sliding
mode control has been used to control position and the error in the sliding surface
is difference between reference steer angle and position sensor angle. To improve
control performance, sensor angle has been estimated by Kalman filter method and
disturbance observer is designed to make system robustly control.
And simulation and hardware test were conducted to validate the proposed
control. The steering reaction module, rack system module and vehicle were
3
modeled for simulation using Matlab Simulink and CAR MAKER software. The
rack force from vehicle model is used in the HILS test. The SBW system
prototype was produced and test environment which can be operated in the real
time is constructed for HILS test. The scenarios of test were general test mode
like weave and transition which are representative test for vehicle.
4
Chapter 2
Steer-by-wire System Architecture
SBW system consists of steering reaction module to provide steering feel to the
driver, rack system module to control vehicle and integrated control system as
shown Fig 2.1.
Figure 2.1 Overall configuration of steer by wire system
② Rack System Module
① Steering Reaction Module
SBW ECU
Electric Signal
5
2.1 Steering Reaction Module
The steering reaction module provide resistive torque to driver that it makes
driver sense steering feel like conventional power steering system. Steering
reaction module consists of steering wheel, torsion bar, reduction gear and actuator
as shown in Fig. 2.2.
Figure 2.2 Configuration of steering reaction module
Tsw is driver’s input torque to operate the steering system and Ktbar represents
steering torque from sensor. The demand torque to driver to make end stop feeling
is over 20Nm, it needs reduction ratio Rbelt to amplify motor torque Tmot. J, B and
FR are system parameters and friction is expressed using hyperbolic tangent
function. Eq(2.1) and Eq(2.2) show the dynamic equations of this system.
Tsw
Jsw
Bsw
FRsw
Jcol
Rbelt
T
mot
Jmot
Ktbar
6
)()tanh( colswtbarswswswswswswsw KFRBTJ (2.1)
beltmotcolcolcolswtbarcolcol RTFRKJ )tanh()( (2.2)
The actuator is assumed DC motor for simulation that it consists of resistance,
inductance and counter electromotive force as shown in Fig. 2.3 and Eq(2.3),
Eq(2.4) and Eq(2.5) show the electrical and dynamic model.
Figure 2.3 DC motor electrical and dynamic model
)()()(
)( tetvdt
tdiLtiR ab
aaaa (2.3)
)()( tiKtT amotmot (2.4)
dt
tdB
dt
tdJtT mot
motm
motmot
)()()(
2
2 (2.5)
Ra La
Rotor ea(t)
+
-
vb(t)
ia(t)
Tmot(t)
θmot(t)
Bmot
Jmot
7
2.2 Rack System Module
Rack system module is apparatus to control vehicle motion that it requires
precise position control. And it is also emphasized on fail-safe issues because it
has no mechanical link so it would be uncontrollable when the actuator doesn’t
operate. To make sure the safety of system, the architecture of rack system
module has dual motor structure as shown in Fig 2.4.
Figure 2.4 Configuration of rack system module
Each actuator system has different reduction gear structure respectively. One has
belt and pulley reduction gear and ball screw transmission structure that it has less
friction and backlash and higher gear efficiency. The other one has worm and
worm-wheel reduction gear and rack and pinion transmission structure that it can
be installed angle sensor on the pinion.
Tmot_rp is rack and pinion side motor and Tmot_belt is belt side motor. rworm is worm-
gear reduction ratio, rc-factor is rack and pinion ratio, rpulley is pulley ratio and rball_lead
Tmot_rp
rworm
TAS
(sensor)
rc-factor
rpulley
Tmot_belt
rball_lead
Mrack
Brack
Krack
FRrack
Fvehicle
8
is length of ball screw lead. M, B, K and FR are the rack system parameters and
Fvehicle is rack force from vehicle. Angle sensor is operated as a system output to
control rack position.
