A New Control Architecture for Robust Controllers in Rear

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 7, SEPTEMBER 2012
1
A New Control Architecture for Robust Controllers
in Rear Electric Traction Passenger HEVs
Rafael Coronel B. Sampaio, Member, IEEE, André C. Hernandes, Member, IEEE,
Vinicius V. M. Fernandes, Member, IEEE Marcelo Becker, Member, IEEE, and Adriano A. G.
Siqueira, Member, IEEE,
Abstract—It is well known that control systems are the core
of Electronic Differential Systems (EDS) in EVs/HEVs. However,
conventional closed-loop control architectures do not completely
match the needed ability to reject noises/disturbances, specially
regarding the input acceleration signal incoming from the
driver’s commands, which turns the EDS (in this case) ineffective.
Due to this, in this paper a novel EDS control architecture is
proposed in order to offer a new approach for the traction
system that can be used with a great variety of controllers (e.g.
classic, artificial intelligence-based, modern/robust theory). In
addition to this, a modified PID controller, an AI-based (artificial
intelligence) neuro-fuzzy controller, and a robust optimal H∞
controller were designed and evaluated in order to observe
and evaluate the versatility of the novel architecture. Kinematic
and dynamic models of the vehicle are briefly introduced.
Then, simulated and experimental results were presented and
discussed. HELVIS-Sim simulation environment was employed
to the preliminary analysis of the proposed EDS architecture.
Later, the EDS itself was embedded in a dSpaceTM 1103 high
performance interface board so that the real-time control of the
rear wheels of HELVIS platform was successfully achieved.
Index Terms—Electronic Differential System, HEV, Control
System, Control Architecture, HELVIS mini-HEV
I. I NTRODUCTION
B
ASED on the global warming issue and the potential
depletion of the oil resources worldwide and following
our tradition of carrying out researches focused on mobile
robotics for transportation systems [1] we recently started studies on the substitution of conventional oil-based vehicles by
HEVs (Hybrid Electrical Vehicles) [2] [3]. Important institutes
[4] [5][6] and industries all over the world are investigating
new technologies in this field and searching for skilled manpower resources, which is still very scarce. Grounded on that
idea, we are giving the opportunity for undergraduate and
graduated students to be in touch with HEVs technologies,
becoming one of the first universities in South America to
have a real line of research currently running in this area.
The “Electric Wheels Project”, is supported by the Brazilian
Electricity Regulatory Agency (ANNEL) and the Innovation
Center of the State of São Paulo Energy Distributor (CPFL).
One of the aims of the group is to bring new technologies in
Copyright (c) 2012 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to [email protected].
Authors are with the University of São Paulo, Brazil, Engineering School
of São Carlos (USP-EESC), Department of Mechanical Engineering (SEM),
Mechatronics Group, Laboratory of Mobile Robotics (LabRoM), e-mail:
([email protected], [email protected], [email protected],
[email protected], [email protected]).
the development of electromechanical wheels to replace the
conventional ones in preexisting passenger vehicles, turning
them into series HEVs. Concrete results of such research
were recently published [7], which has strengthened the group,
encouraging the launching of the project, the design of a
mini-HEV named HELVIS (Hybrid Electric Vehicle In Low
Scale) [8] and the implementation of a parametric vehicular
simulator named HELVIS-Sim [9], all of them have significantly expedited researches on HEVs, specially regarding the
design and evaluation of 2WD/RWD (Two-Wheel Drive/RearWheel Drive) EDS (Electronic Differential System) [10] [11]
for passenger EVs/HEVs [12]. Furthermore, such tools have
proved to be valuable opportunities to encourage researchers
and enthusiasts to develop a new generation of cleaner vehicles
for the new century [13].
Many works in the literature bring relevant results for the
EDS problem. When it comes to numerical analysis [14] and
[15] works must be highlighted. Other works proposed either
classic and non-robust controllers approaches [16] or very
simple plant models [17] [18]. A magnetic flow algorithm was
proposed in [19] while observers were proposed in [20]. The
use of artificial intelligence-base controllers were described
in [21] [22]. Besides of accurate models of the vehicle and
the power train, the core of a well designed EDS lies in
1) the control system ability to quickly and properly apply
the corrective actions and also in 2) its robustness against
noises/disturbances/uncertainties. Maneuverability and stability are considered as direct functions of these two variables.
Thus, the vehicle can ultimately follow Ackerman Geometry
and minimize the slip phenomena [23] [7]. This work focuses
on the design and in both simulated and experimental evaluation of an EDS for rear electric traction HEV that can be
used with a great variety of control systems. In this case, the
optimal H∞ robust controller for HELVIS EDS has shown
to be highly effective [12]. However, the robust control theory
demands the control architecture (and so the EDS architecture)
to be rearranged. Thus, this work also proposes a new control
architecture to match the EDS problem for the optimal H∞
controller [24] [25] [26] [27], which consequently allows
the use of other control systems of different proposes. It is
expected that such novel architecture leads the improvement of
the EDS for a wide class of vehicles, including passenger cars.
Thus, in order to show how in-depth and versatile the novel
EDS module is in terms of performance and operability, two
more distinct control approaches were also tested: one classical
modified PID controller is outlined [28] [29] and one neuro-
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 7, SEPTEMBER 2012
fuzzy control system [30] [31] [32] [33].
