Degrees Of Freedom Vehicle Model Research Articles

Path tracking of varying-velocity 4WS autonomous vehicles under tire force friction ellipse constraints

In this paper, a control scheme is presented to solve the problem of path tracking for varying-velocity autonomous vehicles with higher robust performance while friction force constraints of vehicle tires and ground are considered to avoid appearing the steering lost situation actively in the limit of the tire friction forces by using four wheel steering. To achieve these goals, a new expression of the tire forces and a new controlled system are proposed for the three degree of freedom vehicle model. A longitudinal input-saturation controller is designed to track the desired longitudinal velocity and attenuate the influence of lateral and yaw motions. The virtual control input method is used to design the input-saturation controller and get the desired steering angles to track the desired path for the lateral and yaw motions while a new control problem with desired forces tracking is considered to autonomously avoid the limit of lateral tire friction forces and the steering lost situation appearing. To test these results, lane changing, U-corner turning and straight-line driving for a varying-velocity vehicle are simulated with external disturbances and model uncertainties. Simulation results show that the higher robustness and precise path tracking performances are obtained.

Torque Vectoring Control Strategies Comparison for Hybrid Vehicles with Two Rear Electric Motors

In today’s automotive industry, electrification is a major trend. In-wheel electric motors are among the most promising technologies yet to be fully developed. Indeed, the presence of multiple in-wheel motors acting as independent actuators allows for the implementation of innovative active systems and control strategies. This paper analyzes different design possibilities for a torque vectoring system applied to an originally compact front-wheel drive hybrid electric vehicle with one internal combustion engine for the front axle and two added electric motors integrated in the wheels of the rear axle. A 14 degrees of freedom vehicle model is present o accurately reproduce the nonlinearities of vehicle dynamic phenomena and exploited to obtain high-fidelity numerical simulation results. Different control methods are compared, a PID, an LQR, and four different sliding mode control strategies. All controllers achieve sufficiently good results in terms of lateral dynamics compared with the basic hybrid version. The various aspects and features of the different strategies are analyzed and discussed. Chattering reduction strategies are developed to improve the performance of sliding mode controllers. For a complete overview, control systems are compared using a performance factor that weighs control accuracy and effort in different driving maneuvers, i.e., ramp and step steering maneuvers performed under quite different conditions ranging up to the limits.

Vibration Control and Ride Comfort Analysis of a Full Car with a Driver Model Using Big-Bang Big-Crunch Optimized FLC

The main motive of the active suspension system is to enhance the ride comfort by suppressing the vibrations induced due to road irregularities. The actuator is getting more significance in the automotive industry due to its superior ride comfort for passengers. In this study, an eight Degrees of Freedom (DOF) full car with a driver model is considered for the ride comfort analysis (ISO2631 Standard) and vibration control. The real road terrain is not uniform in nature. Hence an effective intelligent control technology is required to improve the quality of travel. Initially, a conventional Proportional Integral and Derivative (PID) controller is designed for the system. Then a Fuzzy Logic Controller (FLC) is designed for the 8 DOF vehicle model to control the unwanted vibration produced in the vertical and angular directions. The FLC is designed with suitable firing rules, membership functions, and scaling factors using MATLAB/Simulink 2019 environment. The performance of FLC is further enhanced by the Big Bang Big Crunch (B3C) optimization technique, and it can suppress vibrations when the vehicle is travelling over bumpy and imperfect random road terrain as per ISO 8608. The Root Mean Square (RMS), Frequency Weighted RMS (FWRMS), and Vibration Dose Value of seat acceleration are the performance indices to investigate the potency of B3C-tuned FLC against the PID controller, FLC and passive suspension system.