Eq(2.6) shows rack system dynamic model and Eq (2.7) and Eq(2.8) are
relational expressions to convert motor torque to rack force with regard to
reduction gear respectively.
vehiclerackrackrackrackbeltmotrpmot FxFRxKxBxMFF )tanh( __
(2.6)
efficiency
factorc
wormrpmot
rpmotS
rTF
_
_
2
(2.7)
efficiency
leadball
pulleybeltmot
beltmotr
rTF
_
2
_
_
2 (2.8)
2.3 Overall system architecture
The SBW system has 3-ECU system for safety as shown in Fig. 2.4. There are
two ECUs that control each system and there is additional ECU for back up when
the control ECU fails. The structure is designed based on triple modular
redundancy (TMR). It means that there has to be three sensors or ECUs to notice
system failure to the driver.
9
Figure 2.5 Overall system architecture
SBW Controller
ECU2
(Rack)
ECU3
(Steering)
ECU1
(Fail-safe)
10
Chapter 3
State Estimation
3.1 System Requirement
The target torque is determined by vehicle state and steering wheel state.
The SBW system has only angle sensors but the angular velocity and
acceleration is necessary to generate torque reference. In this system, there
are three angle sensors which can be applicable each system for redundancy.
In the steering reaction module, there are steering angle sensor(SAS), torque
angle sensor(TAS) and motor position sensor(MPS). In the rack system
module, there are also three angle sensor that there are two MPSs and pinion
angle sensor(PAS). The angular velocity and acceleration must be
differentiated using angle data but it has divergence problem if the raw data is
used for calculating velocity and acceleration. Therefore it needs to be
filtered and the kalman filtering method is used on this study.
11
3.2 Kalman Filter
Kalman filter is one of the estimators based on optimization process. There is
angle sensor, continuous wiener process acceleration(CWPA) model is applied to
estimate angular velocity and acceleration. Eq (3.1), Eq(3.2) and Eq(3.3) show
the state equations with matrix F, L and H.
)()()( tLWtFxtx (3.1)
)()()( tVtHxty (3.2)
001
1
0
0
000
100
010
HLF (3.3)
The state system has to be discretized to compute in digital system. It can be
approximated based on Eq(3.4) and Eq(3.5)
T
txTtxtx
T
)()(lim)(
0
(3.4)
)()()())1(( kTTLWkTxTFITkx (3.5)
Therefore, the system can be expressed as Eq(3.6), Eq(3.7) and Eq(3.8). And
the matrix F, L and H changed to Fd, Ld and Hd as shown in Eq(3.9)
][][]1[0
kLWdekxekx
T
FFT
(3.6)
12
][][]1[ kWLkxFkx dd (3.7)
][][][ kVkxHky d (3.8)
001
1
0
0
100
001.010
5001.01
)exp(
7
ddd HL
E
FF (3.9)
The estimator of system consists of process update and measurement update as
shown in Eq(3.10) and Eq(3.11)
1
ˆˆkk xFx (3.10)
)ˆ(ˆˆ
kkkkk xHyKxx (3.11)
To set the Kk value, it is assumed that there is no correlation between error and
noise. And Eq(3.12) and Eq(3.13) show the covariance of error.
11])ˆ)(ˆ[(
k
T
k
T
kkkkk QFFPxxxxEP (3.12)
kk
T
kkkkk PHKIxxxxEP )(])ˆ)(ˆ[( (3.13)
Eq(3.14) is cost function to minimize and Eq(3.15) and Eq(3.16) show the
optimal Kk value to minimize covariance.
)(])ˆ()ˆ[( 22
11 kkk PTrxxxxEJ (3.14)
02)()(2)(
kk
T
kk
k
k RKHPHKIK
PTr (3.15)
1)( k
T
k
T
kk RHHPHPK (3.16)
13
Chapter 4
Steering Feel Target
4.1 Reference Torque
The vehicle has own steering feel but it is difficult to say that which one is
excellent because the feeling depends on personal emotion. In spite of this
situation, steering target torque is needed and the steering measurement data would
be used from released vehicle. Steering feel can be expressed as 4-D map as
shown in Fig. 4 that consists of torque, angle, angular velocity and vehicle speed.
