Self-aligning Torque Research Articles

Self-aligning active agents with inertia and active torque.

We extend the study of the inertial effects on the two-dimensional dynamics of active agents to the case where self-alignment is present. In contrast with the most common models of active particles, we find that self-alignment, which couples the rotational dynamics to the translational one, produces unexpected and nontrivial dynamics, already at the deterministic level. Examining first the motion of a free particle, we contrast the role of inertia depending on the sign of the self-aligning torque. When positive, inertia does not alter the steady-state linear motion of an a-chiral self-propelled particle. On the contrary, for a negative self-aligning torque, inertia leads to the destabilization of the linear motion into a spontaneously broken chiral symmetry orbiting dynamics. Adding an active torque, or bias, to the angular dynamics, the bifurcation becomes imperfect in favor of the chiral orientation selected by the bias. In the case of a positive self-alignment, the interplay of the active torque and inertia leads to the emergence, out of a saddle-node bifurcation, of solutions which coexist with the simply biased linear motion. In the context of a free particle, the rotational inertia leaves unchanged the families of steady-state solutions but sets their stability properties. The situation is radically different when considering the case of a collision with a wall, where a very singular oscillating dynamics takes place which can only be captured if both translational and rotational inertia are present.

Measurement of the lateral characteristics and identification of the Magic Formula parameters of city and cargo bicycle tyres

The paper presents measurements of the lateral force and self-aligning torque from cargo and city bicycle tyres. Based on the experimental data, we have determined the parameters for the Magic Formula model, for lateral force and self-aligning torque. We performed tests with VeTyT, an indoor test rig specific for bicycle tyres, under different vertical loads (ranging from 343 N to 526 N), camber angles (−5, 0, 5) deg and inflation pressure (from 300 kPa to 500 kPa). For each condition, we evaluated the cornering stiffness and found that it generally decreases with the increase in inflation pressure for the tour/city bicycle tyres. However, the cargo tyre tested showed an opposite trend, with an increase in the cornering stiffness as the inflation pressure increased from 300 kPa to 400 kPa.

Design of the Steering Feedback Controller of a Steer-by-Wire System Using Admittance Model

The steer-by-wire (SbW) system is a promising system in the realm of automotive engineering. It substitutes the mechanical connection between the steering wheel and the front road wheels with an electronic signal-based functional connection. The SbW system offers several advantages over conventional steering systems, including weight reduction, reduced vibration, and enhanced steering functionality configuration. However, the absence of a mechanical linkage in the SbW system gives rise to certain challenges. The SbW system requires endowing adequate steering feel such as damping and reaction force using feedback motor, and the road wheel needs robust control of pinion motor for normal load variation by passengers and self-aligning torque as external disturbance. The SbW system is composed of the steering feedback module (SFM) and the road wheel module (RWM). This paper proposes a control approach to generate steering feel for SFM, in which steering feel is generated using an admittance model based on velocity control. A disturbance observer is applied to ensure robustness of velocity control. The steering wheel torque versus steering wheel angle (T–A) curve is used to analyze steering feel characteristic and evaluate steering feel. The proposed steering system is validated through experiments that confirm its ability to provide satisfactory steering feel for vehicles. This work may offer a novel solution for the design of advanced steering systems in the field for the future mobility such as an autonomous driving.

Twisting torque – A simplified theoretical model for bicycle tyres

In this paper, the twisting torque of bicycle tyres is studied. The twisting torque is just the self-aligning torque for null lateral slip and non-null camber. The relationship between twisting torque and contact patch area has been analyzed. As the latter increases, twisting torque increases as well. A theoretical model to evaluate twisting torque has been implemented. Since twisting torque is mainly due to longitudinal slip in cambered wheel, increasing the contact patch area the stresses are located at a larger distance from the median plane of the contact patch. The resulting torque will be higher in magnitude.Finally, the model has been validated comparing the outcomes with the experimental data, with a mean error less than 3% for camber angles less than 10°.

Study on the Self-Aligning Torque of BMW and Chevrolet During Driving and Its Influence on Vehicle Dynamic Performance

The existence of self-aligning torque makes the wheel direction of the car consistent with the driving direction, which is the key to ensure the stable straight-line driving of the car. In this paper, we will mainly apply Python to establish the force and motion models of BMWM3 and Chevrolet under different driving modes, and work through the function of the self-aligning torque through the classical calculation model of the self-aligning torque. In our calculation, we examine the variation of self-aligning torque of BMW and Chevrolet with the change of time under various driving conditions. Then, we evaluated the dynamic mechanical properties of the vehicle during driving, and provide reference for the design of vehicle parameters. We also proved their relationship between self-aligning torque and slip angle for the two cars and found the maximum torque values according to the slip angle. Use such model, it becomes possible to calculate the real-time self-aligning torque only with the data measured by python programming.