Simulation of linear two degrees of freedom vehicle model based on Matlab/ Simulink

Simulation of linear two degrees of freedom vehicle model based on Matlab/ Simulink

Autonomous vehicle trajectory tracking lateral control based on the terminal sliding mode control with radial basis function neural network and fuzzy logic algorithm

Abstract. This paper will study a trajectory tracking control algorithm for electric vehicles based on a terminal sliding mode controller. First, a 3 degrees of freedom nonlinear vehicle model and a controller-oriented 2 degrees of freedom vehicle model are established. The preview time is adaptively adjusted based on the preview model. Then, the vehicle trajectory tracking controller, which uses the terminal sliding mode algorithm, is designed. The radial basis function (RBF) neural network algorithm is used to approximate the system variable parameters in the control model online. At the same time, fuzzy logic is used to control the gain parameters of the controller to reduce the chattering of the control system. Finally, the designed controller is verified by simulation. The maximum deviation of path tracking under different speeds is 0.6 m, and the target path can also be well followed under different road friction coefficients. The simulation results show that the controller designed in this paper can effectively carry out the vehicle trajectory tracking and lateral control and reduce the chattering to a certain extent.

Hierarchical Approach for Driver Disturbance Rejection in an Electric Vehicle: The CRONE Approach

This article deals with the control chassis dynamics of a light electric vehicle. In the frame of Global Chassis Control, it proposes a hierarchical control approach focuses on compensating the chassis dynamics against driver disturbances. It is based on a supervisory structure consists of two main levels, a global controller for regulating chassis variables and a local controller to each suspension system. Both controllers are designed using a fractional-order robust controller, namely CRONE controller, to provide an optimized solution for the performance-robustness tradeoff. The main objective is to improve ride comfort for passengers while respecting road holding and handling criteria. In contrast to other studies, random road disturbances are considered to investigate the limits of the proposed approach. Analysis in frequency and time domain has been done to evaluate the performance and robustness of the designed controller. Simulation results based on a full nonlinear 14 degree of freedom vehicle model show that the proposed strategy can effectively improve the ride quality in the field of interest where a significant performance in driver disturbance rejection is reported.

Assessment of Risky Cornering on a Horizontal Road Curve by Improving Vehicle Suspension Performance

Vehicle stability during cornering on horizontal road curves is a risky stage of travel because of additional factors acting. The main stability factor is centrifugal force, which depends on road curve sharpness and is very sensitive to driving speed usually controlled by the driver. However, the counterforce is produced at tire-road interaction, where different pavement types and states cause a wide variation of tire contact forces and vehicle stability. In the paper, the part of vehicle suspension performance while moving on a sharp horizontal road curve with different levels of pavement roughness was simulated by 14 degrees of freedom vehicle model. The model was built in MATLAB/Simulink software with available pavement roughness selection according to ISO 8608. The influence of variable suspension damping available in modern vehicles on risky cornering is analysed when a vehicle reaches the edge of the pavement with its specific roughness. Critical parameters of vehicle stability depending on road curvature, pavement roughness and driving speed are selected to assess the solutions for safe cornering.

Fractional Calculus Control of Road Vehicle Lateral Stability after a Tire Blowout

The lateral stability control of the vehicle can avoid serious traffic accidents when it had a tire blowout during the operation. This article proposes a robust nonlinear control method for controlling vehicle lateral stability after a tire blowout. To be exact, a seven degree of freedom dynamic model of vehicle with modified Dugoff tire model is established. The yaw moment of vehicle is performed by differential braking once the tire blowout occurring. As for control strategy, taking the linear two degree of freedom vehicle model as the reference, using the deviation of yaw rate and the vehicle side angle between the actual value and the reference value as the controller input parameters, the fractional calculus theory is utilized for yaw moment controller which was investigated by regulating the brake moment of blowout vehicle for improving its stability. The results of computer simulation show that the design controller of fractional PID can more effectively enhance the blowout vehicle performance stability compared with the vehicle with the non control, PID control, no matter in straight road or curve road.