Figure 4.1 Reference torque 4-D map
14
As mentioned above, it is hard to define clearly, so it has to be tunable in the
various driving conditions. The form of 4-D map is not good for tuning steering
feel so it can be expressed as 2-D form as shown in Fig. 4.2.
(a) Weave test
(b) Transition test
Figure 4.2 Steering feel in the weave and transition test
Torque
(Nm)
Angle(°)
Hysteresis @ 0deg Hysteresis @ 0Nm
Slope (m1)@(-2.5~2.5deg)
Slope(m2)@
(7.5~12.5deg)
Torque @0deg
Torque@10deg
Angle (˚)
Torque
(Nm)
Slope(m1)@(0~1deg)
Slope(m2)@(7.5~12.5deg)
Torque @0deg
Torque@10deg
15
4.2 Target Torque Generation
These steering feel can be expressed using equations of main reaction curve,
damping, friction and inertia as shown in Eq(4.1), Eq(4.2), Eq(4.3) and Eq(4.4) and
Fig. 4.3
)sinh( 21 aarcaTmain (4.1)
3aTdamp (4.2)
)tanh( 54 aaT friction (4.3)
6aTinertia (4.4)
Figure 4.3 Steering feel modeling
Torque
Angle
Main = a1×arc sinh(a
2 ·θ)
Friction = a4×tanh(a
5θ) ·
Torque
Angle
Damping = a3× θ ·
Torque
Angle
Inertia = a6× θ
··
Torque
Angle
16
The inverse hyperbolic sine function had been adopted to generate main reaction
curve and hyperbolic tangent function had been adopted to make friction effect.
The angular velocity and acceleration is from kalman filtering in chapter. 3
There are 6 tuning parameters, a1 to a6, to generate target torque so it has to be set
by proper value. Before set the parameters, the targets of steering feel are defined
as shown in Table. 4.1
Table 4.1 Steering feel targets
TARGET @ Weave
Friction Feel(Torque 0deg) 1.37 Nm
Stiffness(m1) 0.183 Nm/deg
Torque Build-up(m2/m1) 0.574
Off-center Torque(Torque @10deg) 2.79 Nm
Hysteresis @ 0deg 2.74 Nm
Hysteresis @ 0Nm 15.4 deg
TARGET @ Transition
Friction Feel(Torque 0deg) 0.63 Nm
Stiffness(m1) 0.856 Nm/deg
Torque Build-up(m2/m1) 0.127
Off-center Torque(Torque @10deg) 2.64Nm
17
Therefore, to set the parameters, the sequential quadratic programming (SQP)
method had been adopted for optimization. This method builds a quadratic
approximation to the lagrange function and linear approximations to all output
constraints at each iteration, starting with the identity matrix for the Hessian of the
lagrangian, and gradually updating it using the Broydon-Fletcher-Goldfarb-Shanno)
method. On each iteration, a quadratic programming problem is solved to find an
improved design, until the final convergence to the optimum design. Eq(4.5)
shows the lagrangian and Eq(4.6), Eq(4.7) and Eq(4.8) show the basic concepts of
SQP algorithm.
)()()(),,( xgxhxfxL TT (4.6)
kk
k
k
k
k
k
k
LL
u
x
u
x
12
1
1
1
)( (4.7)
*
*
g
h
ghf
du
dLd
dLdx
dL
Lk
,
00
00
2
2
g
h
ghL
Lk (4.8)
After Optimization, the initial steering feel can be generated as shown in Fig.4.4
18
(a) Weave test
(b) Transition test
Figure 4.4 Steering feel optimization result
Result
Measured Data Torque
(Nm)
Angle (°)
Torque
(Nm)
Angle(°)
Measured Data Result
19
Chapter 5
Control System
5.1 Steering Reaction Module
The target torque Tref is defined in Chapter 4 and there has to be control algorithm
to track the reference torque. The main idea of feedback control is using
impedance model based on target torque. Fig. 5.1 shows overall architecture of
steering reaction module control system.
