Transport electrification is currently a priority for authorities, manufacturers, and research centers around the world. The development of electric vehicles and the improvement of their functionalities are key elements in this strategy. As a result, there is a need for further research in emission reduction, efficiency improvement, or dynamic handling approaches. In order to achieve these objectives, the development of suitable Advanced Driver-Assistance Systems (ADAS) is required. Although traditional control techniques have been widely used for ADAS implementation, the complexity of electric multimotor powertrains makes intelligent control approaches appropriate for these cases. In this work, a novel intelligent Torque Vectoring (TV) system, composed of a neuro-fuzzy vertical tire forces estimator and a fuzzy yaw moment controller, is proposed, which allows enhancing the dynamic behaviour of electric multimotor vehicles. The proposed approach is compared with traditional strategies using the high fidelity vehicle dynamics simulator Dynacar. Results show that the proposed intelligent Torque Vectoring system is able to increase the efficiency of the vehicle by 10%, thanks to the optimal torque distribution and the use of a neuro-fuzzy vertical tire forces estimator which provides 3 times more accurate estimations than analytical approaches.
The need for reducing global warming, air pollution, and oil dependency has motivated not only the use of renewable energies, but also some paradigm changes in other areas, such as transportation systems, where the development of electric vehicles (EV) has become a key strategy [
The integration of electric motors in propulsion systems provides not only better energy efficiency and lower pollution, but also increased controllability, as electric motors offer better response time [
Traditional control approaches have been widely used to implement ADAS during the last decades. However, electrified propulsion systems offer wider complexity (and multiple topologies) than internal combustion propulsion systems. Due to this, intelligent control approaches have become one of the main research interests lately, as they can manage complex systems more easily than traditional approaches.
One of the most complete ADAS for enhancing the dynamic behaviour and stability of an electric vehicle with per-wheel motors is Torque Vectoring (TV) [
Torque distribution approaches have been implemented conventionally using a wide variety of control algorithms. Among the traditional approaches, simpler ones, such as proportional-integral-derivative control (PID) based ones [
In order to achieve an effective driving torque distribution, the knowledge of the tire forces is crucial [
Among the approaches proposed to estimate the vehicle tire forces, the most common one is the use of estimators based on tire models, such as the linear tire model [
In summary, intelligent approaches have been demonstrated to be a suitable alternative to ADAS development, providing balanced performance versus computational cost. However, proper tire force estimations are required to guarantee this theoretical performance in a real-case scenario. In the literature, most works consider perfect estimations or use estimators based on physical variables difficult to measure, which require expensive sensors, or use complex models whose parameters are difficult to identify. This issue reduces the implementability and performance of the approaches proposed in most works in real-case scenarios.
In order to solve these issues, this work presents a novel intelligent Torque Vectoring approach, composed of two intelligent algorithms: first, an adaptive neuro-fuzzy inference system (ANFIS) estimator for the tire vertical forces based on exclusively measurable variables; second, a fuzzy yaw moment controller, which controls both vehicle yaw rate and sideslip angle, as they are some of the most representative vehicle dynamics variables. The proposed approach is able to enhance electric vehicle dynamics and their efficiency. To demonstrate its effectiveness, the ANFIS estimator and the resulting intelligent TV system have been validated considering several scenarios in the Dynacar high fidelity dynamic simulator, using an E-Class vehicle and comparing the obtained results with other previous works from the literature.
The rest of the paper is divided as follows: In Section
In this section the proposed intelligent Torque Vectoring system is detailed. Its main purpose is to distribute the driving torque among the different actuated wheels, so that vehicle handling and stability is improved. It can be divided into 5 subsystems (Figure
Proposed intelligent torque vectoring system.
The developed intelligent TV system approach is composed of a lateral torque distribution approach and a longitudinal one. The first is based on the control of the yaw moment of the vehicle; this is, it requires an appropriate yaw rate reference for its proper performance.
For the calculation of the desired yaw rate reference, the well-known
It must be noted that this model of reduced complexity is exclusively used for real-time execution in the controller. In addition, some of these simplifications are reasonable for passenger cars, as they are not driven until the limits of the tires.