Comparative Analysis of MacAdam Model and PI Control in a Predictive Driver Model

Autonomous vehicles are the future of automotive engineering and understanding how this systems work is critical. In these vehicles, controller models are usually needed to generate signals that would normally be imposed by the driver e.g., steering angles, acceleration inputs and braking commands. Intuitively, each control method utilized has its peculiarities and presents different behaviours. In such situation, this paper aims to develop an error comparison between a car displacement and its reference path due the use of two different predictive driver controllers: The proportional-integrative and the MacAdam model. For this purpose, a 14 degrees of freedom vehicle model is used with the aid of MATLAB Simulink, whereas simulations were made using the double-lane change manoeuvre, a commonly used manoeuvre to analyse the vehicle dynamics performance. At the end of this paper, lateral acceleration, displacement and steering wheel angle analysis led the conclusion that the vehicle behaviour is smoother with the use of the proportional-integrative control regardless of longitudinal velocity. Nevertheless, the trajectory error is smaller for MacAdam model than PI controller is and therefore it is easier to follow the reference path with this one, although in aggressive maneuverers it can cause more discomfort and increase the risk of rolling when compared to the PI controller in a vehicle with the same body stiffness.

Vehicle dynamics and tire models: An overview

Stability control system plays a significant role in vehicle dynamics to improve the vehicle handling and achieve better stability performance. In order to study and evaluate the performance of the vehicles in addition to how to control it, it is necessary to identify obtain some models related to the dynamics of the vehicle as well as the tire models. This paper presents fundamentals of vehicle dynamics by introducing vehicle models and tire model, which have been widely adopted for vehicle motion control. This helps to get a basic idea of what parameters and states of a vehicle are important in vehicle motion control. This work is separated into four sections: vehicle planar model, full vehicle model, two degrees of freedom vehicle model (bicycle model) to design the controller, and wheel dynamic model.

Ergonomic Path Planning for Autonomous Vehicles-An Investigation on the Effect of Transition Curves on Motion Sickness

Motion sickness in self-driving cars is a key human factor that aggravates the passengers’ health in autonomous vehicles and is investigated in the following pages. As drivers turn into passengers and passengers dwell into other activities, the probability of car sickness is inevitable in self-driving cars. Path planning could serve an important role in reducing sickness. The present study establishes thresholds that contribute to motion sickness from a vehicle’s dynamic point of view to generate at first the most susceptible reference track to motion sickness, then redesigned using B-spline, Bezier, and Hermite curves to investigate the thresholds. Trajectory tracking of an eight degree of freedom vehicle model within the Autodriver algorithm is then studied using curvature dependent and curvature independent controllers to draw a comparison. Results are then compared and evaluated to find the optimal transition curve to minimize motion sickness probability. Furthermore, the findings are applied to lane changing maneuvers using various transition curves. Results indicate that four out of five of the motion sickness thresholds were successfully addressed in this investigation. Further research is recommended to address the fifth motion sickness threshold by utilizing the transition curve’s key characteristics like local control and non-uniformity.

An integrated torque-vectoring control framework for electric vehicles featuring multiple handling and energy-efficiency modes selectable by the driver

A key feature achievable by electric vehicles with multiple motors is torque-vectoring. Many control techniques have been developed to harness torque-vectoring in order to improve vehicle safety and energy efficiency. The majority of the existing contributions only deal with specific aspects of torque-vectoring. This paper presents an integrated approach allowing a smooth coordination among the main blocks that constitute a torque-vectoring control framework: (1) a reference generator, that defines target yaw rate and sideslip angle; (2) a high level controller, that works out the required total torque and yaw moment at the vehicle level; (3) a low level controller, that maps the required force and yaw moment into individual wheel torque demands. In this framework, the driver can select one among a number of driving modes that allow to change the vehicle cornering response and, as a second priority, maximise energy efficiency. For the first time, the selectable driving modes include an “Energy efficiency” mode that uses torque-vectoring to prioritise the maximisation of the vehicle energy efficiency, thus further increasing the vehicle driving range. Simulation results show the effectiveness of the proposed framework on an experimentally validated 14 degrees of freedom vehicle model.