Event-triggered adaptive sliding mode control for steer-by-wire systems with actuator fault

The event-triggered tracking control is studied for the steer-by-wire (SbW) system with actuator fault, inaccurate dynamic model, and external disturbance. First, an adaptive sliding mode control based on event-triggering mechanism is proposed. The lumped nonlinearity, including friction torque and self-aligning torque of SbW systems, is approximated by an adaptive robust radial basis function neural network (RBFNN). Robust terms of sliding mode control attenuate the negative effects of the actuator fault, modeling error, external disturbance, and event-triggering error on control performance. More importantly, the sliding-mode high-frequency switching control appears in the high-order derivative of sliding variable without increasing the input–output relative degree, thereby eliminating chattering. Furthermore, the designed method can achieve the practical finite-time stability. The proposed event-triggering mechanism can strictly exclude Zeno behavior and economize the communication resources. Finally, simulations and experiments show the effectiveness of the proposed algorithm.

Research on compliance steers of strut type front suspension subject to lateral force and self-aligning torque during cornering

In this paper, mechanism of compliance steers for lateral force and self-aligning torque is studied for strut type front suspension, which is commonly used in front wheel drive vehicle with transverse engine. First, through qualitative consideration, it is clarified that both of the compliance steers for lateral force and self-aligning torque consist of changes in toe-angle of three modes. Mode I is the change in toe-angle due to difference of displacements of the points on steering knuckle. Mode II is the change in toe-angle due to rotation of the lower arm. Mode III is the change in toe-angle due to displacement of the upper support of the suspension. In addition, it is shown that effects of design specifications of the suspension on the modes of compliance steer for lateral force and those for self-aligning torque are different. Based on this consideration, guidelines for design of strut type front suspension in terms of compliance steers for lateral force and self-aligning torque are presented. Then, CAE analysis for a suspension model based on a commercial vehicle is performed to confirm validity of the qualitative consideration as well as to show that compliance steer for self-aligning torque can have significance greater than that for lateral force.

Selection of the Optimal Tire for an FSAE Vehicle based on Evaluation of Key Performance Parameters

Tires are the components which physically connect the vehicle body to the ground, thus choosing the correct set of tires is important, not only to achieve the most out of the car but also to provide the platform, based on which the suspension and steering geometry of the vehicle are designed. This selection has to be based on the comparison of various available sets of tires and evaluating them based on key performance parameters, such as peak lateral force (Fy), peak self-aligning torque (Mz), instantaneous cornering stiffness and instantaneous camber stiffness. The tire which gives the best possible combination of all these parameters would help achieve sufficiently good acceleration and speed, and also have a sufficiently large window of operation, where it is robust and less sensitive to changes. Thus, the tire, which achieves the best balance of properties between performance, driveability, cost and robustness would be the chosen tire for the car, which forms the basis of the next steps of the chassis design.

Adaptive control of dual-motor autonomous steering system for intelligent vehicles via Bi-LSTM and fuzzy methods

In order to achieve better trajectory tracking of intelligent vehicle on different road surfaces, which include underling the weather of rain and snow, an adaptive tire cornering stiffness strategy (ACS) and a trajectory tracking autonomous steering control strategy were proposed in this paper. Firstly, the tire–road friction coefficient estimator was designed to obtain the tire–road friction coefficient based on Bi-LSTM neural network, then combining the tire cornering stiffness coefficient by fuzzy controller to obtain the online tire cornering stiffness. Secondly, considering the uncertainty of tire cornering stiffness, a trajectory tracking upper-level controller based on model predictive control (MPC) algorithm was proposed to calculate the optimal front wheel angle. Thirdly, in order to better adapt to various road conditions, a dynamic equivalent stiffness model is proposed to replace the self-aligning torque model during vehicle steering, and a lower-level controller for pinion gear target position tracking was designed based on the sliding mode control (SMC) algorithm. In addition, this paper also designed a dual-motor control strategy, which cooperates with the pinion gear target position tracking lower-level controller to quickly and accurately achieve the target front wheel angle. Finally, the simulation and HiL test results show that the proposed control algorithm greatly improves the trajectory tracking accuracy and stability of the intelligent vehicle on roads with different tire–road friction coefficients.

An Adaptive PI Controller by Particle Swarm Optimization for Angle Tracking of Steer-by-Wire

In this article, a novel steer-by-wire system architecture called iSteer is designed to realize the high performance of steering angle tracking for self-driving vehicles (especially, self-driving trucks), where the vehicle steers in response to the virtual driver’s command instead of the driver’s hand wheel. Based on a newly steering dynamical model of the iSteer system,an adaptive proportional-integral controller with parameters tuning by particle swarm optimization is developed for real-time or embedded application. Hence, the fast and efficient computation plays an essential role in our control law design. The developed steering controller not only meets this computational demand but also takes into account the self-aligning torque and ground resistance torque (as the disturbances to the iSteer control system). According to the system transfer function, the one-step prediction of steering angle is utilized to find the best particle of the swarm. Through a graph analysis using Nyquist stability criterion, we prove that the steering control system is stable and the error of steering angle tracking is convergent. Some experiments are tested on the physical iSteer system with the developed steering controller, the results of which further verify the effectiveness of the designed architecture and the high performance (e.g., high precision in tracking and fast response time) of the developed control law for steering angle tracking in self-driving vehicle without hand wheel.

