Improved DTC Strategy of An Electric Vehicle With Four In-Wheels Induction Motor Drive 4WDEV Using Fuzzy Logic Control
Improved DTC Strategy of An Electric Vehicle With Four In-Wheels Induction Motor Drive 4WDEV Using Fuzzy Logic Control
Improved DTC Strategy of An Electric Vehicle With Four In-Wheels Induction Motor Drive 4WDEV Using Fuzzy Logic Control
Corresponding Author:
Nair Nouria
Departement of Technology
Tahri Mohammed University
B. P 417 route Kendsa, University of Tahri Mohammed, Bechar, Algeria
Email: nouria0479@gmail.com
1. INTRODUCTION
Today, in the automotive sector, manufacturers are moving towards improving internal combustion
engines and hybridization with electric motors to minimize CO2 emissions. A more ambitious alternative is
to do without the internal combustion engine, and therefore so-called zero emission propulsion [1], [2].
In general, the most commonly used electric actuators in the majority of industrial applications are built
around the induction motor [3], [4]. The induction motor in particular is characterized by its robustness,
reliability, low cost and does not require regular maintenance. However, its dynamic behaviors are often very
complex, because it's modeling results in a highly coupled nonlinear multivariate system of equations [5],
[6]. Additionally, some of its state variables, including flows, cannot be measured. Different drive techniques
for induction machines have been introduced to provide variable frequency speed control. Most of them are
based on rigorous mathematical formalisms. Among all the control methods, DTC or direct torque control is
considered particularly interesting.
Takahashi's theory is to specifically evaluate the control pulses used for voltage reversing switches
to maintain electromagnetic torque and stator flow within two predefined depenbrock hysteresis bands [7],
[8]. Such an application of this technique allows decoupling of torque and flow control without the need for
pulse width modulation (PWM) or coordinate transformation. Several studies are still underway to improve
the main classic drawbacks of DTC. Among these drawbacks are torque ripples and stator flux [8], [9].
In this article, we mainly describe the implementation of a robust and efficient control law the
DTFC, which stands for direct fuzzy torque control. Fuzzy logic is a fuzzy linguistic approach used by a type
condition (Si-Then) based on the imitation of approximate qualitative aspects of human reasoning [10]. And
to apply it in our work, we will study a traction system of an electric vehicle (4WDEV). The 4WDEV is
equipped with four asynchronous motors ensuring the drive of the driving wheels controlled by a direct fuzzy
torque control. The proposed control law ensures good stability of the 4WDEV in different road topologies,
curves and slopes and increases the autonomy of the electric vehicle. The second method is introduced to
replace the torque hysteresis controllers, flow rate controllers, and switch table used in the CDTC with fuzzy
logic controllers. The main objective of the DTFC method is to improve the dynamic performance of electric
vehicles and to reduce torque and flow ripples.
Figure 1. General structure of the EV4WD four-wheel drive electric vehicle studied
− Froul is the rolling resistance force related to the rolling coefficient of the wheels (Crr ). The rolling
resistance force is: Froul ≈ gMScooter Crr .
Improved DTC strategy of an electric vehicle with four in-wheels induction motor … (Nair Nouria)
652 ISSN: 2088-8694
− Faero is the aerodynamic resistance force, proportional to the air density, to the square of the wind
speed, to the frontal section of the vehicle and to its air penetration coefficient(Cpx ). Its expression
is given by (2).
1
Faero = ρSf Cpx (Vveh − Vwind )2 (2)
2
Frontal section of the vehicle and to its air penetration coefficient(Cpx ). Its expression is given
by (3).
1
Faero = ρSf Cpx (Vveh − Vwind )2 (3)
2
− Fpente is the resistance force of the slope to be climbed. In the case where the electric vehicle would
have to climb a corner slope (αp )as shown in Figure 2, there is an additional force proportional to
the total mass of the vehicle that is applied to its forward motion this force is given by:
Facc is the dynamic term for the acceleration or deceleration of the electric vehicle.
dVveh
Facc = Mveh = Mveh γ (5)
dt
− The angular velocity ω_(r-i) (rad/s) of each driven wheel is related to the vehicle speed by (8).
