Stability and local bifurcation analyses of two-wheeled trailers considering the nonlinear coupling between lateral and vertical motions

The nonlinear dynamics of two-wheeled trailers is investigated using a spatial 4-DoF mechanical model. The non-smooth characteristics of the tire forces caused by the detachment of the tires from the ground and other geometrical nonlinearities are taken into account. Beyond the linear stability analysis, the nonlinear vibrations are analyzed with special attention to the nonlinear coupling between the vertical and lateral motions of the trailer. The center manifold reduction is performed leading to a normal form up to third degree terms. The nature of the emerging periodic solutions, and, thus, the sense of the Hopf bifurcations are verified semi-analytically and numerically. Simplified models of the trailer are also used in order to point out the practical relevance of the study. It is shown that the linearly independent pitch motion affects the sense of the Hopf bifurcations at the linear stability boundary. Namely, the constructed spatial trailer model provides subcritical bifurcations for higher center of gravity positions, while the commonly used simplified mechanical models explore the less dangerous supercritical bifurcations only. Domains of loss of contact of tires are also detected and shown in the stability charts highlighting the presence of unsafe zones. Experiments are carried out on a small-scale trailer to validate the theoretical results. A good agreement can be observed between the measured and numerically determined critical speeds and vibration amplitudes.

An Energy Efficient Control Strategy for Electric Vehicle Driven by In-Wheel-Motors Based on Discrete Adaptive Sliding Mode Control

This paper presents an energy efficient control strategy for electric vehicle (EV) driven by in-wheel-motors (IWMs) based on discrete adaptive sliding mode control (DASMC). The nonlinear vehicle model, tire model and the IWM model are established at first to represent the operation mechanism of the whole system. Based on the modeling, two virtual control variables are used to represent the longitudinal and yaw control efforts to coordinate the vehicle motion control. Then DASMC method is applied to calculate the required total driving torque and yaw moment, which can improve the tracking performance as well as the system robustness. According to the vehicle nonlinear model, the additional yaw moment can be expressed as a function of longitudinal and lateral tire forces. For further control scheme development, a tire force estimator using unscented Kalman filter is designed to estimate real-time tire forces. On these bases, energy efficient torque allocation method is developed to distribute the total driving torque and differential torque to each IWM, considering the motor energy consumption, the tire slip energy consumption and the brake energy recovery. Simulation results of the proposed control strategy using co-platform of Matlab/Simulink and CarSim® demonstrate that it can accomplish the vehicle motion control in a coordinated and economic way.

A Universal Approach to Tire Forces Estimation by Accelerometer-Based Intelligent Tire: Analytical Model and Experimental Validation

ABSTRACT Efforts to improve the performance and safety of vehicles include placing active sensing components (e.g., embedded microsensors) within tires result in intelligent tires. One application of intelligent tire is tire force estimation based on accelerometers. However, its development is limited due to the difficulty of relating the tire force to kinematical information by model-based theory. In this manuscript, a universal approach to tire forces estimation by the accelerometer-based intelligent tire is formulated and experimentally validated. First, a microelectromechanical system accelerometer-based intelligent tire prototype is established with the function of on-board monitoring of tire forces. Then, a theoretical rolling kinematics model is proposed for illustrating the mechanisms of acceleration fields, resulting from the coupling effect of rigid body motion and elastic deformation. An analytical model is formulated to estimate the vertical force in real time. Furthermore, the beam model is adopted to describe lateral deformations of the tire belt, directly linking lateral acceleration and lateral force. Finally, the lateral force can be estimated by lateral acceleration and vertical force already estimated. Based on a universal analytical model, the lateral force estimation method realizes high accuracy under different circumstances, even with unified coefficients, by clarifying and eliminating the influence of ply steer. A field test and two bench experiments have been conducted to fully validate the developed model. It can be concluded that the theoretical-analysis-based estimation model realizes an encouraging tire force estimation application with an intelligent tire hardware system.

Vehicle Dynamic Control with 4WS, ESC and TVD under Constraint on Front Slip Angles

To enhance vehicle maneuverability and stability, a controller with 4-wheel steering (4WS), electronic stability control (ESC) and a torque vectoring device (TVD) under constraint on the front slip angles is designed in this research. In the controller, the control allocation method is adopted to generate yaw moment via 4WS, ESC and TVD. If the front steering angle is added for generating yaw moment, the steering performance of the vehicle can be further deteriorated. This is because the magnitude of the lateral tire forces are limited and the required yaw moment is insufficient. Constraint is imposed on the magnitude of the front slip angles in order to prevent the lateral tire forces from saturating. The driving simulation is performed by considering the limit of the front slip angle proposed in this study. Compared to the case that uses the existing 4WS, the results of this study are derived from the actuator combination that enhances performance while maintaining stability.