At the end, simulated and experimental results, both performed in HELVIS-Sim simulation environment and HELVIS
mini-HEV are respectively presented and analyzed.
2
V̇cgx
II. EDS P ROBLEM S TATEMENT
A. Vehicle Dynamic & Kinematic Modeling
The EDS formulation is based on a 2D rigid body dynamic
model [7]. Figure 1 illustrates the body diagram of a front
steering rear traction hybrid electric passenger vehicle and
Table I shows all parameters that are involved in such model.
l2 cosδ1
l2 cosδ2
+
+ l1
2
2
!
P4 (t)
1
P3 (t)
+
+
bΩ
m Vcgx + bΩcg
Vcgx − 2cg
2
!
CψF sinδ1
Vcgy + l1 Ωcg
−
δ1 −
bΩ
m
Vcgx + 2cg
!
CψF sinδ2
Vcgy + l1 Ωcg
−
δ2 −
bΩ
m
Vcgx − cg
Vcgy − l2 Ωcg
2 − b2 Ω
Vcgx
4 cg
!
µg
= Vcgy Ωcg −
L
(1)
2
V̇cgy
2Vcgx CψR
= −Vcgy Ωcg −
m
µgl2
(sinδ1 + sinδ2 )
2L
!
CψF cosδ1
Vcgy + l1 Ωcg
+
δ1 −
m
Vcgx + 2b Ωcg
!
Vcgy + l1 Ωcg
CψF cosδ2
δ2 −
+
m
Vcgx − 2b Ωcg
−
Ω̇cg =
Fig. 1. Body diagram of a front steering rear traction hybrid eletric passenger
vehicle.
TABLE I
TABLE OF THE VARIABLES INVOLVED IN THE MODEL
Variable
l1
l2
L
µ
g
m
Iz
CψF
CψT
b
r
δ1,2
Rcg
Ro
Ri
Vcg
V3
V4
ω3
ω4
Ωcg
U1..4
S1..4
P1..4
Description
Distance between center of gravity/mass and front axle (m)
Distance between center of gravity/mass and rear axle (m)
Distance between axles (m)
Coefficient of friction (-)
Gravitational acceleration (m/s2 )
Vehicle mass (kg)
Moment of inertia over z axis (kg · m2 )
Slip coefficient of the front wheels (-)
Slip coefficient of the rear wheels (-)
Axle’s length (distance between wheels) (m)
Tire radius (m)
Steering angles (rad)
Instantaneous maneuver radius (m)
Distance between the curve center and the outside wheel (m)
Distance between the curve center and the inside wheel (m)
Linear velocity of the vehicle at its CG (m/s)
Linear tangent velocity of the left wheel (m/s)
Linear tangent velocity of the right wheel (m/s)
Angular velocity of the left wheel (rad/s)
Angular velocity of the right wheel (rad/s)
Vehicle angular velocity around the turning center (rad/s)
Wheel longitudinal forces (N )
Wheel lateral forces (N )
Power applied to the wheels (W )
From the free body diagram of the vehicle it results the
following dynamic equations that represent the kinematic
behavior of the car:
(2)
µmgbl2
µmgl1 l2
(cosδ2 − cosδ1 ) −
(sinδ1 + sinδ2 )
4LIz
2LIz
!
b
P3 (t)
P4 (t)
−
+
bΩ
2Iz Vcgx + bΩcg
Vcgx − 2cg
2
!
CψF
Vcgy + l1 Ωcg
b
+
δ2 −
l1 cosδ2 + sinδ2
bΩ
Iz
2
Vcgx − 2cg
!
CψF
b
Vcgy + l1 Ωcg
+
l
cosδ
−
sinδ
δ1 −
1
1
1
bΩ
Iz
2
Vcgx + 2cg
!
2Vcgx l2 CψR Vcgy − l2 Ωcg
+
2 − b2 Ω
Iz
Vcgx
4 cg
(3)
The above equations are solved from the amount of power
individually applied to both rear actuators and therefore, in
practice, show how the control action will change the dynamic
behavior of the vehicle. Considering exclusively the EDS
problem, the desired angular velocities for both rear wheels
must to be calculated and it can be obtained from two of
the kinematic parameters which are the velocity of the car Vx
and the maneuver radius Rcg respectively. The first one can be
extracted from Eq. 1 and the second can be calculated from the
steering angles which are related to the Ackerman Geometry,
whose formalism is described in [23]. Finally, the calculated
angular velocities of both rear wheels can be determined by
using Eqs. 4 and 5 [7].
Vcg q 2
b
2
Rcg − l2 −
(4)
ω3 =
Rcg r
2
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 7, SEPTEMBER 2012
b
Vcg q 2
2
Rcg − l2 +
ω4 =
Rcg r
2
(5)
One important aspect is that, regardless of the dynamic
model ability to predict the vehicle’s accelerations from the
power that is applied to each wheel (which is very useful to
simulation evaluation), it represents only an indirect measurement. In practical terms, the vehicle speed can be easily read
from the CAN bus network embedded in the real scale car. The
maneuver radius can be estimated by placing an IMU (Inertial
Measurement Unit) close to the CG (Center of Gravity) of the
vehicle. Real time IMU reading ensures the accuracy of the
system even at small slip situations. This procedure is feasible
and has been commonly accomplished in many experiments
in “SENA Project” in Mobile Robotics Laboratory [1]. Such
sensor fusion has proved to be useful and has been widely used
in many mechatronics applications, including transportation
systems.