Theoretical Tire Model Considering Two-Dimensional Contact Patch for Force and Moment

ABSTRACT The new theoretical tire model for force and moment has been developed by considering a two-dimensional contact patch of a tire with rib pattern. The force and moment are compared with the calculation by finite element method (FEM). The side force predicted by the theoretical tire model is somewhat undervalued as compared with the FEM calculation, while the self-aligning torque predicted by the theoretical tire model agrees well with the FEM calculation. The shear force distribution in a two-dimensional contact patch under slip angle predicted by the proposed model qualitatively agrees with the FEM calculation. Furthermore, the distribution of the adhesion region and sliding region in a two-dimensional contact patch predicted by the theoretical tire model qualitatively agrees with the FEM calculation.

Hybrid adaptive learning neural network control for steer-by-wire systems via sigmoid tracking differentiator and disturbance observer

Steer-by-Wire (SbW) systems are usually affected negatively by the friction torque and self-aligning torque. This paper proposes a hybrid learning neural network controller to achieve precise control for the SbW system. Firstly, a sigmoid tracking differentiator (STD) is introduced to obtain the velocity signal with the angle measurement only. Secondly, by combining the model-free technology, the neural network is applied to overcome the lumped uncertainty including the friction torque and self-aligning torque. Different from the related literature, a second-order identification model is designed to construct the learning law so that the neural network can be adjusted by the tracking error and modeling error simultaneously. Finally, a disturbance observer is proposed for the compensation of compound disturbance including the external disturbance and neural network approximated error. The advantages are that the proposed control scheme not only ensures good tracking performance using the least sensors but also can handle uncertainty and attenuate measurement noise. Lyapunov stability theory proves that the tracking error is uniformly ultimately bounded. Numerical simulations and experiments show the effectiveness and superiorities of the proposed control method.

Discrete-time adaptive neural network control for steer-by-wire systems with disturbance observer

This paper investigates the design and implementation of the discrete-time adaptive neural network control with disturbance observer (DO) on a steer-by-wire (SbW) system, to simultaneously realize accurate tracking and anti-interference performance. Specifically, to approximate the lumped system uncertainty including the friction torque and self-aligning torque, the neural network is employed. To improve the steering tracking performance, the discrete-time identification model is proposed so that the tracking error and modeling error can be utilized to adjust the neural network updating law. Then, the unknown compound disturbances caused by external disturbance, Euler approximation errors and neural network approximation error are restrained by two DOs. Finally, the Lyapunov stability theory shows that the system tracking error is uniformly ultimately bounded. Both numerical simulations and experiments are implemented to show the superiority of the proposed controller.

Design and experimental implementation of observer-based adaptive neural network steering control for automated vehicles

In this paper, an observer-based adaptive neural network controller is developed for the Steer-by-Wire (SbW) system of automated vehicles with uncertain nonlinearity and unmeasured state. An observer is introduced to estimate the angular velocity of the front wheels, so the hardware cost and the complexity of mechanical structure and electronic circuits are reduced. Then, an observer-based adaptive neural network controller is proposed for the SbW system to achieve excellent steering precision. A radial basis function (RBF) neural network is used to model the uncertain nonlinearity, which mainly includes self-aligning torque and unknown friction torque with strong nonlinearity. The adaptive law of the RBF neural network designed by fuzzy basis functions rather than by its filtering is derived by Lyapunov stability theory and the Strictly Positive Real (SPR) condition. The tracking error and the observation error can be guaranteed to converge asymptotically to zero. Simulation and experimental results for two paths highlight the effectiveness of the proposed control algorithm.

Observer-based event-triggered control of steer-by-wire systems with prespecified tracking accuracy

This paper addresses the event-triggered tracking control problem of the SbW system subject to unavailable steering angular velocity of front-wheels, time-varying external disturbance, and uncertain dynamics, including friction torque and self-aligning torque. First, an adaptive state observer is proposed to estimate the unavailable steering angular velocity of front-wheels. The uncertain nonlinearity and time-varying disturbance can be estimated by the adaptive interval type-2 fuzzy logic system (IT2 FLS) and the disturbance observer, respectively. An event-triggered control is proposed for SbW systems to guarantee the prespecified control performance and save communication resources in the controller-to-actuator channel. Much importantly, the nested robust terms are incorporated in the control scheme to counteract the observation error and overcome the negative influence of the event-triggering error. Theoretical analysis shows that the prespecified arbitrary tracking accuracy can be guaranteed within finite time, and the Zeno-behavior can be strictly avoided while saving communication resources in the controller-to-actuator channel. Finally, simulation and vehicle experiment results and some comparisons are given to evaluate the effectiveness of the proposed method.

