Artificial intelligence-enhanced DTC command methods used for a four-wheel-drive system

ABSTRACT


INTRODUCTION
There is no doubt that the preservation of the environment is a necessity given almost irreversible harmful climatic changes caused, among other things, by pollution due to the emission of greenhouse gases [1], [2].Among the currently recommended solutions, the development of the electric vehicle (EV) is found.It must progressively replace the internal combustion engine vehicle.The related research and development programs are being implemented by the States (USA, China, India) [3] and the major automobile industries.The current automotive market has three variants [3], internal combustion vehicles, hybrid vehicles, and electric vehicles.The motive power of the EV is based on the electric actuator that provides its drive.The choice of the propulsion machine and its control strategy play a key role from a technical and economic point of view (ease of manufacture of equipment, cost reduction, reduction of torque and flow oscillations, solidity in the face of road constraints) [4].Induction motors are chosen as propulsion motors because of their higher efficiency, and low maintenance [4], [5].These motors can only work optimally if they are driven by a proper control strategy such as direct torque control (DTC) [6].
EVs are gaining popularity due to their quiet, smooth, and emission-free operation, as well as their safety benefits, portable charging system, and improved fuel economy [7].However, these vehicles have challenges such as excessive charging time and low energy density, which provide possible research areas for their improvement.These limitations can be overcome by implementing an effective control strategy.At this level, in modern research, the integration of artificial intelligence (AI) has gained importance due to the need to select the most appropriate parameters, allowing the most efficient results [8], [9].
Thus in [10], a review of several direct torque control (DTC) schemes associated with fuzzy logic (FL), artificial neural networks (ANN), sliding mode control (CMG), and genetic algorithms (GA) were presented to improve the performance of an induction motor (IM).A comparison was made between these control systems in terms of algorithm complexity, parameter sensitivity, ripple reduction, switching loss, and speed tracking.The authors concluded that it was very difficult to choose an appropriate control scheme because it depended on the application, accuracy, hardware availability, reliability, and system cost.An ANN-based DTC scheme was introduced for an electric vehicle powered by a fuel cell [11].This scheme used the flux of the stator as a control variable and the flux level was adjusted according to the torque demand of the EV to achieve high drive performance.In this paper, the authors examined the performance of an IM drive for EV propulsion without considering the actual vehicle dynamics (road load), range, and fuel economy.
Thus in [12], an improved direct instantaneous torque control (DITC) based on adaptive terminal sliding mode control (ATSMC) was proposed.This is a new DTC technique for motors.A DTC scheme based on a stator flux optimization algorithm to increase the range of an electric vehicle in terms of driving a 3 kW induction motor at full load is tested by considering the effect of core losses and leakage inductance as explain in [13].Araria et al. [14] presented a DTC scheme for a battery and fuel cell-powered front-wheeldrive EV with an ANN speed PI controller allows for accurate reference speed tracking compared to traditional PI controllers using standard driving cycles such as the US environmental protection agency (EPA) and the new European driving cycle (NCCE).A comparative study between ANN and GA is done on an EV propulsion system to examine the torque setting, EV behavior in terms of range, speed, and fuel efficiency as elaborated in [7].An evaluation of the percentage of charge rate and the energy consumption are made under various road conditions.
This study proposes to evaluate two direct torque control (DTC) methods combined with artificial intelligence for a four-wheel-drive system of an electric vehicle.A comparison is made between fuzzy logic (FL) and artificial neural network (ANN) tuning.Both algorithms are used to adjust the error of the electromagnetic torque and magnetic flux to reduce the magnitude of their ripples.The proposed propulsion system was tested on the standard worldwide harmonized light vehicles test procedure (WLTP) driving cycle and performance parameters such as range and fuel efficiency were evaluated.The responses of the two intelligent algorithms are observed in terms of algorithm complexity, torque and flow ripple, control efficiency, improved flexibility, speed tracking, and ease of implementation.The performance obtained by the simulations indicates their adaptability to the use of such a propulsion system.

SYSTEM DESCRIPTION AND MODELLING 2.1. EV dynamics
The architecture of the EV developed in this paper is a twin-engine EV as shown in Figure 1.It contains key components of the conventional EV.Dynamics of vehicle are described by yaw rate, and speed both longitudinal and lateral as (1)-(3) [15], [16]: When analyzing Figure 2 presented, different forces applied to the vehicle are mentioned for a better understanding.Then, in (4) indicating the EV resistance opposes to any movement can be easily carried out.Following forces, the tire rolling resistance   , aerodynamic resistance in drag   , levelling resistance 1985 and acceleration resistance   are needed for a calculation of the required total force all these resistances are discussed detailly in [17]- [19]. Where: =    (7) The longitudinal forces of four-wheel motors can be calculated using as ( 9) [20].
The model of drive system can be described as ( 10) and ( 11) [20], where Tri is the resistive couple;     , are normal front and rear forces calculated using as ( 12) and ( 13) [20]: with a linear tire model, front and rear cornering forces can be expressed as the product of the cornering stiffness.(  ,   ) and sideslip angle (  ,   ) [20].
Sideslip angles of the wheels are expressed using the side length and angular speeds, as well as the steering angle .The explicit expressions of sideslip angles for front and rear axles are represented by ( 16) and ( 17) [20]. ) The longitudinal slip needs to be determined for all four wheels as (18): where: i = 1,2,3 and 4 correspond to front left, front right, rear left and rear right (= , , , ) wheels, respectively; R is the radius of wheel; i is the angular speed of motor in the wheel, and  is the linear speed at which the contact zone moves on the ground.Inter relationships between slip ratio  and the traction coefficient  can be described by various formulas.In this study, the widely adopted magic formula [21], [22], is applied to describe relationship between sliding and tensile forces in order to build a vehicle model in which following simulations are indicated by (19) [23], [24].