III. C ONTROL S YSTEMS D ESIGN & T HE N EW C ONTROL
A RCHITECTURE
The most important element of the EDS design is the control
system that act over the adjustment of the electric wheels
angular speeds. It is essential that the control system quickly
provides the actuators with the correct amount of current in
order to produce the least possible error and the least overshoot
so that the wheel can roll without sliding. A great variety of
control approaches based on different techniques match the
EDS problem [14] [15] [16] [17] [18] [19] [20] [21] [22].
Thus, in this work three different control approaches has been
proposed [7], as follows:
•
•
•
Classic approach, through the use of the modified PID
equations;
Artificial intelligence approach, through the use of the
neuro-fuzzy controller;
Robust approach, through the use of the optimal H∞
controller;
A. Modified Classic PID Controller
The implementation of a modified PID controller considers
the rearrangement of the recurrence equations for a discrete
PID controller, as described in [28], in order to improve
the quality of the process response. One weighting variable
is added to the proportional gain, as well as filters are
implemented into both derivative and integrative terms [29].
It also considers the positional form with backward difference
approximation to the integrative term (I) and Tustin approximation to derivative term (D), whose control laws for proportional, integrative and derivative terms can be respectively
represented by:
P (k) = Kp [βr(k) − y(k)];
I(k) = I(k − 1) +
Kp T
e(k − 1)
Ti
(6)
(7)
D(k) =
3
2Kp Td N
2Td − T N
D(k − 1) +
(y(k) − y(k − 1))
2Td + T N
2Td + T N
(8)
Variable Kp is related to the proportional action, Ti refers
to the integral action and Td is related to the derivative action.
Variable r(k) is the reference (desired) value, y(k) is the
process output signal and e(k) refers to the error. Variable
T is the sample time, N is a scalar such that the realizability
of the controller is ensured (in practice, values in the interval
of 3 ≤ N ≤ 20 are commonly used). Proportional action
fine tunning is achieved by inserting a parameter β over the
reference signal [28] so that considerable improvement in both
steady state error and transitory response are observed.
The reset-windup effect occurs over the integrative action,
and could be suppressed through the implementation of an
anti-reset-windup filter [28]. Regarding the derivative action,
it can also present an unexpected behavior regarding to the
system’s stability in determined circumstances, e.g., high frequencies. At this point, derivative contribution adds a rising
gain to the plant, which is commonly referenced as quick
derivate effect. In this case, an anti-quick derivate filter is
implemented in order to decrease the closed loop gain. It turns
out that, from the derivative part in the PID controller (Eq. 8),
the presence of one pole in the infinity is observed, which
implies in the indefinite growth of the derivative gain as the
frequency raises. That turns the system significantly unstable
due to the saturation of the control output. The anti-quick
derivate filter aims to add a pole to the derivative equation, in
order to improve the controllability of the plant.
B. A.I.-Based Neuro-Fuzzy Controller
The design of a neuro-fuzzy controller is based on two
distinct and very well defined stages [30] and is inspired in
combining the benefits of the knowledge extraction provided
by the fuzzy logic plus the low computational cost offered by
the ANN (Artificial Neural Networks), which yields a very
efficient class of controllers.
The first stage regards the design of a fuzzy controller,
involving fuzzification, inference and defuzzification, which
originates a fuzzy control surface, consisting of two input and
one output variables. The second stage consists in the process
of training a neural network that can be able to learn how
the fuzzy controller behaviors. Figure 2 illustrates all distinct
parts that composes the design of the neuro-fuzzy controller.
Phase (A) comprehends the establishment of the rule base,
fuzzification, inference and defuzzification, so that the fuzzy
control surface is generated (B). The vectors containing all
data that define the fuzzy control surface are then sent to the
ANN (C). It is expected that the neural network can reproduce
the very same fuzzy control surface (D).
1) Fuzzification, Inference and Defuzification: Fuzzy logic
executes a rule-based controller, instead of a model-based one.
This approach is useful because even if a reliable model is
available, non-linearities often raise in maneuvers [7]. The
controller inputs are the angular speed error (E) and its
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 7, SEPTEMBER 2012
4
The MAX-MIN composition and center-of-gravity method
were used in the defuzzification process [33]. Thus, the final
result of the design of a fuzzy controller is illustrated in Fig.
4.
Fig. 2. Illustration of the body diagram of the design of the neuro-fuzzy
controller.
derivative (dE). The control action defines the output (dU ).
Fuzzification involves the representation and the decision
making based on linguistic notations, as for inputs (E, dE) as
well as for outputs (dU ). In our work, it is determined through
the following variables:
•
•
•
•
•
•
•
NL: Negative Large
NM: Negative Medium
NS: Negative Small
Z: Zero
PS: Positive Small
PM: Positive Medium
PL: Positive Large
Gaussian functions were used to represent the membership
functions for E, dE and dU because when compared with
other shapes (trapezoidal and triangular), they presented the
best response. Mandani method was used to the inference
process and a set of 49 rules were established, as one may
observe on Fig. 3. The decision making procedure was based
in those rules. Each combination between each value of E and
dE corresponds to a particular control level dU .