Study on optimization algorithm of tuned mass damper parameters to reduce vehicle-bridge coupled vibration

A vehicle-bridge tuned mass damper (TMD) coupled dynamic analysis and vibration-control model was established to optimize TMD damping effects on a steel-box girder bridge bearing vehicle loads. It was also used to investigate optimization efficiency of different algorithms in TMD design parameters. This model simulated bridges and vehicles with the use of a 7 degrees of freedom curved-beam element model and a 7 degrees of freedom vehicle model, respectively. The TMD system was simulated with the use of multiple rigid-body systems linked with springs and dampers. Road surface condition, as a vibration source, was simulated with the use of a frequency equivalent method based on a power spectrum. A variably-accelerated pattern search algorithm was proposed in line with the initial TMD parameters calculated by Den Hartog formula. Visual software was compiled by Fortran and used for an optimization study of vibration reduction. A three-span, curved, continuous steel-box girder bridge was used as the numerical example. Optimized effects and computational efficiency of vibration reduction under different methods were compared. The comparison included a single variable optimization based on Den Hartog formula, an ergodic search method, an integer programming method, a traditional genetic algorithm, a traditional pattern search algorithm, and a variably-accelerated pattern search algorithm. The results indicate that variably-accelerated pattern search algorithm is more efficient at improving TMD optimal parameter design. Final TMD parameter optimization values obtained by different methods are quite close to each other and tends verify the reliability of the optimization results.

Real-time control for at-limit handling driving on a predefined path

ABSTRACTAutonomous driving at at-limit handling represents a big challenge due to the nonlinear behaviour of a vehicle. In this paper, a hierarchical control scheme composed of two Nonlinear Model Predictive Controls (NMPCs) for path following is proposed. This structure allows for real-time feasibility without having to simplify excessively the vehicle model. The higher level NMPC operates on a long prediction horizon with a point-mass model which constraints are given by a tyre dependant ‘g–g diagram’. The output of the higher level is a velocity profile which is used as terminal constraint by the lower level NMPC. This operates on a short horizon and is based on a seven degrees of freedom vehicle model with full Pacejka Magic Formula tyre formulation on all tyres, load transfers and Limited Slip Differential. Because of the terminal set computed by the higher level, it is possible to use a short horizon and exploit the vehicle performance in real-time. For both controllers, the full Nonlinear Optimisation Problem is solved at each step. The algorithm is tested in a Model-in-the-Loop environment where a validated Vi-Grade vehicle model is controlled in co-simulation. The results show the effectiveness and feasibility of real-time control with complex vehicle models.

Adaptive Control Allocation with Communication Delay for In-Wheel Propulsion Electric Vehicles

In this paper, an integrated, fault-tolerant control approach for yaw stability of ground vehicles is outlined in the presence of actuator and sensor network delay. In order to simultaneously control all actuators in the vehicle, an adaptive control allocation method is used. The proposed control scheme consists of a high level controller that creates a virtual control input vector and a low level control allocation that distributes the virtual control effort among redundant actuators. Virtual control input consists of desired traction force, desired yaw moment and required lateral force correction to ensure stability while following a given reference. Based on this virtual control input vector, the allocation module determines front steering angle correction, rear steering angle, traction forces at each wheel. Presented control structure is simulated by using a 10 Degree of freedom vehicle model. Results show that the proposed approach can follow the references despite the loss of actuator effectiveness in the driving cycle with the presence of delay in the communication system while the system with no adaptive allocation fails to stay on course.

Simulation analysis of efficiency and stability for vehicle’s ABS control on combined steering and braking maneuvers

Eight degrees of freedom vehicle model was established. Using the method of fuzzy control, the ABS control algorithm was designed based on slip ratio. Simulation analysis was done at speed of 15m/s, 20m/s, 25m/s under turning braking. The results show that the vehicle braking performance and vehicle stability at middle or low speed was improved by using the ABS controller, but qualitative analysis shows that phenomenon of vehicle instability was appeared at high-speed conditions. The turning braking stability under ABS controller was judged quantificationally by the stability judging formula. The results show that the requirements of stability control could not meet with only Anti-lock Braking System.