Modeling of the electronic differential (ED)
The ED allows the management of the driving wheel speeds of the EV.On a straight path, it maintains the two speeds of the driving wheels at the same value.And for a curvilinear trajectory, depending on whether we are going left or right, it allows the speed of the wheel at the outside position of the curve to be greater.This prevents the tires from losing traction [4].Figure 3 shows a sketch of an electronic differential used in EV modeling.The notations   ,   and δ represent the wheelbase, the distance between driving wheels and the steering angle, respectively.The speeds   * and   * are the drive speeds of right and left motors.So when: δ> 0 → Turn right, δ = 0 → Straight ahead, and δ <0 → Turn left It is possible to determine the reference speeds in relation to the driver's requirements.When vehicle arrives at the start of a path, the driver applies a steering angle on its wheel [21], [27].The ED acts instantly on both motors, reducing the speed of the wheel drive located at the inside position of the curve, thus increasing the speed of the driving wheel outside the curve.The angular speeds of the driving wheels are given by the relations: The difference between the angular speeds of the driving wheels can be expressed by (22) [8], [28]: with   =   +

Variable master slave control (VMSC)
This is a switchable master-slave control strategy.In this system, it makes it possible to regulate the stator flux of machines placed in parallel.This is because the power to these machines is provided by a single converter, and it may happen that these machines do not undergo the same loads.This implies that the functioning of some can hamper that of others (for example, the magnetic circuit of one machine can become saturated without that of the other).To avoid this, a means must be found so that voltage vectors delivered by the converter supply each machine equitably by enabling it to develop speeds and torques which are respectively required of them.In this case, it is a matter of regulating the stator flux of one machine at a time.This machine will be called master and thus makes the other a slave.While the stator flux of the master machine is controlled, that of the slave machine evolves naturally without respecting the set point so as to avoid saturation.The master machine is the one with the lowest torque.We, therefore, observe that when the torque of a machine increases, its stator flux decreases and vice versa.

ARTIFICIAL INTELLIGENCE BASED DTC DEVELOPMENT 3.1. Direct torque control by artificial neural networks (DTNC)
The DTNC control for multi-machine systems is shown in the Figure 4.The inputs that provide the network are:  1 ;  2 (error between the torques developed by the motors and the corresponding references);   (error between the modulus of the stator flux and the fixed reference) and   (position of the stator flux vector in the complex plane (, ).And the outputs are the pulses Sa; Sb; Sc necessary to drive the converter allowing to feed the motors adequately.During the training of the network with the data provided by the simulation of the conventional DTC control, when data is presented at the input of the network, the output is obtained by a calculation propagated from the input layer to the output layer.The calculation of the quadratic sum of the errors is obtained by (23): (23) with:   the desired output;   the computed output;  the number of iterations and  the amount of data in the training database.And so, according to the method of retro propagation of the error, the error is propagated from the output to the inputs causing a modification of the synaptic coefficients of the network according to as (24): () (24) with:   the weight of the connection between the j-th neuron and the i-th neuron of the previous layer and  the learning constant.The network studies have the following characteristics: − 4 layers, including 2 hidden layers each composed of 10 neurons.The input and output layers are composed of 3 neurons each.

Direct torque control with fuzzy logic (DTFC)
The second technique proposed in this article is the DTC associated with fuzzy logic.The block diagram of this command (DTFC) for a multi-machine system is shown in Figure 1  The stake around the control for multi-machine systems with one converter is to ensure the optimal functioning of the actuators in parallel.Indeed, it must be ensured that the converter provides an adequate voltage vector to meet the demands of the machines.Thus, just like the conventional DTC command applied to this type of system, the DTFC command comprises in its structure a control loop as shown Figure 5 of an electromagnetic torque regulation based on a Mamdani type fuzzy regulator.Thus, it includes two inputs:  1 =   1 −  1 * for motor 1 and  2 =   2 −  2 * for motor 2 and an exit   .The universe of discourses for each set is represented is being as: For   we have: N (negative) and P (positive); and For  1 ,  2 we have: N (negative), Z (zero), and P (positive).
Trapezoidal and triangular membership functions were chosen.The torque error entry is made up of three fuzzy sets: N (negative), Z (zero) and P (positive) as shown in Figure 6 as shown in.This fuzzy regulator is governed by all the rules set out as shown in Table 1.1989 The output obtained will be used for the selection of the adequate voltage vector by another fuzzy regulator with as other inputs: i) The stator flux error; and ii) The position of the stator flux vector   .The position of the stator flux vector is subdivided into six sectors.And for the outputs, the pulse signals used for the selection of the voltage vectors by the inverter are   ,   , and   [20].Thus, the rules obtained for the new method proposed can be deduced from the principle previously illustrated in the Table 1.

