Possibilities to evaluate the vehicle’s accelerations through MATLAB Simulink simulations

This scientific present paper explores the methods for assessing the longitudinal and lateral accelerations of a vehicle through the combination of experimental validation and MATLAB Simulink simulations. Comprehending these accelerations is essential for a number of uses, such as stability, overall performance analysis, and vehicle safety. The first step of the study is building a detailed Simulink model of the car. With an emphasis on lateral and longitudinal accelerations, this model makes it easier to simulate a range of driving scenarios and explore how a vehicle handles and behaves under different circumstances. A key element of the study is the experimental validation of the Matlab Simulink model, which involves gathering real-world data from vehicle testing and contrasting it with simulated outcomes. Simulink model iterative refinement is made possible by the integration of simulation and experimentation, which ultimately improves the model’s predictive accuracy. The study’s conclusions demonstrate the integrated approach’s potential to advance vehicle dynamics analysis and make cars safer and more effective. Furthermore, it offers insights into the optimization of vehicle designs and the development of innovative control strategies to enhance overall road safety and vehicle performance.


Aim and objectives of the present paper
Accurate measurement of the lateral and longitudinal accelerations of vehicles is critical in modern automotive research to maximize safety, efficiency, and control systems.Present-day techniques typically depend on isolated experimental testing or theoretical models, which frequently lack the comprehensive insights needed for in-depth analysis.
This research paper closes this gap by presenting a novel method that combines experimental validation with MATLAB Simulink simulations in a seamless manner, providing a comprehensive understanding of vehicle dynamics.The combination of these methods represents a significant breakthrough in automotive engineering and has the potential to improve control schemes, safety features, and vehicle design.

State of the art
Several studies have been conducted using this tool for vehicle dynamics simulations, such as [1], in which the advantages of using Simulink for modeling and simulating vehicle dynamics is highlighted, IOP Publishing doi:10.1088/1757-899X/1303/1/012040 2 including its ease and flexibility.Another relevant study is [2], where authors use Simulink for modeling and analyzing the dynamics of a vehicle's suspension system.It also highlights the importance of accurate models for the suspension system, to better understand how performance and safety can be improved.
Moreover, the paper [3] presents a mathematical model for the kinematics and dynamics of a fourwheeled vehicle using MATLAB Simulink.The authors demonstrate the effectiveness of this simulation tool in accurately modeling vehicle dynamics and for evaluating the influence of different parameters on vehicle's performance and safety, together with providing insights into the use of Simulink.
The paper [4] presents a model for evaluating tire rolling resistance using MATLAB Simulink by modeling the interaction between tires and deformable pavements.The authors highlight the effectiveness of the model in accurately simulating tire and road surface interaction and evaluating the impact of pavement texture and tire characteristics on rolling resistance.The study provides insights into improving tire design for the reduction of fuel consumption.
Simulink can also be used to model and evaluate the dynamics of electric vehicles.Thus, the study [5] proposes an acceleration slip regulation (ASR) strategy for four-wheel drive electric vehicles based on sliding mode control (SMC).The authors show the effectiveness of the proposed ASR-SMC strategy in improving vehicle stability and maneuverability under different road conditions and different dynamic loads on vehicles' axles.The study provides information regarding the use of SMC for developing advanced ASR systems in electric vehicles.
In terms of experimental tests for studying vehicle dynamics, the scientific paper [6] proposes a method for estimating a vehicle's lateral load transfer and normal forces using experimental data from accelerometers and gyroscopes.The method is based on a dynamic model of the vehicle and can estimate these critical quantities accurately even under dynamic conditions.This information is critical for developing vehicle control systems, such as anti-lock braking systems, traction control systems and electronic stability control systems, which are meant to improve vehicle handling and passenger safety.

Working methodology 2.1. Experimental test
For the experimental test, an M1 category automobile was considered, for which the main functional and dimensional parameters are presented in Table 1.The technical condition of the automobile was verified prior to the tests, i.e. tire pressure, uniformity of tires wear and suspension system through EUSAMA test.The experimental dynamic tests must be conducted on a road section with dry asphalt.Its longitudinal and transverse inclination should be as small as possible.The device for measuring the stability parameters contains an MPU6050 module and Arduino Uno board.The MPU6050 is a module composed of a motion measurement sensor (figure 1), which integrates a 3-axis accelerometer (on X, Y and Z directions), a 3-axis gyroscope, a digital motion processor and additional circuits that serve for the communication of the module with the microcontroller.It allows the measurement of angular velocity around all three axes, static acceleration due to gravity and dynamic acceleration due to motion, shock or vibration.The module is positioned so that its three axes (X, Y, Z) correspond to the axes of the vehicle's center of gravity.The collected and processed data are transmitted to the computer, thus displaying the results to the user in the Serial Monitor.The device was placed on a universal support (figure 2), that can be used for any vehicle model, and located in the center of gravity in the passenger compartment.The monitored parameters were the accelerations of the vehicle on the Y axis, the rotational speed of the vehicle around the X axis in order 4 to determine the roll, and the rotational speed of the vehicle around the Z axis in order to be able to determine the route traveled.The tests were carried out at 40 km/h and nominal tire pressure at 2.4 bars.