Figure 5.1 Steering reaction module overall control architecture
+
-
Target
System Controller
(Sliding Mode Control)
Ang.Vel u(t)
Kalman
Filtering Target Torque Angle
Angle
Ang.Vel
Ang.Acc
Veh.Speed
Impedance Model
Tsw=Jθ+T
ref
..
20
Steering feel curve shows its nonlinearity that it is hard to express with linear
system. Target torque with nonlinear function is defined in Chapter 4, so it can be
used to impedance model which is the desired torque to the driver. Eq.(5.1)
shows the steering torque dynamics based on target torque.
J
TT refsw d
(5.1)
Therefore, the desired angular velocity can be obtained by integration of angular
acceleration and it is reference of feedback loop.
In the feedback loop, it demands controller and system dynamics for SBW system.
Eq(5.2) shows the system dynamics for simulation that consists of inertia, damping,
stiffness and control input.
)(tuKBJT swswswsw (5.2)
The feedback controller is sliding mode control which can compensate system
nonlinearity and uncertainty. Eq(5.3) shows the error between desired and
measured angular velocity.
swd e (5.3)
Eq(5.4) shows sliding surface which has to make it converge to zero.
21
eλes 1 (5.4)
Eq(5.5) shows lyapunov function and Eq(5.6) shows differentiated lyapunov
function which has to make it under zero. The basic idea to make Eq(5.6) under
zero, let the differentiated sliding surface always have minus sign. It becomes
Eq(5.7) after substituting error dot.
2
2
1sV (5.5)
0)( 1 eesssV (5.6)
)))(
(( 1eJ
tuKBT
J
TTsV swswswrefsw
(5.7)
And the control input u(t) can be determined to make Eq(5.7) zero as shown in
Eq(5.8)
JeKBTtu swswref 1)( (5.8)
And to make sure the stability of feedback loop, the additional sign function based
on sliding surface is applied. And the sign function is expressed using saturation
function to prevent from chattering problem as Eq(5.9)
)()( 1
s
AsatJeKBTtu swswref (5.9)
22
5.2 Rack System Module
The rack system module has rack and pinion structure as shown in Fig. 5.2 that
has high friction to prevent gear rattle noise. And there are a lot of road
conditions like wet, dry, ice and spilt mu road typically. In terms of rack system
module, the high friction makes system nonlinear and the various road conditions
give system disturbance.
Figure 5.2 Rack system module architecture
5.2.1 Sliding Mode Control
In this situation, rack position has to be controlled precisely and the position
target is decided from steering wheel angle and upper controller as Eq(5.10). C-
factor is ratio of pinion angle and rack displacement and AFS is additional angle
from upper controller.
Steering Reaction Module
Rack System Module
- High friction system
- Variable road condition
Rack and Pinion
Ball Srew
23
AFSfactorCX swrack 360
1 (5.10)
The system and controller consist of feedback controller and disturbance observer
as shown in Fig. 5.3. Sliding model control is used for position control and the
disturbance observer is to robust control of system.
Figure 5.3 Rack system control system structure
In the position control, the error is difference of target displacement and measured
displacement as Eq(5.11).
rackd xxe (5.11)
The vehicle system consists of mass, damping, stiffness, friction and disturbance
as Eq(5.12)
edisturbancrackrackrackrackrack FxFRKxxCxMF )tanh( (5.12)
+
Controller
(Sliding Mode Control) System
Disturbance observer
Ang
Q-filter
noise
d
+ _
u(t) +
+
-
Target Ang
+ -
d ^
24
However, the system dynamics contains uncertainty so the Eq(5.12) can be
express as Eq(5.13) which consists of nominal and uncertainty parameters
)tanh()ˆ()ˆ( rackrackrackrackrack xFRxKKxCCxMF (5.13)
Eq(5.14) shows sliding surface which has to make it converge to zero.
eλes 1 (5.14)
Eq(5.15) shows lyapunov function and (5.16) shows differentiated lyapunov
function which has to make it under zero. To make Eq(5.16) under zero, let the
differentiated sliding surface always have minus sign. It becomes Eq(5.17) after
substituting system dynamics to double dot of error.
