Nonlinear Tire Research Articles

Coordination control strategy of motion stability and tire slip for electric vehicle driven by in-wheel-motors

The Direct Yaw Moment Control (DYC) is a widely utilized technique for electric vehicles equipped with In-Wheel Motors (IWMs) to ensure yaw stability. However, most existing DYC studies calculate the additional control yaw moment solely based on the torque differences among the four IWMs, disregarding the nonlinear tire characteristics and wheel rotational movements. When road conditions are poor or torque changes are intense, the tire may slip, preventing it from generating the required longitudinal tire force for the desired direct yaw moment. To address this challenge, this study introduces a coordination control strategy for motion stability and tire slip in electric vehicles (EV) driven by IWMs. To enhance control performance, the nonlinear tire characteristics and wheel rotational movements are integrated into the modeling process when calculating tire forces. Additionally, a state and parameter coupling estimation algorithm is utilized to obtain feedback on tire parameters and vehicle motion states. Using these estimation results as a foundation, a coordination strategy is developed to achieve reference motion state tracking and tire slip ratio control. The Model Predictive Control (MPC) algorithm is employed to solve the control problem with constraints on both control inputs and outputs, and the estimation results are utilized to update the control model as well as provide states feedback. Simulations and experiments are conducted to validate the feasibility and effectiveness of the proposed control strategy. The results demonstrate that our proposed control strategy effectively improves vehicle stability by coordinating vehicle motion and tire slip control.

Interacting multiple model-based yaw stability control for distributed drive electric vehicle via adaptive model predictive control algorithm

The vehicle lateral stability control is a challenging problem due to the tire nonlinearity and the immeasurable sideslip angle. Thus, an adaptive model predictive control (AMPC) scheme based on interacting multiple model (IMM) vehicle sideslip angle observer is proposed in this paper. First, the observer is composed of the Extended Kalman filter (EKF) and the Unscented Kalman filter (UKF), which improves the real-time performance as well as the observation accuracy. Then, a multi-objective controller based on adaptive vehicle model prediction is designed using model predictive control algorithm. This controller aims to achieve a balance between the actuation and state constraints. The T-S fuzzy algorithm is used to observe the tire cornering stiffness and design an adaptive vehicle model. By utilizing the appropriate objective function and a quadratic programing solver, the controller output is obtained to achieve vehicle stability control. Finally, the effectiveness of the designed AMPC scheme under various working conditions is verified by Carsim-Simulink joint simulation platform and hardware-in-the-loop (HIL) test.

Design of Active Posture Controller for Trailing-Arm Vehicle: Improving Path-Following and Handling Stability

To address the question of which posture trailing-arm vehicles (TAVs) should be adopted while driving, this study introduces an innovative active posture controller (APC) to improve both path-following and handling stability performance. Leveraging a nonlinear tire model that considers corner load variation and wheel camber, alongside the kinematics and double-track model of TAVs, the impact of vehicle body posture on handling performance has been investigated. To fully utilize the four-wheel independent drive and posture adjustable characteristics of the TAV mechanisms, an integrated nonlinear model predictive control (NMPC) combining APC and tire forces distribution is devised. Through simulations conducted using Simulink-Multibody (2023a), the effectiveness of the proposed controller is demonstrated, particularly when compared to the scheme that does not account for the unique posture adjustment mechanisms of TAVs.

Model Predictive Control for Trajectory Planning Considering Constraints on Vertical Load Variation

To address the issue of centrifugal force affecting the vertical load during the stability and trajectory planning of autonomous vehicles during high-speed cornering and obstacle avoidance, a model predictive control of trajectory planning and tracking is proposed that considers the roll factor using only a two-degrees-of-freedom vehicle dynamics model. Firstly, a trajectory planning controller is designed. As a predictive model, a dual-track two-degrees-of-freedom vehicle dynamics model is established. This model describes the relationship between tire lateral forces and vertical loads using a quadratic nonlinear tire model. To reflect the actual dynamic state of the vehicle, the controller incorporates a nonlinear constraint that considers vertical load variations. The nonlinear optimization problem is transformed into a simplified quadratic programming problem by using the Jacobian matrix method to linearize the constraints. By fitting a fourth-degree polynomial curve to the discrete points calculated by the replanning algorithm, an optimal collision-free trajectory is obtained. Secondly, an MPC trajectory tracking controller is designed to control the vehicle in real time along the optimal trajectory from the planning, incorporating control quantity constraints, control increment constraints, and lateral angle constraints to maintain the vehicle’s motion state. We transform the trajectory tracking control problem into a quadratic programming problem, solving for the optimal control sequence for the autonomous vehicle to track the trajectory, achieving an optimized solution and rolling time domain control. Finally, the effectiveness of the vehicle’s obstacle avoidance planning and tracking under high-speed double-lane-change maneuver conditions is validated using the Simulink simulation platform. The results indicate that the designed planning and tracking controllers effectively improve the obstacle avoidance planning and tracking control for high-speed autonomous vehicles.