Path Tracking Control of Autonomous Vehicle Based on Nonlinear Tire Model

The tire forces of vehicles will fall into the non-linear region under extreme handling conditions, which cause poor path tracking performance. In this paper, a model predictive controller based on a nonlinear tire model is designed. The tire forces are characterized with nonlinear composite functions of the magic formula instead of a simple linear relation model. Taylor expansion is used to linearize the controller, the first-order difference quotient method is used for discretization, and the partial derivative of the composite function is used for matrix transformation. Constant velocity and variable velocity conditions are selected to compare the designed controller with the conventional controller in Carsim/Simulink. The results show that when the tire forces fall in the nonlinear region, two controllers have good stability, and the tracking accuracy of the controller designed in this paper is slightly better. However, after the tire forces become nonlinear, the controller with linear tire force becomes worse, the tracking accuracy is far worse than the controller with the nonlinear tire model, and the vehicle stability is also degraded. In addition, an active steering test platform based on LabVIEW-RT is established, and hardware-in-the-loop tests are carried out. The effectiveness of the designed controller is verified.

A New Torque Distribution Control for Four-Wheel Independent-Drive Electric Vehicles

Torque distribution control is a key technique for four-wheel independent-drive electric vehicles because it significantly affects vehicle stability and handling performance, especially under extreme driving conditions. This paper, which focuses on the global yaw moment generated by both the longitudinal and the lateral tire forces, proposes a new distribution control to allocate driving torques to four-wheel motors. The proposed objective function not only minimizes the longitudinal tire usage, but also make increased use of each tire to generate yaw moment and achieve a quicker yaw response. By analysis and a comparison with prior torque distribution control, the proposed control approach is shown to have better control performance in hardware-in-the-loop simulations.

Vertical Tire Forces Estimation of Multi-Axle Trucks Based on an Adaptive Treble Extend Kalman Filter

Vertical tire forces are essential for vehicle modelling and dynamic control. However, an evaluation of the vertical tire forces on a multi-axle truck is difficult to accomplish. The current methods require a large amount of experimental data and many sensors owing to the wide variation of the parameters and the over-constraint. To simplify the design process and reduce the demand of the sensors, this paper presents a practical approach to estimating the vertical tire forces of a multi-axle truck for dynamic control. The estimation system is based on a novel vertical force model and a proposed adaptive treble extend Kalman filter (ATEKF). To adapt to the widely varying parameters, a sliding mode update is designed to make the ATEKF adaptive, and together with the use of an initial setting update and a vertical tire force adjustment, the overall system becomes more robust. In particular, the model aims to eliminate the effects of the over-constraint and the uneven weight distribution. The results show that the ATEKF method achieves an excellent performance in a vertical force evaluation, and its performance is better than that of the treble extend Kalman filter.

Modular estimation of lateral vehicle dynamics and application in optimal AFS control

The paper introduces a novel modular estimation approach for lateral vehicle and tire dynamics using a simplified vehicle model and a non-linear estimation algorithm. A dynamics-oriented representation of lateral tire forces with a single track lateral vehicle model (STVM) has been introduced. Subsequently, extended Kalman filter (EKF) based distributed observer modules for each dynamical parameter has been designed and combined into a Unified Estimation Scheme (UES). Finally, a linear quadratic regulator (LQR) based Active Front Steering (AFS) control system has been designed using the estimated parameters. The accuracy and computational efficiency of the designed scheme has been analyzed and compared to non-modular UKF, EKF, and Particle Filter (PF) algorithms, through Monte-Carlo Simulations using the CarSim dataset for both high and low [Formula: see text] surfaces, followed by further validation using real-time dataset. The results show that the proposed system significantly improve the accuracy and speed of estimation, as well as stable performance in closed loop control.

Should a Vehicle Always Deviate to the Tire Blowout Side? - A New Tire Blowout Model with Toe Angle Effects

As a severe tire failure, tire blowout during driving can significantly threaten vehicle stability and road safety. Tire blowout models were developed in the literature to conclude that a vehicle always deviates to the tire blowout side. However, this conclusion is proved to be inaccurate in this paper, since one important factor was largely ignored in the existing tire blowout models. Toe angle, as a basic and widely-applied setup on ground vehicles, can provide preset and symmetric lateral tire forces for normal driving. However, when tire blowout occurs, different toe angle setups can impact vehicle motions in different ways. For the first time, the toe angle is explicitly considered and integrated into a tire blowout model in this paper. For different tire blowout locations, driving maneuvers, and drivetrain configurations, the impacts of different toe angle setups on the variations of tire friction forces and vehicle motions are analyzed. The developed tire blowout model with toe angles is validated through both high-fidelity CarSim® simulation results and experimental results of a scaled test vehicle. Both simulation and experimental results show that a vehicle may not deviate to the tire blowout side, depending on the toe angle setups and driving maneuvers. Moreover, the experimental results also validate that the proposed tire blowout model can accurately evaluate the tire blowout impacts on vehicle dynamics.