Vehicle sideslip angle estimation for a heavy-duty vehicle via Extended Kalman Filter using a Rational tyre model

Vehicle sideslip angle is a key state for lateral vehicle dynamics, but measuring it is expensive and unpractical. Still, knowledge of this state would be really valuable for vehicle safety systems aimed at enhancing vehicle safety, to help to reduce worldwide fatal car accidents. This has motivated the research community to investigate techniques to estimate vehicle sideslip angle, which is still a challenging problem. One of the major issues is the need for accurate tyre model parameters, which are difficult to characterise and subject to change during vehicle operation. This paper proposes a new method for estimating vehicle sideslip angle using an Extended Kalman Filter. The main novelties are: i) the tyre behaviour is described using a Rational tyre model whose parameters are estimated and updated online to account for their variation due to e.g. tyre wear and environmental conditions affecting the tyre behaviour; ii) the proposed technique is compared with two other methods available in the literature by means of experimental tests on a heavy-duty vehicle. Results show that: i) the proposed method effectively estimates vehicle sideslip angle with an error limited to 0.5 deg in standard driving conditions, and less than 1 deg for a high-speed run; ii) the tyre parameters are successfully updated online, contributing to outclassing estimation methods based on tyre models that are either excessively simple or with non-varying parameters

Study on the generalized formulations with the aim to reproduce the viscoelastic dynamic behavior of polymers

Appropriate modelling of the real behavior of viscoelastic materials is of fundamental importance for correct studies and analyses of structures and components where such materials are employed. In this paper, the potential to employ a generalized Maxwell model and the relative fraction derivative model is studied with the aim to reproduce the experimental behavior of viscoelastic materials. For both models, the advantage of using the pole-zero formulation is demonstrated and a specifically constrained identification procedure to obtain the optimum parameters set is illustrated. Particular emphasis is given on the ability of the models to adequately fit the experimental data with a minimum number of parameters, addressing the possible computational issues. The question arises about the minimum number of experimental data necessary to estimate the material behavior in a wide frequency range, demonstrating that accurate results can be obtained by knowing only the data of the upper and low frequency plateaus plus the ones at the loss tangent peak

Tyre-road adherence conditions estimation for intelligent vehicle safety applications

It is well recognized in the automotive research community that knowledge of the real-time tyre-road friction conditions can be extremely valuable for intelligent safety applications, including design of braking, traction, and stability control systems. This paper presents a new development of an on-line tyre-road adherence estimation methodology and its implementation using both Burckhardt and LuGre tyre-road friction models. The proposed strategy first employs the recursive least squares to identify the linear parameterization (LP) form of Burckhardt model. The identified parameters provide through a Takagi-Sugeno (T-S) fuzzy system the initial values for the LuGre model. Then, it is presented a new large-scale optimization based estimation algorithm using the steady state solution of the partial differential equation (PDE) form of LuGre to obtain its parameters. Finally, real-time simulations in various conditions are provided to demonstrate the efficacy of the algorithm

Transient tire slip losses using the brush theory

Tire slip losses have been shown to have a significant impact on vehicle performance in terms of energy efficiency, thus requiring accurate studies. In this paper, the transient dissipation mechanisms connected to the presence of micro-sliding phenomena occurring at the tire–road interface are investigated analytically. The influence of a two-dimensional velocity field inside the contact patch is also considered in light of the new brush theory recently developed by the authors. Theoretical results align with findings already known from literature but suggest that the camber and turn spins contribute differently to the slip losses and should be regarded as separate entities when the camber angle is sufficiently large. The present work shows that an additional amount of power which relates to the initial sliding conditions is generated or lost during the unsteady-state maneuvers. A simple example is presented to illustrate the discrepancy between the microscopic and macroscopic approaches during a transient maneuver

Analytical results in transient brush tyre models: theory for large camber angles and classic solutions with limited friction

