Abstract and Figures

Fully electric vehicles with individually controlled powertrains can achieve significantly enhanced vehicle response, in particular by means of Torque Vectoring Control (TVC). This paper presents a TVC strategy for a Formula SAE (FSAE) fully electric vehicle, the “T-ONE” car designed by “UninaCorse E-team” of the University of Naples Federico II, featuring four in-wheel motors. A Matlab-Simulink double-track vehicle model is implemented, featuring non-linear (Pacejka) tyres. The TVC strategy consists of: i) a reference generator that calculates the target yaw rate in real time based on the current values of steering wheel angle and vehicle velocity, in order to follow a desired optimal understeer characteristic; ii) a high-level controller which generates the overall traction/braking force and yaw moment demands based on the accelerator/brake pedal and on the error between the target yaw rate and the actual yaw rate; iii) a control allocator which outputs the reference torques for the individual wheels. A driver model was implemented to work out the brake/accelerator pedal inputs and steering wheel angle input needed to follow a generic trajectory. In a first implementation of the model, a circular trajectory was adopted, consistently with the "skid-pad" test of the FSAE competition. Results are promising as the vehicle with TVC achieves up to ≈ 9% laptime savings with respect to the vehicle without TVC, which is deemed significant and potentially crucial in the context of the FSAE competition.
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AIMETA 2019
XXIV Conference
The Italian Association of Theoretical and Applied Mechanics
Rome, Italy, 15-19 September 2019
TORQUE VECTORING CONTROL FOR FULLY ELECTRIC SAE
CARS
Valentina De Pascale1,2, Basilio Lenzo1, Flavio Farroni2, Francesco Timpone2, and
Xudong Zhang3
1 Department of Engineering and Mathematics, Sheffield Hallam University
Howard Street, S1 1WB, Sheffield, UK
e-mail: vdepascale93@gmail.com, basilio.lenzo@shu.ac.uk
2 Industrial Engineering Department, University of Naples “Federico II”
Via Claudio 21, 80125 Naples, Italy
{flavio.farroni, francesco.timpone}@unina.it
3 National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology
5 South Zhongguancun Street, Beijing, 100081, China,
xudong.zhang@bit.edu.cn
Keywords: Torque Vectoring Control, Driver Model, Fully Electric Vehicle, Formula SAE.
Abstract. Fully electric vehicles with individually controlled powertrains can achieve signifi-
cantly enhanced vehicle response, in particular by means of Torque Vectoring Control (TVC).
This paper presents a TVC strategy for a Formula SAE (FSAE) fully electric vehicle, the “T-
ONE” car designed by “UninaCorse E-team” of the University of Naples Federico II, featur-
ing four in-wheel motors. A Matlab-Simulink double-track vehicle model is implemented, fea-
turing non-linear (Pacejka) tyres. The TVC strategy consists of: i) a reference generator that
calculates the target yaw rate in real time based on the current values of steering wheel angle
and vehicle velocity, in order to follow a desired optimal understeer characteristic; ii) a high-
level controller which generates the overall traction/braking force and yaw moment demands
based on the accelerator/brake pedal and on the error between the target yaw rate and the
actual yaw rate; iii) a control allocator which outputs the reference torques for the individual
wheels. A driver model was implemented to work out the brake/accelerator pedal inputs and
steering wheel angle input needed to follow a generic trajectory. In a first implementation of
the model, a circular trajectory was adopted, consistently with the "skid-pad" test of the FSAE
competition. Results are promising as the vehicle with TVC achieves up to 9% laptime sav-
ings with respect to the vehicle without TVC, which is deemed significant and potentially cru-
cial in the context of the FSAE competition.
V. De Pascale, B. Lenzo, F. Farroni, F. Timpone, and X. Zhang
1 INTRODUCTION
Formula SAE is an international student design competition which challenges worldwide
students to conceive, design, fabricate and compete with small formula-style racing cars [1].
While the competition was historically based on internal combustion engines (since 1981),
recently there has been an increasing interest towards electric-powered Formula SAE vehi-
cles, with the first Formula SAE Electric competition taking place in 2013 [2]. Most of the
solutions adopted so far include two or four in-wheel electric motors, without differential.
That allows Torque Vectoring Control (TVC), i.e., the individual control of each drivetrain
[3-7]. By imposing an uneven distribution of torque demand between the left and right side of
the vehicle, a direct yaw moment can be generated and appropriately exploited to improve
vehicle performance and, ultimately, reduce laptime.
This paper deals with the development and assessment of a torque vectoring strategy for
the Formula SAE vehicle T-ONE of the UninaCorse E-team from the University of Naples
Federico II (Fig. 1), featuring four in-wheel motors, and with main parameters shown in Table
1. The vehicle model and simulations were implemented in Matlab-Simulink.
Section 2 describes the vehicle model. Details regarding the torque vectoring algorithm are
given in Section 3. Section 4 deals with the reference trajectory and the driver model. Prelim-
inary results are presented in Section 5, and conclusions are in Section 6.
Figure 1: The Formula SAE vehicle "T-ONE".
2 VEHICLE MODEL
A double-track vehicle model was implemented. The Adapted ISO sign convention [8] and
the vehicle reference frame and schematic in [9] were adopted in this study. Hence, the -axis
represents the forward direction, the -axis indicates the lateral direction (positive to the left),
the -axis is vertical (positive upwards). The longitudinal and lateral components of the veloc-
ity of the centre of mass of the vehicle are respectively u and v, while r is the vehicle yaw
rate.