Computational simulation
The validation of obtained results was conducted through the Driving Scenario Designer tool of MATLAB.The first stage of the simulation was represented by the digitization process of the used trajectory during the experimental tests.The considered track was extracted from the Open Street Maps (OMS) platform, its format allowing for direct selection of roads.The OSM file was uploaded to the Driving Scenario Designer, thus digitizing the track automatically.
In the second stage, the vehicle used in the experimental test was defined, together with the considered trajectory.When defining the vehicle, its dimensional parameters were considered, such as total length, trackwidth and total height.The defined trajectory is also highlighted in figure 3.In order to extract data from the computational simulation, the vehicle was equipped with an Inertial Navigation System (INS) module.This Simulink module is responsible for the acquisition of data regarding the accelerations that occur during the vehicle's movement, being positioned in the vehicle's center of mass, similarly to the acquisition of data from the experimental test.After defining the model, all considered movement scenarios were simulated, identical to the ones considered in the testing phase.The model implemented in Simulink is depicted in figure 4.

Obtained results
The experimental test was conducted with a quasi-constant travel velocity of the vehicle, hence the longitudinal acceleration (on the X axis) has values around zero.The increase in the longitudinal acceleration from the first 15 s of the experimental test is due to the time needed for the vehicle to stabilize its velocity.Also, in cornering conditions, the driving velocity was slightly variable due to the test conditions.The lateral acceleration (on the Y axis) has peaks in cornering, with positive values for left cornering and with negative values for right cornering.The vertical acceleration is also variable, depending on the surface of the road and the gravitational acceleration, as observed in figure 5.According to the data obtained from the computational simulations in MATLAB Simulink, there is a quasi-null longitudinal acceleration (on the X axis of the vehicle), given by the constant travel velocity of the considered vehicle.On the Y axis, there are the peaks in acceleration with positive values when the vehicle is cornering.At the same time, the vertical acceleration (on the Z axis) has negative values for the same cornering conditions, as shown in figure 6.In terms of accelerations obtained from the experimental testing (see figure 5) and computational simulation (see figure 6), it is observed that the shape of the graphs is similar, while the values may differ because of the test and simulation conditions.The relative error (figure 7) for each the directions of acceleration was calculated with the following relation: where   is the relative error,   -the acceleration obtained experimentally and   -the acceleration obtained from computational simulation.The maximum absolute values of the relative errors appear in cornering conditions, being higher for the lateral acceleration.The average values of the relative error between the accelerations measured during road test and those obtained from the computational simulations, are included in Table 2.

Conclusion
In this study, an integrated approach that combines MATLAB Simulink simulations with experimental validation to assess both longitudinal and lateral accelerations in a vehicle was successfully explored.
Understanding and accurately evaluating these accelerations is critical for improving vehicle stability, performance analysis, and safety.The development of a detailed Simulink model with a focus on lateral and longitudinal accelerations aided in the simulation of various driving scenarios, allowing for a better understanding of the vehicle's behavior under various conditions.
Collecting real-world data and comparing it to simulated results was a critical component of experimental validation.This integration enabled iterative refinement of the Simulink model, which improved its predictive accuracy.We discovered a strong qualitative similarity in the shape of acceleration graphs when comparing experimental and simulation data, despite quantitative differences due to test and simulation conditions.We also computed relative errors for each acceleration direction, which provided useful information about the model's accuracy and reliability.
In the end, this integrated approach could lead to safer and more efficient vehicles on the road by making significant advancements in vehicle dynamics analysis.It also provides opportunities for improving road safety and vehicle performance through creative control strategy development and vehicle design optimization.

Figure 1 .
Figure 1.The device used for measuring the stability parameters.

Figure 2 .
Figure 2. The universal support and acquisition device for the stability parameters.

Figure 3 .
Figure 3.The digitized track using the OMS format file, with the defined trajectory in Simulink.

Figure 5 .
Figure 5. Accelerations on the three axes obtained from the experimental test.

Figure 6 .
Figure 6.Accelerations on the three axes obtained from the computational simulation.

Figure 7 .
Figure 7. Variation of the relative error for accelerations in time.

Table 1 .
Main functional and dimensional parameters of the considered vehicle.

Table 2 .
Mean values for the relative error between the accelerations determined experimentally and from the Simulink model.
Wang H, Qian J and Zhou H 2021 Evaluation of tire rolling resistance from tiredeformable pavement interaction modeling, Journal of Transportation Engineering Part B Pavements, DOI: 10.1061/JPEODX.0000295.[5] He H, Peng J, Xiong R and Fan H 2014 An acceleration slip regulation strategy for four-wheel drive electric vehicles based on sliding mode control, Energies, DOI: 10.3390/en7063748.[6] Doumiati A, Victorino A, Charara A and Lechner D 2009 Lateral load transfer and normal forces estimation for vehicle safety: experimental test, Vehicle System Dynamics, Vol.47, p. 1511-33, DOI: 10.1080/00423110802673091.