Sideslip Angle Fusion Estimation Method of Three-Axis Autonomous Vehicle Based on Composite Model and Adaptive Cubature Kalman Filter

A sideslip angle fusion estimation strategy of three-axis vehicle based on adaptive cubature Kalman filter is investigated in this paper. According to the dynamics model, kinematics model of the three-axis vehicle, and considering the influence of tire nonlinearity, the vehicle state estimators under different conditions are designed by using the adaptive cubature Kalman filter algorithm. The dynamic-model-based estimator with linear tire model, dynamic-model-based estimator with nonlinear tire model, and kinematical-model-based estimator are proposed, then, according to the application characteristics of different estimators, a fusion estimation strategy of vehicle sideslip angle based on adaptive fuzzy weight controllers is designed, so as to improve the overall estimation accuracy by integrating the advantages of the three estimators. The simulation and experimental results show that the presented fusion estimation strategy can effectively improve the estimation accuracy of vehicle sideslip angle, and the comprehensive estimation accuracy reaches 94.37%.

Development of Coordinator for Optimal Tireforces Distribution for Vehicle Dynamics Control Considering Nonlinear Tire Characteristics

Development of Coordinator for Optimal Tireforces Distribution for Vehicle Dynamics Control Considering Nonlinear Tire Characteristics

Nonlinear tyre model-based sliding mode observer for vehicle state estimation

Nonlinear tyre model-based sliding mode observer for vehicle state estimation

Direct yaw moment control of eight-wheeled distributed drive electric vehicles based on super-twisting sliding mode control

This paper proposed a novel direct yaw moment control (DYC) system to enhance vehicle stability and handling performance in various driving conditions and overcome the chattering problem of traditional sliding mode control. Accordingly, a DYC strategy is developed for eight-wheeled DDEVs by utilizing a super-twisting sliding mode (STSM) algorithm. Initially, a three-degrees-of-freedom model, nonlinear tire model, and motor model are established for vehicles. Subsequently, the reference yaw rate is obtained based on the reference model of the vehicle to serve as a control target. The DYC strategy is then established using the error between the actual yaw rate and the reference yaw rate as the input. Moreover, a traditional sliding mode (SM) controller is developed to enhance vehicle stability. A second-order SM controller is designed by incorporating a STSM control algorithm to address the chattering problem associated with traditional SM controllers. The algorithm adaptively adjusts the sliding surface and controls the gains based on the dynamic state of the vehicle. The effectiveness of the proposed control strategy is validated via hardware-in-the-loop simulations.

Tire Performance and Testing under Longitudinal and Combined Slip States: Induced vs Resultant Wheel-Related Slip

ABSTRACT Tires influence many overall vehicle characteristics, including safety, performance, comfort, and handling. Testing is needed to characterize tires for the selection of original equipment manufacturers submissions as well as for the development of other suspension and chassis components. The reality that tire responses are highly nonlinear and change significantly with temperature, wear, and surface pairing makes testing to adequately characterize tires for vehicle development difficult. Furthermore, achieving robust, repeatable braking and driving measurements is particularly challenging. Unlike cornering tests, the test rig input is directly opposed to the tire response vector. Moreover, using an estimated parameter (e.g., slip ratio) as a control value prohibits a clear distinction between the linear test rig input and the nonlinear tire response. In this paper, the influence of the wheel-related slip control on tire performance under longitudinal and combined slip conditions is investigated. Two different tire types are measured in a laboratory environment on an MTS Flat-Trac CT+ tire test rig. A variety of test procedures are used to consider the influence of slip and torque rates under different operating conditions (e.g., wheel loads). A recommendation is given for a low-wear and cost-efficient testing methodology for an improved assessment of tire longitudinal and combined slip characteristics by using a linear test rig input.