Analysis and optimization of coupled vibration between substructures of a multi-axle vehicle

The vibration from transport vehicles may negatively affect the ride comfort in the cab and the product safety in the carriage. A 15 degrees of freedom vehicle model consisted of a cab, a carriage, a chassis, and mounts and suspensions between them are introduced to present the vibration behavior of a three-axle vehicle. Two indices, the coupling factor and the vibration attenuation factor, are employed to quantify the correlation between structures and the vibration isolation capability of subsystems. A sensitivity analysis is carried out with a 43-factor optimal Latin hypercube design, concerning the effect of mass properties, geometries, stiffness, and damping on the vibration coupling effect and the vibration attenuation of subsystems. Results show obvious trade-offs between the vibration coupling effect and the vibration attenuation among different subsystems. Based on the significant factor identified, multi-objective optimizations are conducted to improve the vibration performance of both the cab and the carriage and simultaneously reduce the correlations between structures using different algorithms. Comparison between different optimal results indicates that a compromise can be achieved between the ride comfort and the cargo safety based on a lightweight constraint.

Analysis of dynamic characteristics of nonlinear vehicle suspension system with five degrees of freedom

With the rapid development of the automobile industry, the performance requirements of the automobile has been becoming higher and higher which shows the great significance of the study on vehicle suspension characteristics. Based on the structural characteristics of the vehicle, a five degree of freedom vehicle model is established. The dynamic equation of the vehicle model is listed by using the vibration law of the multi degree of freedom damping system. The simulation model of five degree of freedom linear and nonlinear system of automobile is established by using MATLAB/SIMULINK. The simulation analysis of ride comfort is carried out based on simulated nonlinear stiffness: Compared with the results of linear and nonlinear parameters, the nonlinear stiffness coefficient alpha is monotonically decreasing in -0.4∼0, which can improve the ride comfort of the vehicle. The nonlinear stiffness mainly affects the seat acceleration, the centroid acceleration and the pitching acceleration. The nonlinear system is optimized by the obtained law concluded from simulation. The results show that the performance of the suspension system can be greatly improved, the mean square root value of the centroid acceleration is reduced by 38.67 % and the mean square root value of the pitching acceleration is reduced by 44.54 %, the mean square root value of the seat acceleration is reduced by 11.31 %, and the improvement of vehicle ride comfort is very obvious.

Study of YSC used for all Electric Independent Driving and Braking Electric Vehicle based on Fuzzy PI Control

Vehicle handling and stability performance is the premise of giving full play to the performance advantages of all electric independent driving and braking electric vehicle (abbr. AIDBEV). This paper presents the working principle of yaw stability control (abbr. YSC) used for AIDBEV. The YSC adopts fuzzy PI control algorithm. For verifying the control effect of YSC, a simulation platform based on fifteen degrees of freedom vehicle model is built. The sinusoidal steering with amplitude and period increasing is used for simulation. According to the simulation results, the yaw rate can be controlled near the target value when YSC works, but the vehicle is unstable when YSC does not work. Take front left wheel as an example, the maximum braking torque of EMB is reduced by 372.9Nm, accounting for 58% of the total braking torque, and the working time of EMB is reduced by 0.265s, accounting for 49.53% of total working time. This can provide potentiality to optimize EMB. By coupled brake, IWM can recover energy 18.77kJ. It has certain energy saving effect, too.

Research on the compensation method of Indirect Tire Pressure Monitoring under Sinusoidal Driving Condition

Indirect tire pressure monitoring method (ITPMS) is based on the wheel speed signal differences indirectly infer that the change of the tire pressure. In the steering mode, there is a large yaw rate, and there is a big deviation between the four wheels’ speed. The traditional indirect tire pressure monitoring method based on wheel speed comparison method is invalid. That the automobiles which is matched electronic stability control system estimate the four-wheel speed according to the yaw rate and steering wheel angle become an important method to improve the accuracy of Indirect tire pressure monitoring. Four-wheel vehicle kinematics model for turning condition is established to compensate for the wheel speed in the steering mode, avoid the misjudgment of indirect tire pressure monitoring system. The seven degree of freedom vehicle model and the four wheel speed model are established firstly, and analyse the four wheel speed change of the vehicle under the condition of a certain corner input in the simulation. Then conduct a test on the vehicle road, calculated using the four wheel speed distribution module model of vehicle wheel speed on the theoretical value of the actual value of the wheel speed compensation, so it can monitor the tire pressure in turning vehicle. When the error of the wheel speed is beyond the threshold, the wheel can be judged to be in the state of lack of gas.