2
2
1sV (5.15)
0)( 1 eesssV (5.16)
))tanh((1
( 1
rackrackrackrackdes xFRKxxCF
MxesV (5.17)
Therefore the control input can be determine as Eq(5.18)
)()tanh(1
s
KsateM
xMxFRKxxCF desrackrackrackrack
(5.18)
25
As mentioned above, there are system uncertainties so the system parameters have
to be identified. The lyapunov function for adaptation parameters as Eq(5.19) and
differentiated lyapunov function as Eq(5.20) and Eq(5.21)
))()((2
1 2
2
2
1
2 KCsV (5.19)
0))(())(( 21 KKCCssV (5.20)
The control input has been decided in Eq(5.18), The differentiated lyapunov
function becomes Eq(5.21)
)ˆ)(()ˆ)(()]([ 211 KKCC
sKsatKxxC
MsV rackrack
(5.21)
And the adaptation parameter can be determined as Eq(5.22) and Eq(5.23)
1
1ˆ
M
xsC rack
(5.22)
2
1ˆ
M
xsK rack (5.23)
26
5.2.2 Disturbance Observer
The road condition is various and the changing force from road condition affects
to the system as disturbance. The block diagram of disturbance observer (DOB)
is as shown in Fig. 5.4.
(a) Basic Structure
(b) System with uncertainty
Figure 5.4 DOB block diagram
System
P(s)
Ang
ξ
d
+
_
u(t)))+
+
-
d ^(t)
Pn-1
Q(s)
+
Pn(s)
ξ
1
1 − 𝑄(𝑠)
Q(s) Pn-1
d
u
Δ(s)W2(s)
27
The DOB consists of inverse nominal plant and Q filter. And the transfer
functions related to control input, disturbance and noise are as Eq(5.24), Eq(5.25)
and Eq(5.26).
)()]()()[(
)()()(
sPsPsPsQ
sPsPsG
nn
n
uy
(5.24)
)()]()()[(
)](1)[()()(
sPsPsPsQ
sQsPsPsG
nn
n
dy
(5.25)
)()]()()[(
)()()(
sPsPsPsQ
sQsPsG
nn
uy
(5.26)
The control law can be set to reject the disturbance low frequency and reject noise
in high frequency. Therefore the Q-filter form should be set as Eq(5.27) like 1st
delay filter. And the W2(s) is weight factor to compensate uncertainty can be set as
Eq(5.28).
ssQ
1
1)( (5.27)
2,
2,
1,
1,
2/1
/1
/1
/1)(
p
z
p
z
s
s
s
ssW
(5.28)
And the DOB loop is robustly stable if and only if Eq(5.29).
1||)()(||)( 22 sQsWsW (5.29)
28
Chapter 6
HILS Test Results
6.1 HILS System Configuration
The HILS system components consist of steering reaction module, rack system
module, MicroAutobox as ECU, CAN communication system, vehicle model and
hydraulic actuating system as shown in Fig. 6.1.
Figure 6.1 Overall HILS system configuration
Sensor Sensor
Command Command
Rack System Module Steering Reaction
Module
MicroAutobox
Vehicle model Command
29
The existing ECUs in the modules are not for SBW system. So the control
logics are imbedded in the MircroAutobox and the ECU operates only motor drive
as shown in Fig. 6.2.
Figure 6.2 Controller configuration
Sensor
Torque
Angle
CAN
Autobox
Calculation
Rack System Module
Logic
Steering Reaction Module
Logic
ECU
MOTOR
Motor Drive
Assist Control
Damping Control
CAN Interface
Motor State Command
Veh.Speed
Angle
Ang.Vel
30
The vehicle is replaced by vehicle model using software, CarMaker. The force
and rack displacement from vehicle model are implemented in the hydraulic
actuating system as shown in Fig. 6.3.