Fig. 3.
Rules matrix established to the electric wheels control.
Fig. 4.
Fuzzy control surface as the result of the fuzzy design.
2) Feedforward Artificial Neural Network Training Process:
Artificial Neural Networks present a satisfactory performance
in terms of low computing cost. In particular, feedforward
ANN are indicated in classification problems, where each input
vector is associated to an output vector [30]. This affirmation
perfectly meets the problem of controlling the electric wheels
since there is a corresponding control output dU to each couple
error-derivative E-dE. Thereby a four-layered feedforward
ANN was designed with (Nc /2) + 3 hidden layers where Nc
is the number of inputs. Such configuration presents superior
performance compared to a three-layered feedforward ANN
regarding the number of parameters that are necessary for the
training process. Regarding the NN inputs and outputs, a pair
(k)
(k)
of inputs x = (x1 , x2 ) was considered, representing the
(k)
error E and its derivative dE. Also, the output y = y1 ,
representing the increase/decrease in the control action [32],
was also considered. A MATLABTM toolbox was used employing the Levenberg-Marquardt algorithm. it is important
to highlight that the training performance was in compliance
with MSE (Mean Square Error) criteria.
3) The Neuro-Fuzzy Controller: When the ANN training
process is well succeeded, both control surfaces must be
very similar (remember that the fuzzy control surface was
reconstructed by the ANN). Figure 5-(a) shows the fuzzy
control surface itself, obtained from the implementation of the
fuzzy controller, whereas Fig. 5-(b) shows the surface provided
by the ANN after the training process. It is clear that the
four-layered feedforward neural network has reconstructed the
original surface. This indicates that the ANN could successfully learn how to eventually provide the EDS with the proper
control actions, as if it is in charge of a essentially fuzzy-based
controller.
The accuracy of the ANN can be quantified by comparing
the then reconstructed control surface and the original one
obtained by the fuzzy system. The MSE (Mean Square Error)
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 7, SEPTEMBER 2012
(a)
(b)
Fig. 5. Obtained fuzzy control surface (a) the reproduced surface after the
training process of the feedforward ANN.
criteria was used to compute an mean error value of e ≈
5 · 10−5 .
C. Robust Optimal H∞ Controller
The synthesis of the optimal H∞ controller was based on
[24], [25], [26] and [27], considering the fact that the plant
is stabilizable and detectable. Thus, the resulting augmented
plant Gap , the respective block diagram is represented in Fig.
6.
5
disturbances/noises/uncertainties, it is necessary that the gains
of S are low at low frequencies so that noises/disturbances
rejection can be guaranteed, that is, |We S| ≤ 1. On the other
hand, R gains must be low at high frequencies to achieve the
same noise rejection level, that is, |Wu R| ≤ 1. The previous
two robustness criteria are directly related to: 1) stability
against model parametric variations, 2) stationary error → 0,
3) robustness even with open-loop uncertainties and variations,
4) robustness against noises which are inserted into the plant.
Actually, the sensitivity function must ideally satisfy the peak
sensitivity Ms and also the bandwidth ωb , so that the following
relation must be respected:
s
(10)
|S(s)| ≤ s
Ms + ωb The closed-loop value for the bandwidth is such that ωb ≈
ωn . Also, for a good control design it is desirable that Ms does
not reach high values. Values for both bandwidth and peak
sensitivity are chosen empirically, observing the frequency
responses and the natural frequency of the plant. Thus, the
best values are Ms = 160 and ωb = 50. Thus, both weighting
functions obtained through the γ-iteration algorithm and the
robustness criteria are given by Eqs. (11) and (12) as follows:
We (s) =
0.00625s + 50
s + 0.05
(11)
s+1
(12)
0.1s + 9 · 108
From Eqs. (11) and (12) and all previous described
procedures, the following controller K is achieved:
Wu (s) =
K(s) =
Fig. 6.
Augmented plant of the EDS module, representing the transfer
function Tzw .
The γ-iteration algorithm was employed, aided by a
MatlabTM toolbox, through which the γ value is reduced until
the optimal value of γopt is achieved so that, at the end of the
procedure, both error and control action weighting functions
(We and Wu , respectively) and the controller K(s) itself are
obtained. Thus, the norm of the closed loop transfer function
Tzw between w and z1,2 must satisfy the following condition:
We S = We S < γ
Tzw = (9)
Wu KS Wu R ∞
∞
Where We and Wu represents the weighting functions of
the controller K . Values from γmin = 0.05 to γmax =
150 where used for the iterative process. The value of γ
achieved is 0.1366, which is in compliance to the optimal
H∞ aims to minimize the norm of the transfer function
Tzw . Sensitivity function was given by S while R is the
transfer function between the control action and the reference
input. In order to guarantee stability and robustness relative to
5.103s2 + 4.592 · 1010 s + 1.714 · 1011
s3 + 7776s2 + 3.061 · 107 + 1.508 · 106
(13)
D. The New Control Architecture
Generally, the driver’s throttle input is intuitively added to
the control signal, in an attempt to simply superimpose the
control actions computed by the EDS. Such control architecture and strategy were proposed in [18] and is shown in Fig. 7.