This way, the yaw rate reference equation is [
However, for safety reasons it is necessary to limit the value of the yaw rate reference generated. In this case, the limit has been set as follows [
The fuzzy yaw moment controller handles the lateral torque distribution (
This subsystem is based on fuzzy logic, which is an extension of Boolean logic by Zadeh in 1965 [
The most common fuzzy logic system structure is shown in Figure
General diagram representing fuzzy logic approaches.
The proposed fuzzy logic controller is based on the Mamdani fuzzy model, as it provides a more intuitive tuning [
The actual vehicle sideslip angle value is calculated using the following equation [
For the design of the fuzzy system the following structure has been implemented. First, a distribution of 5 membership functions has been chosen for the yaw rate error
And finally, for the output, the torque percentage to be applied to each side of the vehicle,
The structure of the developed fuzzy controller is shown in Figure
Fuzzy logic controller proposed.
Subsequently the corresponding rules have been implemented based on the knowledge about the system and human driving datasets. Table
Membership functions names.
Names | Description |
---|---|
NVL | Negative very large |
NL | Negative large |
NM | Negative medium |
NS | Negative small |
ZE | Zero |
PS | Positive small |
PM | Positive medium |
PL | Positive large |
PVL | Positive very large |
Rules for negative yaw rate error derivative.
| | |||||
---|---|---|---|---|---|---|
| | | | | | |
| ZE | NS | NM | NL | NVL | |
| ZE | ZE | NS | NM | NL | |
| ZE | ZE | ZE | NS | NL | |
| PM | PS | ZE | ZE | NS | |
| PL | PM | PS | ZE | ZE |
Rules for zero yaw rate error derivative.
| | |||||
---|---|---|---|---|---|---|
| | | | | | |
| ZE | NS | NM | NL | NVL | |
| PS | ZE | NS | NM | NL | |
| PM | PS | ZE | NS | NM | |
| PL | PM | PS | ZE | NS | |
| PVL | PL | PM | ZE | ZE |
Rules for positive yaw rate error derivative.
| | |||||
---|---|---|---|---|---|---|
| | | | | | |
| ZE | ZE | NS | NS | NM | |
| PS | ZE | ZE | NS | NS | |
| PM | PS | ZE | ZE | ZE | |
| PL | PM | PS | ZE | ZE | |
| PVL | PL | PM | PS | ZE |
The dynamic behaviour of the vehicle depends heavily on the tire forces, as these model the contact force between the wheels and the road. However, their estimation is one of the most complex issues in vehicle dynamics, as the tire/road contact dynamics depends on a number of different variables. Direct measurement of these forces is not always a solution either, as these forces are very difficult to measure.
In this section, a novel ANFIS vertical tire forces estimator is proposed. The proposed estimator provides real-time and accurate estimations of the tire forces, which can be exploited by ADAS to increase the safety, stability, and efficiency of vehicles. Hence, this estimator will be used to perform the longitudinal dynamics torque distribution.
The proposed estimator is based on an ANFIS that is based on a fuzzy system that uses a learning algorithm derived from neural network theory to determine its parameters (fuzzy sets and fuzzy rules) by processing data samples [
ANFIS structure [
The proposed estimator uses measurable variables to operate, which is one of the main contributions of this work compared with those analyzed in the bibliography. The input data is composed of 10 variables: the steering angle; the
ANFIS estimators structure.
The proposed ANFIS estimator is composed of 4 layers. In the first of them 7 membership functions for each input have been developed. These membership functions are of Gaussian type, as they provide better precision than triangular ones [
The method selected for the generation of the fuzzy inference system is Subclustering, due to the high number of inputs. The training method chosen is the hybrid method, which is a combination of least squares and backpropagation gradient descent method. The parameters of this process are detailed in Table
Parameters of the hybrid method training.