Vveh
ωr−i = (8)
2Rω
𝑥̇ = 𝐴𝑥 + 𝐵𝑢 (9)
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such as:
𝑇 𝑇
𝑥 = [𝑖𝑠𝛼 𝑖𝑠𝛽 𝜑𝑠𝛼 𝜑𝑠𝛽 ] , 𝑢 = [𝑢𝑠𝛼 𝑢𝑠𝛽 ] (10)
𝜔𝑟 1
−𝜂 𝜔𝑟 𝐾 0
𝜎𝐿𝑠 𝜎𝐿𝑠
𝜔𝑟 1
𝜔𝑟 −𝜂 − 𝐾 ;𝐵= 0 (11)
𝜎𝐿𝑠 𝜎𝐿𝑠
𝑅𝑠 0 0 0 1 0
[0 𝑅𝑠 0 0 ] [0 1]
with:
𝑀2 𝐿𝑠 𝐿𝑟 1 1 1 1
𝜎 =1− , 𝑇𝑠 = , 𝑇𝑟 = , 𝜔𝑟 = 𝑝Ω𝑟 , 𝐾 = ,𝜂= − ( + ) (12)
𝐿𝑠 𝐿𝑟 𝑅𝑠 𝑅𝑟 𝜎𝐿𝑠 𝑇𝑟 𝜎 𝑇 𝑇 𝑟 𝑠
t
φsβ = ∫0 (vsβ − R s isβ ) dt (14)
The 𝑁𝑖 field in which the vector 𝜑𝑠 is located is determined from the components 𝜑𝑠𝛼 and 𝜑𝑠𝛽 the angle 𝜃𝑠
between the repository (α-β) and the vector𝜑𝑠 [18].
φsβ
θs = arctg ( ) (16)
φsα
When the two flux components are reached, the electromagnetic torque can be calculated by [19].
3
Tem = p[φsα isβ − φsβ isα ] (17)
2
Improved DTC strategy of an electric vehicle with four in-wheels induction motor … (Nair Nouria)
654 ISSN: 2088-8694
Figure 3. Conventional DTC for induction motor drive in the wheels used in the 4WDEV
Figure 4. Schematic diagram of the direct fuzzy control (DTFC) of the MI integrated in the wheels of the EV
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Figure 5 displays the membership functions for the fuzzy inference method input and output
variables. Trapezoidal and triangular association functions have been selected. The input of the torque error
consists of 3 fuzzy sets N (negative), Z (zero) and P (positive). Two fuzzy sets were considered for the flow
error membership functions, N (negative) and P (positive) [23]. The stator flux angle can be defined by six
linguistic variables(𝜃1 ⟶ 𝜃6 ), to have a fine adjustment. The inferential device output variable is divided
into eight individualtons, two null voltages (V0 and V7) and six null voltages. The output variable
membership functions are shown in Figure 5. The different possible combinations of 3 fuzzy sets for torque
error, 2 fuzzy sets for flux error and six sectors for stator flux angle form 36 rules in the basis of the inference
system.
Figure 5. The membership functions for the input and output variables of the fuzzy inference system
The rule base is based on a stator flux diagram (α-β) in the plane. For example, if the angle θs of
the stator flux lies in the value of θ2if one wants to slowly decrease the torque and quickly increase the flow
then the vector V1 is the most suitable alternative. The same rationale is used to construct the rule base for
the fluid direct torque control in Table 3. The laws are the fluid control inferior engine. They express in
a relation between elementary fluffy proposals or conjunctions of fundamental proposals [21], [23].
With 𝐴𝑖 , 𝐵𝑖 and deare the linguistic variables of the flux error, the torque error and the stator flux angle,
respectively. 𝑉𝑖 is the output linguistic variable and 𝑅𝑖 is rule number i.
Improved DTC strategy of an electric vehicle with four in-wheels induction motor … (Nair Nouria)
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𝜇𝐴𝑖 (𝑒𝜑𝑠 ), 𝜇𝐵𝑖 (𝑒𝑇𝑒𝑚 ), 𝜇𝐶𝑖 (𝜃𝑠 ) and (v) 𝜇𝑉𝑖 (𝑣) designating respectively the degrees of membership of 𝑒𝜑𝑠 ,
𝑒𝑇𝑒𝑚 , 𝜃𝑠 andt 𝑣 to the fuzzy sets 𝐴𝑖 , 𝐵𝑖 , 𝐶𝑖 and 𝑉𝑖 .
In our case, the output is constituted by a set of singletons, we will apply the MAX method (21). The
value corresponding to 𝜇𝑉𝑜𝑢𝑡 (𝑣) should then be converted to a voltage vector. In the proposed fuzzy
controller for defuzzification the method of the center of gravity was used. Figure 6 shows the characteristic
surface of the proposed fuzzy controller, it expresses the variations of the actual value of the controller output
as a function of the inputs when the latter are traversing the speech universe.
36
μVout (v) = maxi=1 (μVi (v)) (21)
Degree of membership
n p PP
1 N Z P
1 GN PN Z PP GP 1 GN PN Z GP
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Such that, for the 𝑖 𝑡ℎ rule: 𝜇𝑐𝑖 is its degree, 𝑋𝐺𝑖 is the abscissa of its center of gravity and 𝑆𝑖 is the
surface of the output fuzzy subset. The rule base for deciding the output of the inference system consists of
25 If-Then rules in this case because there are 5 fuzzy sets in each of the inputs. Table 4 shows representing
the inference rule base.