In the case of HELVIS EDS, the H∞ controller acts as a filter,
degrading the driver’s acceleration input, turning any attempt
to impose new acceleration commands into a noise [12].
Figure 8 shows the exploded view of the proposed architecture, which matches the EDS application with robust controllers. The kinematics block
calculates
T the desired left and
right rear angular speeds ωld ωrd
based on reading the
T
states of the state vector V˙x V˙y Ω˙x Vx Vy Ωx x y z
.
In practice, the driver’s throttle command β is considered as
the representation of the desired speed of the vehicle (which,
in turn, represents the angular speeds of the wheels). Similar to
the calculus of the desired angular speeds based on the speed
of the car Vx and on the maneuver radius (through reading data
from IMU), the kinematics block calculates βr and βl using
Eqs. 4 and 5. These results are used in order to provide the
controllers with βr and βl as if they were the reference values
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 7, SEPTEMBER 2012
6
Driver’s Inputs
-
Controller
+
+
+
Throttle
Input
-
Acceleration
Steering
HELVIS
Kinematics
Motor
To
Dynamics
Blockset
EDS
HELVIS
Dynamics
-
-
Fig. 7. Unsuitable feedback block diagram due to the high ability of noise
rejection by the H∞ controller.
Steering
Angles
T
), since Vx in both equations is represented by
( ωld ωrd
β. The states of the speeds are provided by the
dynamics block
c c c c T
i
i
e
e
delivered to the
from both voltage and current
l r r l
motors, which allows the estimation of the power involved
T
[Pl Pr ] for each wheel. As for the IMU data, it provides
the EDS with real measurements regardless of a possible tire
slipping, which turns the overall system more accurate and
robust.
The control loop is then rearranged so that the throttle input
is the signal with highest priority. However, the subtraction of
the desired speeds, provided by the kinematics and based on
the dynamics of the vehicle, ensures that the driver’s throttle
command is assured. Thus, in practice, the controller senses
the resulting error:
d
c
e = 2βl,r − ωl,r
− ωl,r
Steering
Command
Control
System
Control
System
Driver
Driver
Left
Motor
Right
Motor
Encoder
Encoder
Fig. 8.
(14)
5
4.5
Novel EDS control architecture proposed in this work.
Throttle Input
HELVIS Control Architecture
Conventional Architecture
Throttle Input Computed
T
Where ωlc ωrc
is the vector with the measured values
for both rear wheels angular speeds.
The efficiency of the the new proposed control architecture
over the conventional one could be attested in a bench test
experiment where the performance of both approaches could
be evaluated. As this paper is related and focused on robust
controllers, both the new architecture and the conventional
one were submitted to such experiment with the optimal
H∞ controller in charge of the EDS, while the driver input
command was subject to observation. Figure 9 shows that,
in fact, the throttle input is rejected as a noise, when the
architecture of Fig. 7 is employed. Indeed, any attempt to
request new acceleration inputs (continuous curve) will be
degraded (dotted curve), since it is considered an external
disturbance. Regardless of the magnitude of the throttle input
command, the H∞ controller always acts in order to minimize
such disturbance, converging the throttle signal to a minimum
value.
That is, the architecture proposed in Fig. 7 cannot be
applied to our case ultimately. The figure still shows that
the proposed architecture in this work preserves the throttle
command imposed by the driver, which is input intact to the
kinematics block (dashed curve).
Angular Speed (rad/s)
4
3.5
3
2.5
Throtthe Input Degrading
2
1.5
1
0.5
0
1
2
3
4
5
6
7
8
9
Time (s)
Fig. 9. Behavior of the throttle input signal using the novel proposed HELVIS
control architecture.
IV. S IMULATION AND E XPERIMENTAL T OOLS
All following tests concerning the proposed architecture
for the EDS as well as the three control approaches are
first evaluated in simulation environment and then analyzed
through experimental tests. Thus, a simulation toolbox and a
low scale HEV are next presented.
A. The HELVIS mini-HEV Platform
As both dynamic and kinematic models for the vehicle are
parametrized and the calculus of the desired angular speeds
are essentially linear, which allows the scalability of the EDS
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 7, SEPTEMBER 2012
module, all experimental tests were extended to a mini-HEV
platform named HELVIS (Hybrid Electric Vehicle In Low
Scale), which has been successfully constructed and has been
presented in VPPC 2011 [8].
The HELVIS platform, Fig. 10, is a low scale rear electric
traction series HEV endowed with a steering mechanism (that
is in compliance with Ackerman Geometry). The vehicles’s
EDS is part of a 2WD/RWD (Two-Wheel Drive/Rear-Wheel
Drive) electric drive train [11], composed by two DC motors
each one with planetary gears which can deliver 10W of power
to each rear wheels. The general architecture of the HELVIS
drive train is shown in Fig. 11. It can be classified as a
series hybrid drive train, since an electrical coupler handles
the power incoming from two distinct sources, in this case,
the battery and the generator [10]. In this configuration, the
ECU (Electronic Control Unit) deals with many functional
tasks, e.g., incoming data from sensors, battery SOC (State of
Charge), IC engine RPM and, obviously, the EDS powering
and data processing. Some of the most important constructive
parameters of the HELVIS platform are listed in Table II.