Range of influence | 0.5 |
Squash factor | 1.25 |
Accept ratio | 0.5 |
Reject ratio | 0.15 |
The data used for the training and testing of the proposed ANFIS structure have been obtained from a simulation of a vehicle running on the Nurburgring circuit during one lap (simulation time of 800 s and sample time of 50 ms). The simulation has been obtained from the high fidelity vehicle dynamics simulator Dynacar [
The proposed longitudinal torque distribution approach calculates the longitudinal torque distribution percentage
This way, this subsystem allows sending greater torque commands to the motors whose wheels have more grip. For that purpose, a simple but effective torque distribution algorithm is proposed, based on the maximum normal force that can be applied in an axle (the front one has been taken as reference). This way,
This subsystem calculates the exact motor torque command to be applied to each wheel
In this section the validation methodology used is explained, including the selected vehicle, the simulation environment, and the proposed manoeuvres and testing scenarios.
Figure
General test framework, based on Dynacar [
The vehicle model is implemented in Dynacar, which is a high fidelity vehicle dynamics simulation platform developed by Tecnalia Research & Innovation [
One of the features of Dynacar is the possibility of activating an automated driver mode, which simulates a standard driver. This allows reducing the effect of the driver ability when analyzing the results of the developed ADAS and, hence, allowing better comparison.
Dynacar’s vehicle physical model simulation engine is based on a multibody model and integrated in C code [
Table
Vehicle principal characteristics.
Mass | 1830 |
| 928.1 |
| 2788.5 |
| 3234.0 |
Wheelbase | 3.05 |
Front axis track | 1.6 |
Rear axis track | 1.6 |
The control block is implemented in a Xilinx Zynq XC7Z020 SoC, whose inputs and outputs are connected to Dynacar. This allows testing the real-time performance of the proposed intelligent TV control approach and does not require the use of a whole vehicle thanks to the Dynacar’s model-in-the-loop approach.
The selected hardware is composed of two parts. The first is the programmable logic part, which is a full FPGA. And the other part is the processing system, which is composed of an ARM CPU of two cores and 800 MHz clock rate. In addition, this board has several I/O peripherals, such as digital and analog inputs/outputs ports and communication buses.
The ARM core has been used to implement the different subsystems of the proposed intelligent TV approach (Figure
Dynacar’s framework allows simulating and testing the developed intelligent TV controller in different scenarios and with a set of different standardized manoeuvres: a skid-pad [
Skid-pad test [
Double lane change test [
On the one hand, the objective of the skid-pad test is to measure the car’s cornering ability on a flat surface while making a constant-radius turn. This test is one of the FSAE Dynamics Events [
On the other hand, the double lane change manoeuvre is detailed in the ISO 3888 specification [
In this section the results obtained during the validation of the developed intelligent TV control approach are analyzed. For that purpose, first the proposed ANFIS vertical force estimator is validated with the results obtained with Dynacar and the analytical estimator proposed in [
In order to test the effectiveness of the approach, the data obtained from the proposed estimator is compared with (a) Dynacar’s internal high fidelity tire model and (b) the model-based analytical estimator proposed in [
Figures
Skid-pad results.
ANFIS | Model | ||
---|---|---|---|
FL | RMSE | 250.192 | 702.36 |
NRMSE | 2.37 | 6.656 | |
FR | RMSE | 211.58 | 698.56 |
NRMSE | 2.015 | 6.635 | |
RL | RMSE | 143.544 | 412.77 |
NRMSE | 2.0474 | 5.8874 | |
RR | RMSE | 245.871 | 434.997 |
NRMSE | 3.4764 | 5.5628 |
Double lane change results.
ANFIS | Model | ||
---|---|---|---|
FL | RMSE | 114.23 | 787.905 |
NRMSE | 1.3491 | 5.944 | |
FR | RMSE | 151.0323 | 775.32 |
NRMSE | 1.607 | 5.185 | |
RL | RMSE | 107.986 | 412.77 |
NRMSE | 1.4629 | 6.782 | |
RR | RMSE | 164.2598 | 434.997 |
NRMSE | 2.0457 | 5.982 |
In addition, the real-time performance of the proposed estimator has been analyzed, requiring
In order to validate the ability of the proposed intelligent TV approach to enhance the dynamic handling, first, the results associated with the skid-pad test will be analyzed.
