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)