7
DC Motors
IC-Engine
Magnetic
Encoder
Generator
Steering
Mechanism
Fig. 11. General architecture and physical parameters of the series-hybrid
HELVIS mini-platform.
Fig. 10.
The HELVIS mini-HEV 2WD/RWD series platform.
TABLE II
HELVIS CONSTRUCTIVE PARAMETERS .
Variable
mass
wheelbase (distance between axles)
track (distance between wheels)
center of mass (x)
center of mass (y)
radius of the wheels
moment of inertia
Value
4
335
214
107
55
60
0.087475
Unit
Kg
mm
mm
mm
mm
mm
Kg · m2
useful SimulinkTM -based simulator named HELVIS-Sim, is
briefly presented [9]. HELVIS-Sim is a parametric simulator
that emulates, among many other functions, the HELVIS
platform EDS module. Besides, as the simulation architecture
is basically constructed over a set of blocks, SimulinkTM
perfectly fits to this project, since it eases the insertion of brand
new blocks and also the integration to our dSpaceTM real time
interface board to run the experimental evaluation of HELVISSim [8]. In this paper, the focus is on the control of the EDS
module. HELVIS-Sim considers the driver’s input commands,
vehicle both dynamics and kinematics, sensors, actuators,
control systems, signal conditioning, and other functions. It
is important to emphasize that this simulator allows users to
experience different classes of controllers in the torque split
up problem.
The HELVIS-Sim EDS architecture is displayed in Fig. 12.
In this figure, one may observe that the EDS related modules
are displayed, such as torque and wheel speed calculation,
control system, motor dynamics, kinematics & dynamics,
drivers commands, and steering mechanism.
V. E VALUATION OF R ESULTS FOR THE EDS C ONTROL &
N EW A RCHITECTURE
B. The HELVIS-Sim Simulation Environment
In the case of EVs/HEVs, a simulation tool can be even
more useful if one considers the fact that EVs/HEVs component parts are not easy to be obtained since those types of
vehicles are not as trivial as conventional vehicles are. In this
context, a simulation tool can aid engineers and students in the
development and manufacturing of specific pieces for general
and also for a specific function in an EV/HEV. Henceforth, an
Since bench tests have proved the efficiency of the new
control architecture over the conventional one, the EDS has
been set up with the proposed architecture. Then, it was
submitted to both simulated and experimental tests. The EDS
performance could be evaluated while the three previously
designed controller were individually applied.
Two situations were observed, both for simulation and
experimental tests, as follows:
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 7, SEPTEMBER 2012
EDS
8
Lateral & Longitudinal
Forces
Torque &
Wheel Speed
Calculation
Frictional
Forces
HELVIS
Dynamics
Control
Module
Accelerations
Steering Mechanism + Magnectic
Sensor Transfer Function
Throttle
Motors
Dynamics
HELVIS
Kinematics
Steering
Command
Drivers Inputs
Performance
Analysis
Anti-Slip
Control
EDS Controller
Evaluation
Trajectory
Control
Fig. 14. Expanded view of the HELVIS-SIM simulation response for the
proposed EDS module, adjusted by the modified PID controller, to a constant
speed and steering maneuver.
Fig. 12. General architecture and functional blocks of HELVIS-Sim simulation environment.
•
•
Case I: Acceleration of the platform from zero to 2 m/s
with both sides steering and maximum steering angle;
Case II: Gradual attenuation of the acceleration percentage from 2 m/s following sinusoidal pattern with both
sides steering and maximum steering angle;
A. Results Achieved from the HELVIS-Sim
1) Case I: Acceleration of the platform from zero to 2 m/s
with both sides steering and maximum steering angle: Figure
13 shows the results obtained from the control of the EDS by
the modified PID controller, where it is visible that the system
adjusts the rear wheels speeds as the maneuver occurs. One
may also observe a minimum value for the steady state error
and quick response. Figure 14 shows the expanded view of
the response of the rear wheels angular speeds.
Fig. 15. HELVIS-SIM simulation response for the proposed EDS module,
adjusted by the neuro-fuzzy controller, to a constant speed and steering
maneuver.
Fig. 16. Expanded view of the HELVIS-SIM simulation response for the
proposed EDS module, adjusted by the neuro-fuzzy controller, to a constant
speed and steering maneuver.
Fig. 13. HELVIS-SIM simulation response for the proposed EDS module,
adjusted by the modified PID controller, to a constant speed and steering
maneuver.
Figure 15 shows the response of the process of control of
the EDS by the neuro-fuzzy controller. A millisecond-order
response delay occurs as the steering maneuver runs, although
the steady state error is not present. Figure 16 illustrates the
expanded view of the response of the rear wheels angular
speeds.
Figure 17 shows the results of the control of the EDS by
the optimal H∞ controller. Both steady state error and time
delay are not sensed as the vehicle is subject to steering. The
expanded view of the response of the rear wheels angular
speeds can be observed in Fig. 18.
2) Case II: Gradual attenuation of the acceleration percentage from 2 m/s following sinusoidal pattern with both sides
steering and maximum steering angle: Figure 19 shows the
responses of the adjustment of both rear wheels angular speed
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 7, SEPTEMBER 2012
Fig. 17. HELVIS-SIM simulation response for the proposed EDS module,
adjusted by the optimal H∞ controller, to a constant speed and steering
maneuver.