and

are, respectively, the longitudinal and lateral forces at the corner , where
1,2 for front and rear axles, and 1,2 for left and right sides. The wheel steering angle,
, is assumed to be the same for both front wheels.
V. De Pascale, B. Lenzo, F. Farroni, F. Timpone, and X. Zhang
Quantity Symbol Value and unit
Wheel radius 0.26 m
Front semi-wheelbase 0.990 m
Rear semi-wheelbase 0.660 m
Vehicle mass 350 kg
Moment of inertia along the vertical axis 400 kg
Wheelbase l 1.650 m
Track t 1.200 m
Height of the centre of mass h 0.32 m
Table 1: Main parameters of the Formula SAE vehicle T-ONE.
The longitudinal equilibrium equation is

1
2
(1)
which includes the aerodynamic drag, where is the air density, the drag coefficient, and S
the frontal area of the vehicle.
The lateral equilibrium equation is
1
2
 (2)
where is the lateral drag coefficient.
The moment balance equation in the direction leads to:



 + (3)
where is the yaw moment generated via the TVC (see Section 3).
The congruence equations, under the assumption of small sideslip angles, read


2 (4)


2(5)


2 (6)


2(7)
V. De Pascale, B. Lenzo, F. Farroni, F. Timpone, and X. Zhang
where  is the tyre slip angle at the corner .
The constitutive equations were implemented using a PAC2002 Pacejka formulation, start-
ing from the .tir file of the used tyre, i.e. Hoosier 13''. The adopted formulation provides the
lateral forces  as functions of camber angle, , vertical load, , slip angle, , and
wheel radius, , in pure lateral conditions. , instead, were obtained with an even distribu-
tion among the four wheels of the overall desired longitudinal force, , provided by the driver
model (see Section 3). The vertical loads are
 (8)
 (9)
 (10)
 (11)
where the downforce and longitudinal load transfer contributions are

2
(12)

2
(13)
and the lateral load transfers are
 1
 (14)
 1
 (15)
where h is the height of the centre of mass, d the height of the roll centre below the centre of
mass,  and  the front and rear aerodynamic lift coefficients,  e  the front
and rear relative roll stiffness values, 
and 
the static front and rear
vertical loads are, the gravity acceleration, and the vehicle longitudinal and lateral
accelerations.
3 TORQUE VECTORING CONTROL
The developed TVC strategy is based on the scheme proposed in [10]. A reference yaw
rate value, , is generated through a look-up table which takes as input the wheel steering
angle, , and the vehicle velocity, . The look-up table was built considering steady-state
conditions and a desired vehicle cornering response (a.k.a. understeer characteristic), shaped
as in Equation 17. With respect to the baseline vehicle, i.e. the vehicle without TVC, the cor-
nering response is designed so as to: i) decrease the understeering gradient; ii) extend the re-
gion of linear relationship between dynamic steering angle, , and lateral acceleration, up
to
; iii) increase the maximum lateral acceleration achievable, ,, which is very im-
portant in the interest of laptime minimisation. Specifically, the look-up table was built by
defining vectors of and , then using the following relationships:

(16)
V. De Pascale, B. Lenzo, F. Farroni, F. Timpone, and X. Zhang
Then, to relate the dynamic steering angle to the overall steering angle, the kinematic steering
angle (Ackermann angle), , was obtained as

(18)
and added to the dynamic contribution to obtain the total wheel steering angle:
(19)
Finally, the table was inverted in order to have wheel steering angle and vehicle velocity as
input, and reference yaw rate as output.
A PID controller was implemented to track the yaw rate, specifically taking as input the er-
ror between the reference yaw rate and the current yaw rate, , and giving as output the value
of yaw moment, , to be generated.
Once the value of desired overall force and yaw moment are known, a "control allocator"
block [4,11] calculates the four wheel torque demands, , as:
2
4 (20)
2
4 (21)
4 REFERENCE TRAJECTORY AND DRIVER MODEL
Among the Formula SAE dynamic tests, this study selected the Skid-pad test [12], in
which the car goes through a figure-of-eight shaped track including two circles with diameter
15.25 m. The car performs two laps in one of the circles, then it moves to the other circle and
it performs other two laps. The best laptime is selected between the second attempt at each
circle. Hence, in a first implementation of this work, it is sufficient to design a circular trajec-
tory with radius R, to be negotiated twice. Specifically, the vehicle starts in (0,0) so the circle
has centre in (0, R). The equations for the reference position are thus:
cos/(22)
sin/(23)
where s is the curvilinear abscissa, which can be calculated as:
(24)
The driver model used in this study is inspired to [13]. It calculates: i) the wheel steering
angle, , through a Proportional controller based on errors on position and orientation of the
vehicle; ii) the acceleration/brake inputs, i.e. the overall longitudinal force demand, , to
achieve the maximum possible vehicle speed.
The reference trajectory is obtained via Equations 22, 23 and 24. The reference orientation
of the vehicle, _, is taken after a speed-dependent "visual" distance, , defined as