In order to determine the effectiveness of the approach, the critical speed of the vehicle has to be defined first. This critical speed is the maximum speed that allows the vehicle to perform the skid-pad test correctly with no TV control. For that purpose, no TV system has been activated, and the skid-pad test has been carried out increasing the speed in each test until the vehicle has not been able to follow the reference trajectory. This critical speed has been experimentally defined as 47 km/h, providing a theoretical lateral acceleration of 0.86 g.
Once this critical speed limit is detected, the skid-pad test has been executed activating the proposed intelligent TV approach and a PID based TV approach. Results are shown in Figure
Skid-pad trajectory.
The undesirable behaviour at the critical speed when no TV is activated can be further appreciated in Figures
Wheels slip ratio.
Wheels slip angles.
Vehicle speed.
Vehicle lateral acceleration.
Yaw rate tracking.
Figure
Moreover, if a mechanical energy consumption analysis is carried out, the proposed intelligent Torque Vectoring approach allows not only a correct yaw rate tracking, increased cornering ability, and reduced slip ratio, but also an increase in the efficiency of the vehicle. Efficiency results are shown in Table
Mechanical energy comparison.
Energy mech [kWh] | |
---|---|
No TV | 0.4219 |
PID TV | 0.2091 |
Intelligent TV | 0.1895 |
After analyzing the skid-pad performance, the double lane change scenario will be studied. In order to perform this test, an initial speed of 50 km/h has been selected, and a constant torque reference has been applied to the motors (2300 Nm total torque). This provides a longitudinal acceleration of 0.35 g approximately, allowing to obtain a final speed of almost 90 km/h, covering the most common speed range of passenger vehicles in medium speed roads.
Simulation results for this scenario are shown from Figures
Double lane change trajectory.
Steering angle.
Wheels slip angles.
Wheel torque.
The development of real-time capable, accurate, and efficient ADAS is a key issue for the development of vehicles with independent in-wheel motors. In this work a novel intelligent Torque Vectoring (TV) system, composed of a neuro-fuzzy vertical tire forces estimator and a fuzzy yaw moment controller, has been proposed.
The proposed approach considers both lateral and longitudinal torque distributions. The longitudinal distribution is based on a neuro-fuzzy vertical tire forces estimator that is based exclusively on measurable variables, which is an important contribution compared with the existing estimators. The estimated forces are used to determine the percentage of torque to be applied to the wheels of the rear and front axles, so that the maximum grip can be achieved.
On the other hand, the lateral torque distribution is achieved using a fuzzy yaw moment controller. This controller allows distributing the torque laterally (right and left wheels), to minimize wheel slip and enhance cornering capabilities. The overall torque distribution is calculated by taking into account both distributions.
Results demonstrate the ability to enhance vehicle dynamics of the intelligent Torque Vectoring System in various scenarios. On the one hand, it was able to increase the stability in an evasive manoeuvre, such as double lane change, allowing the vehicle to follow better the desired trajectory, which is a critical safety issue in such manoeuvre. On the other hand, in the skid-pad test, a significant wheel slip ratio and slip angle reduction (19% and 23°, resp.) have been shown, resulting in an understeering behaviour reduction. This has allowed the vehicle to better match the yaw rate reference (33% error reduction) and then be able to follow the desired trajectory, demonstrating the cornering improvement provided by the correct torque distribution. Additionally, the proposed intelligent TV algorithm presents an improvement regarding a more traditional approach of the state of the art, providing more efficient driving (10% mechanical energy consumption reduction).
Future work will include a more sophisticated design for the use of the estimated tire vertical forces in the intelligent Torque Vectoring controller, resulting in a more elaborate controller, to improve its performance. Moreover, the implementation of the TV System in the logical part of a SoC will be considered in order to decrease its cycle time.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The research leading to these results has been supported by the ECSEL Joint Undertaking under Grant agreement no. 662192 (3Ccar). This Joint Undertaking receives support from the European Union Horizon 2020 research and innovation program and the ECSEL member states.