Fig. 18. Expanded view of the HELVIS-SIM simulation response for the
proposed EDS module, adjusted by the optimal H∞ controller, to a constant
speed and steering maneuver.
by the modified PID controller during the steering maneuver.
Both steady state error and response delay are not observable.
The expanded view of the response of the rear wheels angular
speeds can be observed in Figure 20.
Figure 21 shows the results of the control of the EDS by
neuro-fuzzy controller during the steering maneuver and also
the speed variation. A millisecond-order delay is noted. As a
result of it, a very small steady state error is also perceptible.
Figure 22 shows the expanded view of the response of the rear
wheels angular speeds.
Figure 23 shows the results obtained from the optimal H∞
controller. It is seen that the controller provides high accuracy
and quickness in response, which eliminates both steady state
error and response delay. Figure 24 shows the expanded view
of the response of the rear wheels angular speeds by the
optimal H∞ controller.
An important quantitative analysis can be drawn based
on Tab. III data. This table presents the steady error, time
delay and overshoot mean values acquired in HELVIS-Sim
simulations. Such review can reveal important data which can
significantly determine the choice of the controller that best fits
the EDS application. In this case, all three controllers present
satisfactory values for the three parameters under analysis, although the optimal robust H∞ controller performance presents
the best overview at all. Thus, it can also be concluded that
the novel proposed architecture perfectly matches the EDS
problem, turning it possible to embed different controllers.
9
Fig. 19. HELVIS-SIM simulation response for the proposed EDS module,
adjusted by the modified PID controller, to a speed on sinusoidal pattern and
steering maneuver.
Fig. 20. Expanded view of the HELVIS-SIM simulation response for the
proposed EDS module, adjusted by the modified PID controller, to a speed
on sinusoidal pattern and steering maneuver.
Fig. 21. HELVIS-SIM simulation response for the proposed EDS module,
adjusted by the neuro-fuzzy controller, to a speed on sinusoidal pattern and
steering maneuver.
TABLE III
C ONTROL P ERFORMANCE Q UANTITATIVE C OMPARISON TABLE IN
S IMULATION (M EAN VALUES ).
Controller
PID
NF
H∞
Steady State Error (%)
0.8%
0.8%
0.1%
Time Delay (ms)
18
35
6
Overshoot (%)
0.02
0.034
0.003
B. Experimental Results Achieved from the HELVIS Platform
Experimental results followed the very same inputs previously used to the simulated evaluation of the EDS from
HELVIS-Sim environment. Communication between the real
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 7, SEPTEMBER 2012
Fig. 22. Expanded view of the HELVIS-SIM simulation response for the
proposed EDS module, adjusted by the neuro-fuzzy controller, to a speed on
sinusoidal pattern and steering maneuver.
10
speeds. It is possible to observe that as the vehicle speed
increases and the vehicle steers, the controller follows the
desired values for the calculated/desired angular speeds. Moreover, the EDS alternates the module of the reference signal,
as the vehicle changes the steering direction, which is also
followed by the controller.
Figure 26 shows the expanded view of the response of
both measured rear wheels angular speeds. It is possible to
observe that, indeed, the modified PID controller appropriately
responds to the demands of controlling the actuators. It is
also observed that both time delay and steady state error are
minimum and acceptable.
Figure 27 reflects the behavior of the EDS under the adjust
of the neuro-fuzzy controller. It is notable that the control
of the actuator is satisfactorily accomplished. Low levels of
steady state error and overshoot are observed. The expanded
view in Figure 28 shows that the control actions drive both
measured angular speeds to correctly follow the reference as
the vehicle’s speed changes and the steering maneuver occurs.
The resulting curves for both rear wheels angular speeds
controlled by the optimal H∞ controller can be observed in
Figure 29. In this case the noise suppression can be clearly
noted. Especially in Figure 30, one may note that, in fact, the
optimal H∞ controller is able to reject noises and disturbances
that can eventually or purposely be inserted into the control
plant. Neither steady state error nor time delay response are
observed. Moreover, high control effort is observed, especially
at low frequencies.
Fig. 23. HELVIS-SIM simulation response for the proposed EDS module,
adjusted by the optimal H∞ controller, to a speed on sinusoidal pattern and
steering maneuver.
Fig. 25. Experimental response for the HELVIS platform EDS module,
adjusted by the modified PID controller, to a constant speed and steering
maneuver.
Fig. 24. Expanded view of the HELVIS-SIM simulation response for the
proposed EDS module, adjusted by the optimal H∞ controller, to a speed on
sinusoidal pattern and steering maneuver.
EDS and the control module was achieved by using a high performance dSpaceTM 1103 optical fiber interface board. Control
of both motors was individually accomplished through two
different PWM channels whose duty cycle is of approximately
12kHz which is reasonable to a real time application such as
the EDS control.
Once again, the following cases were evaluated:
1) Case I: Figure 25 shows the EDS response whereas
the modified PID controller adjusts both rear wheels angular
2) Case II: Figure 31 shows the behavior of the EDS under
the control of the modified PID controller. As in Case I, it
is noted that the controller provides the EDS with sufficient
control actions accordingly to project specifications. The low
frequency responses and the consequent control effort is observed in Figure 32, which does not result in any deterioration
in the attempt to maintain the speed of the actuator.