,
ln,

,
(17)
V. De Pascale, B. Lenzo, F. Farroni, F. Timpone, and X. Zhang

2 (25)
where  depends on the driver's behaviour (herein assumed as 0.3 s) and V is the vehicle
speed, i.e. . Denoting the current position with (x, y), the position error is
cossin (26)
and the orientation error is 
_
d
2(27)
where the constant
is needed to guarantee the use of consistent reference frames. Finally,
(28)
where and are calculated according to [13].
The maximum, i.e. target, vehicle speed, , depends on the maximum allowable lateral
acceleration,,:  
, (29)
The target longitudinal acceleration, ,, can be worked out as a function of the maxi-
mum allowable longitudinal acceleration, ,:
,,1 ||
, (30)
The overall longitudinal force demand, , is composed of a feedforward contribution,
,
, to improve the driver promptness (the sign in front of the aerodynamic
drag is positive in acceleration and negative during braking), and a feedback contribution
which is a Proportional Integral controller based on the error . Due to the specific
electric motors used in this project, the individual motor torques are saturated to 21 Nm.
5 PRELIMINARY RESULTS
Based on the vehicle model described in Section 2 integrated with the TVC algorithm de-
scribed in Section 3, and on the driver model presented in Section 4, simulations were per-
formed in Matlab-Simulink to assess the performance of the proposed control strategy. The
circumference radius to be followed by the centre of mass of the car was set to 8.3 m, as it
takes into account the size of the vehicle.
Figure 2 shows the reference trajectory and the actual trajectory during the second lap. The
reference trajectory is perfectly followed, demonstrating the effectiveness of the driver model.
Figure 3 shows the curvilinear abscissa and the yaw rate (negative as the vehicle is negotiat-
ing a right turn, according to the adopted sign conventions) as a function of time for the base-
line vehicle and the TVC vehicle. With the baseline vehicle, the time taken to complete the
trajectory is 4.26 s. By activating the TVC, the laptime decreases to 3.84 s. So, there is a lap-
time improvement of 9% by using TVC with respect to the baseline vehicle.
V. De Pascale, B. Lenzo, F. Farroni, F. Timpone, and X. Zhang
Figure 2: Actual and reference trajectory, which coincide thanks to the driver model.
Figure 3: Comparison between baseline vehicle and TVC vehicle: (top) curvilinear abscissa as a function of
time; (bottom) yaw rate as a function of time.
V. De Pascale, B. Lenzo, F. Farroni, F. Timpone, and X. Zhang
6 CONCLUSIONS
In this paper, a Torque Vectoring Control strategy was presented for a Formula SAE elec-
tric vehicle. Matlab-Simulink was used to implement a double track vehicle model featuring
Pacejka tyres, and a driver model providing the steering angle and the acceleration/braking
input. The implemented Torque Vectoring Control strategy allowed a time saving of around
9% during a skidpad test. Further developments will include the improvement of the simula-
tion model adopted (e.g. by including tyre combined interaction), the assessment of the bene-
fits of the proposed technique along a simulated lap, and the experimental validation on the T-
ONE vehicle.
REFERENCES
[1] https://www.fsaeonline.com/, last accessed 18 May 2019.
[2] https://www.sae.org/attend/student-events/formula-sae-electric/about, last accessed 18
May 2019.
[3] E. Esmailzadeh, A. Goodarzi, and G. R. Vossoughi, Optimal yaw moment control law
for improved vehicle handling, Mechatronics, 13(7), pp.659-675, 2003.
[4] A. Tota, B. Lenzo, Q. Lu, A. Sorniotti, P. Gruber, S. Fallah, M. Velardocchia, E. Gal-
vagno, and J. De Smet, On the experimental analysis of integral sliding modes for yaw
rate and sideslip control of an electric vehicle with multiple motors, International Jour-
nal of Automotive Technology, 19(5), 811-823, 2018.
[5] B. Lenzo, A. Sorniotti, G. De Filippis, P. Gruber, and K. Sannen, Understeer character-
istics for energy-efficient fully electric vehicles with multiple motors, EVS29 Proceed-
ings, Montreal, Quebec, 2016.
[6] B. Lenzo, F. Bucchi, A. Sorniotti, and F. Frendo, On the handling performance of a ve-
hicle with different front-to-rear wheel torque distributions, Vehicle System Dynamics,
57(11), 2019.
[7] X. Zhang, and D. Göhlich, Integrated traction control strategy for distributed drive
electric vehicles with improvement of economy and longitudinal driving stability, Ener-
gies, 10(1), p.126, 2017.
[8] Pacejka, H.B., Tyre and vehicle dynamics, Butterworth-Heinemann, 2006.
[9] Guiggiani, M., The science of vehicle dynamics, Springer, 2018.
[10] L. De Novellis, A. Sorniotti, and P. Gruber, Driving modes for designing the cornering
response of fully electric vehicles with multiple motors, Mechanical System and Signal
Processing, 64, 1-15, 2015.
[11] G. De Filippis, B. Lenzo, A. Sorniotti, K. Sannen, J. De Smet, and P. Gruber, On the
energy efficiency of electric vehicles with multiple motors., 2016 IEEE Vehicle Power
and Propulsion Conference (VPPC), 1-6, 2016.
[12] Formula Sae rules, https://www.fsaeonline.com/content/2017-
18%20FSAE%20Rules%209.2.16a.pdf, last accessed 21 February 2019.
[13] F. Braghin, F. Cheli, S. Melzi, and E. Sabbioni, Race driver model, Computers and
Structures, 86, 1503-1516, 2008.
... The ability to distribute desired amounts of torque at different corners/drivetrains is known as Torque vectoring (TV). TV has been widely explored in the literature, mostly to improve vehicle safety and handling [4,5] as well as performance [6,7]. TV can also be exploited to enhance energy efficiency [8][9][10]. ...
Chapter