Enhanced vehicle shimmy performance using inerter-based suppression mechanism

Shimmy may occur in the vehicle normal driving process, which is a harmful motion and should be controlled in practical engineering. In order to improve the vehicle driving and handling stability, four kinds of passive inerter-based suppression mechanisms are proposed and applied in the vehicle suspension to improve its shimmy performance. The configurations S1 and S2 are composed of one inerter and one damper, which are in parallel-connected and series-connected, respectively, furthermore, an auxiliary spring is added to constitute configurations S3 and S4. Combined with the magic nonlinear tire model, the vehicle shimmy model with four inerter-based suppression mechanisms is established using Lagrange theory, its shimmy performance is studied using bifurcation analysis method, the stable area and limit cycle oscillation (LCO) magnitude of the system are obtained and compared with those of the original suspension system. The effect of the structural parameters of the inerter-based suppression mechanisms on the vehicle shimmy performance is analyzed, and the structural parameter optimization of the inerter-based suppression mechanism is investigated. The results show that the only parallel-connected and series-connected configurations S1 and S2 have little improvement effect on the vehicle shimmy performance. As the configurations S3 and S4 are used, the unstable area dominated by left and right steering shimmy reduces, the shimmy occurred vehicle velocity range becomes narrower and the maximum LCO magnitude of the front wheel swing motion becomes smaller, which suppresses the vehicle shimmy effectively and clarifies the benefits of the inerter and the necessity of adding the auxiliary spring. In addition, larger inertance of the inerter and smaller stiffness of the auxiliary spring is beneficial to improve the vehicle shimmy performance. The optimized structural parameters of the configurations S3 and S4 are obtained, which maintain the vehicle shimmy system stable, and further shorten the time for the vehicle shimmy system to reach stability. Therefore, the inerter-based suppression mechanism can effectively restrain the vehicle shimmy motion and give guiding significance for the design of vehicle shimmy suppression mechanism.

Experimental validation of sensor fault estimation for vehicle dynamics with a nonlinear tire model

Sensor fault estimation in an automotive application is crucial for the safe execution and availability of software functions controlling the vehicle. Especially, in situations at the grip limits of the tires the safety of the passengers is most critical and a nonlinear tire model is required for accurate predictions. However, the influence of a nonlinear tire model for sensor fault estimation in an automotive application is not sufficiently analyzed in the literature.In this paper, the influence of a nonlinear tire model on sensor fault estimation during highly dynamic cornering maneuvers is demonstrated. A two-stage Extended Kalman Filter (TSEKF) based on a simple state transformation is used for the estimation of additive and multiplicative faults in longitudinal/lateral acceleration and yaw rate. The proposed estimation algorithm was implemented in real-time on a dSPACE MicroAutoBox II and experimental results with multiple measurements of an Audi S8 (D5) are used for validation of the results. The estimation performance during the measurements, using a linear and a nonlinear tire model, is analyzed and the influence of the state transformation on the accuracy of the filter is investigated.Using a simple nonlinear tire model the state estimation performance under nonlinear operating conditions can be improved by up to 79%, thereby reducing false positive detections significantly. Furthermore, the results show that for the considered system without the use of a state transformation, i.e., neglecting the state-fault cross-covariance, degrades the estimation performance by less than 1%.

Intelligent vehicle path tracking control strategy considering data-driven dynamic stable region constraints

The path tracking controller can easily reduce the tracking error, but often exceed the limitations of vehicle stability. In this paper, an intelligent vehicle path tracking control strategy considering data-driven dynamic stable region constraints is proposed. Firstly, based on the two-degree-of-freedom (DOF) vehicle model and nonlinear tire model, the vehicle sideslip angle-sideslip angular velocity ([Formula: see text]) phase plane is established. Then, the stable region dataset is made considering the influence of vehicle speed, adhesion coefficient, and front wheel angle. To get the vehicle driving stable region, a back propagation neural network (BP-NN) regression model is trained offline. Subsequently, a path tracking control strategy based on adaptive-model predictive control (MPC) is designed, which considers the vehicle dynamic stable region constraints with the BP-NN predicting online. Finally, model-in-the-loop (MIL) and driving simulator is designed to test the control strategy, which indicates that it has a better performance compared with the linear quadratic regulator (LQR) path tracking controller.