∑25
i=1 μci XGi Si
∆T∗em = (22)
∑25
i=1 μci Si
Improved DTC strategy of an electric vehicle with four in-wheels induction motor … (Nair Nouria)
658 ISSN: 2088-8694
as shown in Figure 1. The objectives of the simulation carried out evaluated the effectiveness of the different
control strategies proposed (conventional DTC and DTFC) on the dynamics of the electric vehicle, and a
comparison was made between the two. This system was simulated using a reference wheel speed given by
the topology shown in Figure 8. The dynamic and aerodynamic characteristics of the vehicle and Table 6
includes induction motor parameters. The aerodynamic torque is reduced with DTFC control relative to
CDTC. 56.6Nm with DTFC and 57.1Nm per CDTC (phase 6, see Figure 10). This value can be explained by
the large frontal zone in the case of CDTC versus DTFC. It can be seen that the overall resistive torque is
improved in DTFC compared to CDTC (see Figure 11).
Figure 10. Vehicle Aerodynamics torque variation with Figure 11. Globally vehicle resistive torque
CDTC and DTFC
The driver provides the steering angle of the front wheels; the electronic differential is centered on
the speeds of the driving wheels. The speeds of the two right-hand drive wheels located on the outside of the
bend (right turn phase 2) Switch at speeds greater than the two inside left drive wheels of the bend. At the
moment t=4s the vehicle is in the second left turn 9 (phase 4); the same thing for the electronic differential
calculates the references of the new speeds to turn the wheels to stabilize the vehicle inside the left turn.
Table 7 shows the speed values for each wheel for both turns (phases 2 and 4).
A Fuzzy Logic Controller (FLC) was used in place of another traditional PI type to help improve the
speed response of the vehicle. The advantage of this controller lies in its robustness against speed variations
and follows the setpoint without overshooting and with good accuracy. Figure 12 shows the simulation
results of the linear velocity of the 4WD vehicle using the two control strategies (DTC with a PI type velocity
controller and DTFC with FLC). From the results we can notice that the effect of the disturbances is clearly
visible in the linear velocity response of the vehicle by using the DTC strategy (where the vehicle is driven
on a 10% slope phase 6 road) with an overtaking of 0.15%. The result of the two control laws can be
summarized in Table 8. On the other hand, the DTFC strategy gives us a good dynamic in terms of following
the instruction (setpoint) without over speeding in the stationary case with a low-rise time and zero static
error.
The evolution of the four electromagnetic torque propulsion engines (IM) of the 4WD electric
vehicle is given in Figure 13 (a) and Figure 13 (b), using both conventional DTC and DTFC control
strategies. The results obtained illustrate quite clearly good torque response dynamic output of the proposed
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DTFC control. In addition, a significant reduction in torque ripple can be seen, compared to conventional
direct torque control (DTC).
Table 7. Values of the four-wheels speed in phases 2 to 4 Table 8. Performances of the DTC and DTFC
Wheel speed Phase 02 Phase 04 in the speed response
(Km/h) CDTC DTFC CDTC DTFC Control Rising Time Over shoot Speed Error
Front left wheel 61,12 61,10 53,54 53,49 Type [Sec] [%] [%]
Front right wheel 55,31 55,25 51,85 51,80
Rear left wheel 45,35 45,15 48,35 48,33 DTC 0.16 0.15 0.01
Rear right wheel 39,52 39,43 47,21 47,19 DTFC 0.11 0 0
(a) (b)
Figure 12. Vehicle Variance of linear speed (a) and error rate (b) at various points
(a)
(b)
Figure 13. Electromagnetic torque response developed by the four motors using (a) conventional DTC,
(b) DTFC
Figure 14 (a) and Figure 14 (b) shows the trajectory of the stator flux vector in the plane (α-β)
related to the stator for the right front (LF) motor. It can be seen that the trajectory of the end of the stator
flux in the case of DTFC control (Figure 14 (b)) takes a uniform circular shape with a radius equal to 0.97Wb
centered at the origin which presents a good decoupling of the flux from the torque.
Improved DTC strategy of an electric vehicle with four in-wheels induction motor … (Nair Nouria)
660 ISSN: 2088-8694
(a) (b)
Figure 14. (a) Trajectory of stator flow in the plane (α-β) of the front left engine using classic DTC and
(b) DTFC
9. CONCLUSION
In this paper, we have focused on the application of one of the methods of artificial intelligence
which is fuzzy logic in a four-wheel drive electric vehicle. after having been able to determine the
performance of DTFC compared to DTC, the law of the proposed new control, i.e. DTFC, ensures a good
stability of the 4WDEV in different road topologies, curves and slopes and increases the autonomy by
reducing consumption of the electric vehicle energy, this was quite clear from the simulation results
(MATLAB/Simulink), from which we noticed the reduction of ripples and the rapidity in the torque and flow
dynamics during the starting phase of the machine.
ACKNOWLEDGEMENTS
This work was financially supported by, Smart Grids & Renewable Energies Laboratory Laboratory,
TAHRI Mohammed University of Bechar Algeria and DGRSDT Algeria.
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Improved DTC strategy of an electric vehicle with four in-wheels induction motor … (Nair Nouria)