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Electric vehicles with multiple motors allow torque-vectoring, which generates a yaw moment by assigning different motor torques at the left and right wheels. This permits designing the steady-state cornering response according to several vehicle handling quality targets. For example, as widely discussed in the literature, to make the vehicle more sports-oriented, it is possible to reduce the understeer gradient and increase the maximum lateral acceleration with respect to the same vehicle without torque-vectoring. This paper focuses on the novel experimentally-based design of a reference vehicle understeer characteristic providing energy efficiency enhancement over the whole range of achievable lateral accelerations. Experiments show that an appropriate tuning of the reference understeer characteristic, i.e., the reference yaw rate of the torque-vectoring controller, can bring energy savings of up to ~11% for a case study fourwheel-drive electric vehicle demonstrator. Moreover, during constant speed cornering, it is more efficient to significantly reduce the level of vehicle understeer, with respect to the same vehicle with even torque distribution on the left and right wheels.
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Fully electric vehicles with multiple drivetrains allow a significant variation of the steady-state and transient cornering responses through the individual control of the electric motor drives. As a consequence, alternative driving modes can be created that provide the driver the option to select the preferred dynamic vehicle behavior. This article presents a torque-vectoring control structure based on the combination of feedforward and feedback contributions for the continuous control of vehicle yaw rate. The controller is specifically developed to be easily implementable on real-world vehicles. A novel model-based procedure for the definition of the control objectives is described in detail, together with the automated tuning process of the algorithm. The implemented control functions are demonstrated with experimental vehicle tests. The results show the possibilities of torque-vectoring control in designing the vehicle understeer characteristic.
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The handling characteristic is a classical topic of vehicle dynamics. Usually, vehicle handling is studied by analyzing the understeer coefficient in quasi-steady-state maneuvers. In this paper, experimental tests are performed on an electric vehicle with four independent motors, which is able to reproduce front-wheel-drive, rear-wheel-drive and all-wheel-drive (FWD, RWD and AWD, respectively) architectures. The handling characteristics of each architecture are inferred through classical and new concepts. The study presents a procedure to compute the longitudinal and lateral tire forces, which is based on a first estimate and a subsequent correction of the tire forces that guarantee the equilibrium. A yaw moment analysis is performed to identify the contributions of the longitudinal and lateral forces. The results show a good agreement between the classical and new formulations of the understeer coefficient, and allow to infer a relationship between the understeer coefficient and the yaw moment analysis. The handling characteristics vary with speed and front-to-rear wheel torque distribution. An apparently surprising result arises at low speed: the RWD architecture is the most understeering configuration. This is discussed by analyzing the yaw moment caused by the longitudinal forces of the front tires, which is significant for high values of lateral acceleration and steering angle.
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With the advent of electric vehicles with multiple motors, the steady-state and transient cornering responses can be designed and implemented through the continuous torque control of the individual wheels, i.e., torque-vectoring or direct yaw moment control. The literature includes several papers on sliding mode control theory for torque-vectoring, but the experimental investigation is so far limited. More importantly, to the knowledge of the authors, the experimental comparison of direct yaw moment control based on sliding modes and typical controllers used for stability control in production vehicles is missing. This paper aims to reduce this gap by presenting and analyzing an integral sliding mode controller for concurrent yaw rate and sideslip control. A new driving mode, the Enhanced Sport mode, is proposed, inducing sustained high values of sideslip angle, which can be limited to a specified threshold. The system is experimentally assessed on a four-wheel-drive electric vehicle. The performance of the integral sliding mode controller is compared with that of a linear quadratic regulator during step steer tests. The results show that the integral sliding mode controller significantly enhances the tracking performance and yaw damping compared to the more conventional linear quadratic regulator based on an augmented singletrack vehicle model formulation. © 2018, The Korean Society of Automotive Engineers and Springer-Verlag GmbH Germany, part of Springer Nature.
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A new optimal control law for direct yaw moment control, to improve the vehicle handling, is developed. Although, this can be considered as part of a multi-layer system, for the traction control of a motorized wheels electric vehicle, but the results of this study are quite general and can be applied to other types of vehicles. The dynamic model of the vehicle system is initially developed and, using the well-known optimal control theory, an optimal controller is designed. Two different versions of control laws are considered here and the performance of each version of the control law is compared with the other one. The numerical simulation of the vehicle handling with and without the use of the optimal yaw moment controller, and assuming a comprehensive non-linear vehicle dynamic model, has been carried out. Simulation results obtained indicate that considerable improvements in the vehicle handling can be achieved whenever the vehicle is governed by the optimal yaw moment control.