Figure 33 shows the control responses of the EDS by the
neuro-fuzzy controller. The controller appropriately follows
the reference values for the angular speeds resulting in a
quasi-zero steady state error and no significant overshoot
levels. When it comes to the time delay response, it is neither
observed (Fig. 34). The system responds appropriately even at
low frequencies, and the control effort also keeps the wheels
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 7, SEPTEMBER 2012
Fig. 26.
Expanded view of the experimental response for the HELVIS
platform EDS module, adjusted by the modified PID controller, to a constant
speed and steering maneuver.
Fig. 27. Experimental response for the HELVIS platform EDS module,
adjusted by the neuro-fuzzy controller, to a constant speed and steering
maneuver.
11
Fig. 29. Experimental response for the HELVIS platform EDS module,
adjusted by the optimal H∞ controller, to a constant speed and steering
maneuver.
Fig. 30.
Expanded view of the experimental response for the HELVIS
platform EDS module, adjusted by the optimal H∞ controller, to a constant
speed and steering maneuver.
no overshoot, as well as a very quick time response.
Fig. 28.
Expanded view of the experimental response for the HELVIS
platform EDS module, adjusted by the neuro-fuzzy controller, to a constant
speed and steering maneuver.
speeds in compliance with the correct calculated speeds.
Finally, Figure 35 shows the EDS response by applying
the optimal H∞ controller for the same case. The control
robustness can be noted, such that the noise that is inserted
into the process is suppressed. The expanded view of the
control responses can be seen in Figure 36. It is observed
that the H∞ presents a high ability to reject the external
disturbances. Furthermore, the control effort and the controller
precision leads the EDS to a quasi-zero steady state error and
Fig. 31. Experimental response for the HELVIS platform EDS module,
adjusted by the modified PID controller, to a speed on sinusoidal pattern and
steering maneuver.
As for the experimental quantitative performance analysis,
it is noted from Tab. IV that all three controllers present
very satisfactory mean values during experimental tests. This
fact directly reflects the vehicle performance since the combination of low levels of steady state error, time delay and
overshoot guarantees a more stable and more maneuverable
car. Moreover, it expresses the accuracy of the overall EDS
while working with the novel proposed architecture, which
proves that it can embed controllers from various classes and
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 7, SEPTEMBER 2012
Fig. 32.
Expanded view of the experimental response for the HELVIS
platform EDS module, adjusted by the modified PID controller, to a speed on
sinusoidal pattern and steering maneuver.
Fig. 33. Experimental response for the HELVIS platform EDS module,
adjusted by the neuro-fuzzy controller , to a speed on sinusoidal pattern and
steering maneuver.
12
Fig. 35. Experimental response for the HELVIS platform EDS module,
adjusted by the optimal H∞ controller , to a speed on sinusoidal pattern and
steering maneuver.
Fig. 36.
Expanded view of the experimental response for the HELVIS
platform EDS module, adjusted by the optimal H∞ controller, to a speed
on sinusoidal pattern and steering maneuver.
VI. C ONCLUSION
Fig. 34.
Expanded view of the experimental response for the HELVIS
platform EDS module, adjusted by the neuro-fuzzy controller, to a speed
on sinusoidal pattern and steering maneuver.
approaches.
TABLE IV
C ONTROL P ERFORMANCE Q UANTITATIVE C OMPARISON TABLE D URING
E XPERIMENTS (M EAN VALUES ).
Controller
PID
NF
H∞
Steady State Error (%)
0.12%
0.18%
0.07%
Time Delay (ms)
7
12
5
Overshoot (%)
0.032
0.048
0.0045
Both EDS and the new control architecture proposed in this
work directly and deeply contributes to the development of
EVs/HEVs regarding improvements in the power train/traction
system. Although other control approaches can handle the
problem of the electronic differential control even with MIMO
systems, the focus of this research is to allow the design
of an electric wheel, which can independently replace the
conventional rear wheel in conventional passenger vehicles.
The proposed architecture is grounded in the fusion between
a high performance IMU sensor and kinematic and dynamic
parametric models, which turns the design of the EDS perfectly scalable to other 4WD rear traction vehicles. Despite
the fact that all tests have been run in a low scale vehicle, it is
feasible to be embedded in a full scale electric and Ackermanbased rear traction vehicle. Both simulated and experimental
results show that the novel control architecture presents good
results, regardless of the type and nature of the controller.
Therefore, the resulting EDS system is extremely flexible in
terms of control. Furthermore, it presents a general in-depth
solution to be used with any kind of control system, in any
circumstances. In terms of visibility, the proposed architecture
module allows clear vision of how the information flows into
the context of the EDS module.
As for the HELVIS platform and HELVIS-Sim simulation
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 7, SEPTEMBER 2012
environment, both are concrete contributions of this research.
They can potentially help spreading the new paradigms of a
new and cleaner transportation paradigm.
ACKNOWLEDGEMENT
Authors would like to thank Brazilian Electricity Regulatory Agency (ANEEL), Companhia Paulista de Força e Luz
(CPFL) and Fundação para o Incremento da Pesquisa e do
Aperfeiçoamento Industrial (FIPAI) for the financial support
for this research.
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