Figure 6.3 Hydraulic actuator configurations
Tire Force
< Rack System Module>
< Actuator >
<Motor2> <Motor1> Rack force
31
6.2 Results of Steering Reaction Module
The test scenario is listed based on weave and transition test which are our
steering feel target as Table. 2. The weave test has been done with various
frequencies, 0.3Hz, 0.5Hz and 1Hz with regard to vehicle speed, 60kph and 80kph.
And the transition test has been done with vehicle speed 60kph and 80kph that the
input signal is 5deg/s.
Table 6.1 Steering reaction module test scenarios
Test Input Vehicle Speed
Weave
0.3 Hz
60 kph
80 kph
0.5 Hz
60 kph
80 kph
1.0 Hz
60 kph
80 kph
Transition 5 deg/s
60 kph
80 kph
32
The Fig. 6.4 shows the filtering performance when the sensor signal has Gaussian
noise.
Figure 6.4 Kalman filtering performance
And the steering target can be generated and the Fig. 6.5 shows the example of the
target when the input signal is sine wave.
Figure 6.5 Weave test target
Filter
NoiseData
Angle
Torq
ue
Target steering feel Target steering feel
33
The HILS test results of weave test at 60kph are shown in Fig 6.6.
(a) 60 kph 0.3Hz
(b) 60 kph 0.3Hz
(c) 60 kph 1.0Hz
Figure 6.6 Results of weave test at 60 kph
34
The HILS test results of weave test at 80kph are shown in Fig 6.7.
(a) 80 kph 0.3Hz
(b) 80 kph 0.5Hz
(c) 80 kph 1.0Hz
Figure 6.7 Results of weave test at 80 kph
35
The HILS test results of transition test at 80kph are shown in Fig 6.8.
(a) 60 kph, 5deg/s
(b) 80 kph, 5deg/s
Figure 6.8 Results of transition test
36
6.3 Results of Rack System Module
The main performance of rack system is preciseness of position control. The Fig.
6.9 shows the step input characteristic and the Table 6.1 shows target performance.
Figure 6.9 Step input characteristic
Table 6.2 Target performance for rack system
Performance Target
Position Error Peak Error < 2deg, Steady state Error <0.6deg
Overshoot No overshoot
Settling Time 0.2sec under 0.4g
Additional Req. Satisfying error requirement under 500 deg / s
37
The test scenarios are listed based on step and weave test as shown in Table 6.3.
Table 6.3 Rack system module test scenarios
Test Input Vehicle Speed
Weave
0.3 Hz
60 kph
80 kph
0.5 Hz
60 kph
80 kph
1.0 Hz
60 kph
80 kph
Step 0.4g
60 kph
80 kph
38
The HILS test results of weave test at 60kph are shown in Fig 6.10
(a) 60 kph, 0.3Hz
(b) 60 kph, 0.5Hz
39
(c) 60 kph, 1.0Hz
Figure 6.10 Results of weave test at 60 kph
The HILS test results of weave test at 60kph are shown in Fig 6.11.
(a) 80 kph, 0.3Hz
40
(b) 80 kph, 0.5Hz
(c) 80 kph, 1.0Hz
Figure 6.11 Results of weave test at 80 kph
41
The HILS test results of step input test are shown in Fig 6.12.
(a) 60kph, 40deg
(b) 80kph, 24deg
Figure 6.12 Results of step test
42
Chapter 7
Conclusions
This paper describes the method about control system for steer by wire system
and test results using control algorithm. First, to control steering feel, the target
torque has been generated using main curve, friction, damping and inertia based on
measured data. And the sequential quadratic programming method is applied to
match measured reference torque and generated target torque. In the controller,
the impedance model is created using target torque and the sliding mode control
method has been applied to track the target velocity. Second, to control rack
position, the target position comes from steering wheel and it has to be controlled
without overshoot and with high preciseness. In the controller, the adaptation is
added to lyapunov function to set the system parameters and disturbance observer
is applied to compensate the changes of vehicle speed and road conditions. The
validation test has been conducted using HILS equipment and the performance
satisfies torque reference and rack position preciseness respectively.