Shimmy Suppression of an Aircraft Nose Landing Gear Using Torsional Nonlinear Energy Sink

Abstract Shimmy motion may occur for an aircraft nose landing gear (NLG) during its takeoff, landing, and taxiing procedure, which is an undesirable motion and should be suppressed. Here, a novel torsional nonlinear energy sink (NES) based on the cam-roller mechanism is proposed and applied in the NLG to improve its shimmy performance. The torsional NES is connected with the upper and lower struts of the NLG and its mechanical characteristic is studied. A seven-dimensional dynamic model of the NLG coupled with NES is built, which considers the NLG torsional and lateral motions, and the nonlinear tire model. The numerical continuation method is applied to analyze its shimmy performance, the stable area and limit cycle oscillation (LCO) amplitude are acquired, further compared with those of the original NLG without using the NES. The results show that as the NES is used in the NLG, the torsional shimmy dominated unstable area reduces significantly and the lateral shimmy dominated unstable area decreases slightly, which results in the increase of the stable area of the NLG; the maximum LCO amplitudes for the NLG torsional and lateral shimmy become smaller, the forward speed ranges as the torsional and lateral shimmy occur become narrower, which indicates that the stable forward speed ranges of the NLG become wider; the NLG shimmy performance improves as the NES has larger torsional inertia and damping, and smaller torsional linear stiffness. Thus, the NES can suppress the NLG shimmy motion and enhance its shimmy performance effectively.

Optimized Active Collision Avoidance Algorithm of Intelligent Vehicles

This research introduces an innovative strategy to impede and lessen lateral and rear-end vehicular collisions by consolidating braking systems with active emergency steering controls. This study puts forward a T-type active emergency steering method, designed to circumvent both lateral and rear-end collisions at vehicular intersections. To secure vehicular stability and condense the time required for steering during the T-type active emergency process, this research formulates a nonlinear dynamic model for the vehicle, in addition to a nonlinear tire model. This study also engages in a thorough analysis of the constraints linked to the initial and terminal states of the steering process. The issue at hand is articulated as an optimization control problem with boundary value restrictions, which is subsequently resolved using the Radau pseudospectral method. Simulation results corroborate that the prompt commencement of the anti-collision strategy can effectively deter potential collisions. This pioneering approach shows considerable promise in augmenting the active safety of intelligent vehicles and bears meaningful implications for high-precision automotive collision evasion systems.

Integrated Control of Steering and Braking for Path Tracking Using Multi-Point Linearized MPC

In this study, we propose an integrated braking and steering model predictive controller for stable and accurate path tracking. To perform model-based longitudinal control and lateral control at the same time, it is necessary to consider nonlinear characteristics caused by changing vehicle speed and nonlinear tire forces. This paper proposes a multipoint linearization method to minimize the linearization error, and a controller with good computational efficiency and accurate consideration of nonlinear vehicle behavior is also introduced. In addition, the proposed model predictive controller (MPC) actively utilizes the road friction limit constraint for each tire force to ensure vehicle stability. Through this, the proposed controller generates optimal braking and steering inputs for situations such as high-speed turns in which braking must be involved. Due to the proposed linearized model, the controller achieves a significant improvement in computational efficiency and good control performance similar to that of the nonlinear MPC. Comparison with other control methods and performance verification for various road conditions are performed through simulations, and the results show very efficient calculation while performing accurate path tracking.

Modeling and Verification of Tire Nonlinearity Effect on Accuracy of Vehicle Yaw Rate Calculation

<div class="section abstract"><div class="htmlview paragraph">The desired yaw rate is a vital target parameter for vehicle stability control, which is currently determined as a steady-state yaw rate by the linear single-track vehicle model. Tire nonlinearity deteriorates the effect of vehicle stability control at larger lateral acceleration. This paper proposes a new calculation method of the steady-state yaw rate considering the tire nonlinearity based on the brush tire model. To validate and verify the proposed method, step steering tests of the target vehicle under different lateral accelerations are carried out on a real proving ground. The results show that when the lateral acceleration is relatively small, the difference between the calculation results of the proposed method and the traditional one is not apparent, and both methods can provide a good estimation for the steady-state yaw rate; however, when the lateral acceleration is relatively large, the difference becomes apparent. It can be shown that the linear tire model cannot be able to calculate the steady-state yaw rate accurately, while the brush tire model agrees well with the observation. This difference shows the importance of considering tire nonlinearity in vehicle stability control, especially in extreme driving conditions. By analyzing the existence of the solution of the yaw rate equation, this paper finds that the vehicle speed upper limit under which the vehicle can be able to achieve steady-state steering is also affected by the tire nonlinearity. A Simulink vehicle model is built to verify the steady-state vehicle speed upper limit for vehicles with different steering characteristics. The results of the modeling and tests provide certain guidelines for developing a vehicle stability control system.</div></div>

