2.3. CONTROLLER DESIGN FOR DIFFERENT DRIVING STYLES 13
Table 2.2: Key parameters of the electric vehicle
Parameter Value Unit
Vehicle mass 1360 kg
Wheel base 2.50 m
Frontal area 2.40 m
2
Gear ratio 7.881 —
Nominal radius of tire 0.295 m
Coeffi cient of air resistance 0.32 —
Motor peak power 45 kW
Motor maximum torque 145 Nm
Motor maximum speed 9000 rpm
Battery voltage 336 V
Battery capacity 66 Ah
2.2.4 EXPERIMENTAL VALIDATION
e models of the electric vehicle with its subsystems were implemented in MAT-
LAB/Simulink. Experimental data measured from vehicle test were used for model calibration.
Key parameters of the systems are listed in Table 2.2. e feasibility and effectiveness of the
models have been previously validated via hardware-in-the-loop experiments and vehicle road
testing [17, 25].
2.3 CONTROLLER DESIGN FOR DIFFERENT DRIVING
STYLES
2.3.1 HIGH-LEVEL CONTROLLER ARCHITECTURE
e high-level supervisory controller adopts a scheduling protocol, asking the architecture and
control objectives of the low-level controller, as well as the parameters of the physical plant, to
dynamically adapt to different driving styles, as shown in Fig. 2.6. In this study, the driving style
of the automated vehicle can be either obtained in the manual mode through the DSR algorithm
developed in the previous section, or actively selected by human operator during autonomous
mode. To avoid unexpected discontinuities in controller output resulted by frequent and fast
transitions between different driving styles, a simple and reliable approach for the application is
to allow the driving style to be actively or passively switched only when the vehicle is stopped,
i.e., the vehicle speed v D 0.
14 2. CO-DESIGN OPTIMIZATION FOR CYBER-PHYSICAL VEHICLE SYSTEM
Acceleration
Tracking Controller
Active-Damping
Controller
Driving Style
Recognition
/Selection
Agressive
Moderate
Conservative
Controller
Physical Plant
SMC Gain Tuning
Moderate Style Para Tuning
Conserv Style Para Tuning
Conserv Style Plant Para Tuning
Moderate Style Plant Para Tuning
Aggressive Style Plant Para Tuning
Online Learning;
Human Option;
Preference Set-Up
…
Y
Human
Inputs
States
Feedback
Figure 2.6: Scheduling-protocol based hierarchical control for different driving styles.
2.3.2 LOW-LEVEL CONTROLLER FOR DIFFERENT DRIVING STYLES
(1) Controller for aggressive driving style: Based on the sporty feature of aggressive driving style,
the vehicle longitudinal control under this condition can be seen as an acceleration tracking
problem, realizing the sporty feel in automated driving for passengers. Because of its ability
to address nonlinearity and achieve good performance with fast response [38], a sliding-mode
control (SMC) scheme is applied.
In designing the sliding-mode controller, the error term is defined as:
e D a a
ref
; (2.16)
where a and a
ref
are the actual and reference values of vehicle acceleration, respectively.
To guarantee zero steady error, an integral-type sliding surface S is chosen as:
S D
Z
edt: (2.17)
One method for designing a control law that derives the system trajectories to the sliding surface
is the Lyapunov direct method. e following Lyapunov function is used:
V D
1
2
SS: (2.18)
To ensure the stability of the system, the derivative of the Lyapunov function should satisfy the
following condition:
P
V D S
P
S 0: (2.19)
us, if
P
S D 0, the above stability condition can be satisfied.
2.3. CONTROLLER DESIGN FOR DIFFERENT DRIVING STYLES 15
For the purpose of controller design, a control-oriented longitudinal vehicle model with-
out considering wheel slip is used [35].
a D
1
mr
i
g
T
m
fg
1
2m
C
D
Av
2
; (2.20)
where r is the nominal radius, C
D
is the coefficient of air resistance, A is the frontal area, is
the air density, f is the friction drag coefficient, and g is the gravitational acceleration.
en, substituting Equations (2.16) and (2.20) into Equation (2.17), when
P
S D 0, the
SMC control law can be derived as:
T
m;ref
D
mr
i
g
a
ref
C fg C
C
D
Av
2
2m
k
SMC
sgn.S/
; (2.21)
where k
SMC
is the positive gain of the SMC controller and sgn.S/ is the sign function defined
as:
sgn.S/ D
8
ˆ
<
ˆ
:
1; S > 0
0; S D 0
1; S < 0:
(2.22)
Remark 2.1 It is well known that in the standard SMC, the discontinuous sign function,
sgn.S/, may cause chattering when the state trajectories are approaching the sliding surfaces.
To avoid this phenomenon, the discontinuous term in Equation (2.21) could be replaced by a
continuous function S, removing the chatter from the control input [39], as shown in Equa-
tion (2.23):
T
m;ref
D
mr
i
g
a
ref
C fg C
C
D
Av
2
2m
k
SMC
S
: (2.23)
(2) Controller for moderate driving style: e moderate driving style features a balanced
performance in vehicle dynamics and ride comfort. To this end, the low-level plant controller
uses a combined feed-forward and feed-back structure, to actively damp powertrain torsional
vibrations, thus mitigating the longitudinal jerk and enhancing drivability:
T
m;ref
D T
ff
C T
fb
; (2.24)
where T
ff
is the feed-forward input term required for tracking and T
fb
is the feedback component
designed to reduce the control error.
Based on the control objective, the feed-forward term can be determined by the target
motor torque T
m;tgt
, which is calculated using the reference acceleration:
T
ff
D T
m;tgt
: (2.25)
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