For the future work, the algorithm of steering feel in this study can’t reflect road
condition or rack force changes, the rack force estimation needs to be developed
and be applied to steering feel.
43
Bibliography
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Feedback Torque Control Algorithm for Driver Steering Feel in Vehicle Steer by Wire
System: Hardware in the Loop”, International Journal of Vehicular Technology, Volume
2015, Article ID 314597
(2) H. Wang et al. “Robust Control for Steer-by-Wire Systems With Partially Known
Dynamics”, IEEE Transaction on industrial informatics, 2014
(3) Lee, D., Jang, B., Yi, K., Chang, S. et al., "A Novel Electric-Power-Steering (EPS)
Control Algorithm Development for the Reference Steering Feel Tracking," SAE
Technical Paper 2016-01-1546, 2016, doi:10.4271/2016-01-1546.
(4) M. Sigilló, M. Dold, C. Delmarco, K. Polmans, “Implementation and testing of
different control strategies on a steer-by-wire research platform”, 6th International
Munich Chassis Symposium, 2015
(5) S. Fankem, S. Müller „Modular concept for the calculation of the desired steering
torque in steer-by-wire systems“, 3rd International Munich Chassis Symposium, 2012
(6) M. T. Do, Z. Man, C. Zhang, H. Wang, and F. S. Tay, “Robust sliding mode-based
learning control for steer-by-wire systems in modern vehicles,” IEEE Transactions on
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(7) H.K. Khalil “Nonlinear Systems”, ISBN: 978-0130673893, 2001
(8) J. Duan, R.Wang, and Y. Yu, “Research on control strategies of steer-by-wire system,”
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(12) Y. Chai, T. Kimura, K. Igarashi, “Nissan Contribution for vehicle dynamics with a
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45
초 록
스티어 바이 와이어 시스템 조향반력 및
랙 위치 제어
본 연구는 자율주행 차량에 적용이 요구되는 조향 신기술인 스티어
바이 와이어 시스템의 조향감을 생성하는 방법론 및 추종 알고리즘
그리고 차량의 모션을 제어하기 위한 랙 시스템의 위치 제어기법을
제안한다. 조향감을 생성하기 위해 차량의 데이터를 기반으로 하여
목표로 하는 조향감을 결정하고, 수식화된 조향감 모델을 구성하여
최적화 과정을 통해 목표 조향감을 생성해낸다. 이때 사용되는
각속도는 조향각 신호를 활용하여 칼만필터를 통해 계산되어 지며 목표
조향감을 조향각, 각속도, 차속에 대한 조향토크를 4차원 형태로 나타낼
수 있다. 목표 조향감을 임피던스 모델을 활용하여 목표 각속도 값을
도출하였으며 슬라이딩 모드 컨트롤 기법을 활용하여 모터 토크를
제어하였다. 차량의 모션을 결정하는 랙 시스템 모듈의 경우 차량의
노면조건, 부품의 마찰 특성에 따라 시스템 특성이 변화한다. 따라서
정확한 위치제어를 위해 기준 차량 조건에서의 시스템 파라메터 값을
Adaptation 기법을 활용하여 설정하였으며, 노면 조건에 의한 외란을
보상하기 위해 외란 추정기 (Disturbance Observer)를 활용하여 위치 제어
성능을 강건하게 확보 할 수 있는 알고리즘을 제안한다. 제안된
알고리즘을 검증하기 위해 Hardware In the Loop System(HILS)을
구성하였으며, 각 모듈 부품, 모터를 제어하기 위한 Autobox, 차량의
46
모션을 구현하기 위한 차량 모델과 모델에서부터 계산된 타이어 힘을
구현할 수 있는 유압식 액츄에이터로 구성이 되며, 실차와 유사한 HILS
환경에서 목표로 하는 조향감과 위치 제어 성능 검증 결과를 제시한다.
주요어: 스티어 바이 와이어, 조향감 목표, 임피던스 제어, 슬라이딩
모드 제어, 외란 추정기, 하드웨어 기반 시뮬레이션
학 번: 2017-28425