Nonlinear model predictive control for autonomous vehicle drifting

In this paper, nonlinear model predictive control (NMPC) is proposed for autonomous vehicle drifting, that is, stabilizing the vehicle at a desired unstable equilibrium point. Firstly, a three-degree-of-freedom vehicle model with a nonlinear tire model is introduced, and the equilibrium points are calculated. The relationship between the desired unstable equilibrium point and the lateral stability region is analyzed based on the phase plane method. Secondly, NMPC is designed to force vehicle states to stay around the desired unstable equilibrium point, that is, to keep the vehicle in sustained drifting. The terminal region and terminal constraint of NMPC are determined off-line to guarantee stability. Thirdly, Koopman operator theory and dynamic mode decomposition with control are introduced to obtain an approximately linear model, by which the nonlinear optimization problem is converted to a quadratic programming problem. Finally, comparative experiments are conducted by simulation, in which various model uncertainties are considered. The effectiveness of the proposed approach to achieve sustained autonomous drifting and to ensure vehicle safety is illustrated, and the efficient implementation of the proposed approach is also shown.

Using a novel fuzzy 3-inputs algorithms to control the active hydraulic stabilizer bar with the complex model of the vehicle nonlinear dynamics.

Under the influence of centrifugal force, the rollover phenomenon may occur. The vehicle rolls over when the wheel is completely separated from the road surface, i.e., the vertical force of the wheel is reduced to zero. To overcome this problem, the active stabilizer bar is used at the front and rear axles of the vehicle. The active stabilizer bar works on the difference in fluid pressure inside the hydraulic motor. This article is aimed at studying the vehicle rollover dynamics when the hydraulic stabilizer bar is used. In this article, the model of a complex dynamic is established. This is a combination of the model of spatial dynamics, the model of nonlinear double-track dynamics, and the nonlinear tire model. The operation of the hydraulic actuator is controlled by a fuzzy algorithm with 3-inputs. The defuzzification rule is determined based on the combination of 27 cases. The process of calculation and simulation is done with four specific cases corresponding to steering angles. In each case, three situations were investigated. Besides, the speed of the vehicle is also gradually increased from v1 to v4. As a result of the simulation, which was performed in the MATLAB-Simulink environment, the output values such as roll angle, change of the vertical force, and roll index were significantly reduced when the active stabilizer bar was used. If the vehicle does not use the stabilizer bar, the vehicle may roll over in both the second, third, and fourth cases. If the vehicle uses a mechanical stabilizer bar, this also occurs in the third and fourth cases (only at a very high velocity, v4). However, the rollover phenomenon did not occur if the vehicle used a hydraulic stabilizer bar controlled by the fuzzy 3-inputs algorithm. In all investigated cases, the stability and safety of the vehicle are always guaranteed. Besides, the responsiveness of the controller is also very good. An experimental process needs to be conducted to verify the correctness of this research.

Robust Gain-Scheduling Path Following Control of Autonomous Vehicles Considering Stochastic Network-Induced Delay

This paper concerns the robust gain-scheduling control issue for autonomous path following systems with stochastic network-induced delay. Firstly, to effectively approximate the highly nonlinear tire dynamics, the linear fractional transformation formulations are employed to describe the tire cornering stiffness with a norm-bounded uncertainty. Secondly, by taking the data dropout and delay encountered in signal computation and transmission into account, a more generalized lumped delay form is proposed to unify the time-varying data dropout and network-induced delay. Moreover, a Markovian process is presented to describe the lumped delay as a stochastic distribution. Thirdly, to address the issue of varying vehicle velocity, a linear parameter varying model is established to capture vehicle lateral behaviors. Based on the stochastic stability theory, a new robust gain-scheduling path following control method is proposed for the autonomous vehicles. Finally, the experimental study is presented to bridge the gap between the theoretical and practical investigations on path following control of autonomous vehicles, and results validate the superior performance of the proposed method compared with existing works.

Efficient Nonlinear Model Predictive Control of Automated Vehicles

In this paper, an efficient model predictive control (MPC) of velocity tracking of automated vehicles is proposed, in which a reference signal is given a priori. Five degree-of-freedom vehicle dynamics with nonlinear tires is chosen as the prediction model, in which coupling characteristics of longitudinal and lateral dynamics are taken into account. In order to balance computational burden and prediction accuracy, Koopman operator theory is adopted to transform the nonlinear model into a global linear model. Then, the global linear model is used in the design of MPC to reduce online computational burden and avoid solving nonconvex/nonlinear optimization problems. Furthermore, the effectiveness of Koopman operator in vehicle dynamics control is verified using a Matlab/Simulink environment. Validation results demonstrate that dynamic mode decomposition with control (DMDc) and extended dynamic mode decomposition (EDMD) algorithms are more accurate in model validation and dynamic prediction than local linearization, and DMDc algorithm has less computational burden on solving optimization problems than the EDMD algorithm.