SIMULATION AND RESULT ANALYSIS
The simulation parameters used in this paper were chosen after an investigation in the literature.They come from the papers of [28], [29] with prototyping but also the papers [20], [27].Table 2 gives the information of the path traveled by the vehicle.The vehicle leaves the stop state to reach the speed of 70 km/h at t = 2s.The driver maintains this speed until t = 4s.Between t = 4s and t = 9.5s the vehicle negotiates a right turn with a steering command of 7° is shown in Figure 7 and a speed of 50 km/h.Back on a straight line between t = 9.5s and t = 12s the vehicle is driving at 70 km/h.Left turn with a stabilized speed of 50 km/h between t = 12s and t=17.5s.Then the Vehicle faces a slope of 10% until t = 19s maintaining a speed of 40 km/h, then returns to a straight road for the rest of the trip at a speed of 50 km/h as shown in Figure 8.Thus, the chosen speed profile allows the vehicle to cover a distance of 290 m in the 20s as shown in Figure 9. Figure 10 allows us to appreciate the action of the electronic differential during the turns, the engines of the right side slower when the turn is on the right contrary to the engines of the left and vice versa.This is explained by the fact that the wheels on the inside of the curve support a significant weight of the vehicle moving towards the inside.
During the start [0s; 2s], the 04 motors that compose the system develop a very important torque to allow the vehicle to overcome the inertia and reach the speed wanted by the driver.During the turns [4s; 9.5s] and [12s; 17.5s], the torques of the motors located inside the turn increase to allow the wheels to keep the desired speed while supporting the weight of the vehicle which moves on their side, the motors located on the opposite side are driven which explains that the developed torques are of negative sign as shown in Figure 11.For conventional direct torque control, oscillations are significant and go beyond the set hysteresis range [-0.5N.m; 0.5N.m].Figures 11(a   Motor speed response is better for DTFC control than for the other two strategies, as shown in Figure 12. Figure 12(a) shows the evolution of the speed curves derived from artificial intelligence and conventional vehicle control.Figure 12(b) shows the system's performance in terms of response.Table 3 shows some performance values.
Overall, the direct torque control strategy ensures good engine and vehicle control.Moreover, the results show the compatibility of this control for an application to multi-machines/mono converter systems,

CONCLUSION
In this paper, two methods of controlling multi-machine systems for electric vehicle propulsion are proposed.The results obtained show that direct torque control combined with fuzzy logic and artificial neural networks, compared with conventional control, delivers high performance in terms of speed, precision, robustness and perfect setpoint tracking despite the strong disturbances imposed by road constraints.The vehicle speed results obtained during the simulations enable a quantitative assessment of the performance of the proposed control strategies.With regard to the results and analyses previously carried out within the strict framework of the hypotheses considered (hysteresis limit range.), it is clear that the DTFC control technique presents better results (response time, static error.)than conventional DTC and DTNC.On the other hand, it can be seen that energy dissipation is a crucial factor in the quality-price ratio of an EV, as it is linked to electricity storage and therefore to battery life (charge and discharge cycle).In addition, consideration of the variation in the number of rules in DTFC and DTNC may be a future line of research to make a definitive statement concerning the comparison between these two techniques in EV modeling.All in all, the use of a twin-engine system with a single converter enables the electric vehicle to save energy.This is observed when using the WLTP driving cycle.

Figure 1 .Figure 2 .
Figure 1.Architecture of the EV under investigation

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ISSN: 2088-8694 Int J Pow Elec & Dri Syst, Vol.14, No. 4, December 2023: 1983-19941988 The activation functions used are linear (purelin) for the input and output layers and sigmoid (logsig) for the hidden layers.− This is supervised learning, and the chosen learning algorithm is the backpropagation of error.− The chosen optimization method is the Levenberg-Marquardt method for its speed and convergence.

Figure 4 .
Figure 4. Neural controller structure for multi-machine system above.The fuzzy regulator includes 4 inputs which are: −   : Difference between the reference stator flux and the estimated stator flux.−  1 : Difference between the reference torque and the electromagnetic torque of motor 1. −  2 : Difference between the reference torque and the electromagnetic torque of motor 2. −   : Position du vecteur de flux statorique.

Figure 5 .Figure 6 .
Figure 5. Structure of a fuzzy regulator for a multimachine system ) and 11(b) illustrate the contribution of artificial intelligence control techniques in reducing these oscillations, with DTFC offering the best result.

Figure 12 .
Figure 12.Right front motor angular speed (a) angular speed and (b) zoom speed

Figure 13 .Figure 14 .
Figure 13.Electrical energy consumed by the vehicle

Table 1 .
Basis of adopted rules Artificial intelligence-enhanced DTC command methods used for … (Ndoumbé MatékéMax)

Table 2 .
Chronology of the journey made by the EV

Table 3 .
Dynamic parameters of the speed response for each motor