Fault diagnosis and prognosis of steer-by-wire system based on finite state machine and extreme learning machine

In this paper, an integrated condition monitoring method combining model-based fault diagnosis and data-driven prognosis is proposed for steer-by-wire (SBW) system. First, the SBW system is modeled by bond graph (BG) technique and a two-degree-of-freedom (2-DOF) state-space model of the vehicle is built. Based on the 2-DOF model, the estimated self-aligning torque is used for the control of feedback motor. The fault detection is carried out by evaluating the analytical redundancy relations derived from the BG model. Since the fault isolation performance is essential to subsequent fault estimation process, a new fault isolation method based on finite state machine is developed to improve the isolation ability by combining the dependent and independent analytical redundancy relations, where the number of potential faults could be decreased. In order to refine the possible fault set to determine the true fault, a cuckoo search (CS)–particle filter is developed for fault estimation. Based on the estimated true fault, prognosis can be implemented which is important to achieve failure prevention and prolong system lifespan. To this end, an optimized extreme learning machine (OELM) is proposed where the input weights and hidden layer biases are optimized by CS. Based on data representing fault values obtained from the fault identification, the OELM model is trained for remaining useful life prediction of failing component. Finally, the proposed methodologies are validated by simulations.

Research on tire cornering force and self-aligning torque at low speeds and high speeds.

Research on tire cornering force and self-aligning torque at low speeds and high speeds.

Design and applications of steering angle tracking control with robust compensator for steer-by-wire system of intelligent vehicle

Abstract The steer-by-wire (SBW) system is a key component for an intelligent vehicle, which is related to the safety, comfort, and drivability of vehicle. Hence, it is supposed to ensure strong robustness and functional safety under various operating conditions, which is one of the main difficulties of SBW. In this paper, a linear quadratic regulator (LQR) with a novel robust compensator is designed for steering angle control of SBW to improve the tracking performance. The SBW actuator is regarded as a permanent magnet synchronous motor (PMSM) control system with parameter perturbation and external disturbance, including Coulomb friction and self-aligning torque. Theoretical analysis proves that the proposed method can ensure the system stability and make the tracking error converge to zero against multiple uncertainties. The main parameters are obtained by offline calculation and the online calculation burden is small, so the proposed method is suitable for vehicle applications. Both simulations and experiments show that the robust compensator is effective.

Transferring From Automated to Manual Driving When Traversing a Curve via Haptic Shared Control

Under certain scenarios, an automated driving system (ADS) might need to transfer steering control to the human driver. Even if the driver is ready to take over, an abrupt control transition when traversing a curve can lead to unstable steering. This is because the steering wheel is balanced by both the self-aligning torque and ADS torque; if the latter suddenly disappears, the balance is lost. In this study, we developed a method for transferring control when traversing a curve via haptic shared control. A driving simulator experiment was conducted to verify the effectiveness of the proposed method. The results demonstrated that the proposed method exhibits better steering and vehicle motion stability than a non-shared control method.

Analysis and Prediction of Tire Cornering Properties for Different Inflation Pressures Based on Deflection Control

ABSTRACT The variation of inflation pressure has an important effect on the mechanical characteristics of tires that can affect vehicle performance, so the influence of inflation pressure should be taken into account in high-precision tire models. Much research has focused on tire mechanical characteristics under different inflation pressures and modeling methods, such as the Improved Magic Formula/Swift Tire model developed by Schmeitz et al. that takes inflation pressure into account. Based on a large number of tire testing data under different inflation pressures, an empirical model can be obtained, but numerous tire tests are expensive and cannot reveal the mechanism. In previous studies, most tire tests were based on load control, wherein the load is constant while the footprint, carcass, and belt stiffness can change with the variation of inflation pressure, making the cornering characteristics much more complicated. Herein, a method of deflection control is used and the contact patch is well maintained. The effect of tire inflation pressure is simplified to be the change of structure stiffness and averaged contact pressure. The effect of inflation pressure on cornering properties under deflection control is systematically observed under different tire deflection values. In addition, a prediction model extended from the Magic Formula model is proposed. The model of Schmeitz et al. [1,2] needs test data from at least three inflation pressures; the model proposed herein requires tests at only two inflation pressures. The validation shows that this prediction method has good accuracy, almost the same as that of the model of Schmeitz et al. The error index of the lateral force is at most 2%, and the error index of the self-aligning torque is 4% at the maximum.