This paper establishes new analytical results in the mathematical theory of brush tyre models. In the first part, the exact problem which considers large camber angles is analysed from the perspective of linear dynamical systems. Under the assumption of vanishing sliding, the most salient properties of the model are discussed with some insights on concepts as existence and uniqueness of the solution. A comparison against the classic steady-state theory suggests that the latter represents a very good approximation even in case of large camber angles. Furthermore, in respect to the classic theory, the more general situation of limited friction is explored. It is demonstrated that, in transient conditions, exact sliding solutions can be determined for all the one-dimensional problems. For the case of pure lateral slip, the investigation is conducted under the assumption of a strictly concave pressure distribution in the rolling direction

Rolling, tilting and spinning spherical wheels: Analytical results using the brush theory

This paper investigates the rolling dynamics of spherical wheels using the theoretical framework provided by the brush models. The analysis is mainly conducted under the assumption of vanishing sliding inside the contact patch. Different types of kinematics are considered: simply rolling wheels, rolling and tilting, and purely spinning. For the first two cases, a complete solution is derived concerning both the steady-state and transient behaviours. Some qualitative trends for the forces and moments generated inside the contact patch are then provided when accounting for limited friction. For the case of a purely spinning spherical wheel, it is shown that steady-state conditions are never possible owing to the assumption of vanishing sliding. Moreover, it is demonstrated that the shear stresses acting inside the contact patch grow unbounded if the additional contribution relating to the deflection of the bristle is not taken into account when calculating the total sliding velocity. In this case, a stationary solution may be eventually recovered as an asymptotic distribution only by assuming limited friction inside the contact patch

Torque Vectoring Control for fully electric Formula SAE cars

Fully electric vehicles with individually controlled powertrains can achieve significantly enhanced vehicle response, in particular by means of Torque Vectoring Control (TVC). This paper presents a TVC strategy for a Formula SAE (FSAE) fully electric vehicle, the “T-ONE” car designed by “UninaCorse E-team” of the University of Naples Federico II, featuring four in-wheel motors. A Matlab-Simulink double-track vehicle model is implemented, featuring non-linear (Pacejka) tyres. The TVC strategy consists of: i) a reference generator that calculates the target yaw rate in real time based on the current values of steering wheel angle and vehicle velocity, in order to follow a desired optimal understeer characteristic; ii) a high-level controller which generates the overall traction/braking force and yaw moment demands based on the accelerator/brake pedal and on the error between the target yaw rate and the actual yaw rate; iii) a control allocator which outputs the reference torques for the individual wheels. A driver model was implemented to work out the brake/accelerator pedal inputs and steering wheel angle input needed to follow a generic trajectory. In a first implementation of the model, a circular trajectory was adopted, consistently with the "skid-pad" test of the FSAE competition. Results are promising as the vehicle with TVC achieves up to � 9% laptime savings with respect to the vehicle without TVC, which is deemed significant and potentially crucial in the context of the FSAE competition

On the estimation of tyre self-aligning moment through a physical model and the trick tool

The understanding of tyre-road interactions plays a fundamental role in the design of advanced vehicle controllers for enhancing performance and safety. Although there are interesting contributions in the literature that look at estimating tyre-road forces, little has been done on estimating the self-aligning moment. This paper proposes a new method to estimate the selfaligning moment, based on a brush model and a tyre force estimator tool. The idea is that: i) the parameters of a physical model (the brush model) can be optimised to match the lateral forces obtained through a reliable tyre force estimator tool; ii) the optimised model can then be used to compute the self-aligning moment, due to a key feature of the brush model, i.e. that it is a physical model. Hence, unlike other contributions, this method does not require experimental measurements of the self-aligning moment, nor the steering torque. A fitting function is also proposed for the length and width of the contact patch of a tyre as a function of the vertical load. Results show the satisfactory estimation of the lateral force and the consequent selfaligning moment trends, based on experimental manoeuvres carried out on a handling track with a performance-oriented vehicle

A real-time thermal model for the analysis of tire/road interaction in motorcycle applications

While in the automotive field the relationship between road adherence and tire temperature is mainly investigated with the aim to enhance the vehicle performance in motorsport, the motorcycle sector is highly sensitive to such theme also from less extreme applications. The small extension of the footprint, along with the need to guarantee driver stability and safety in the widest possible range of riding conditions, require that tires work as most as possible at a temperature able to let the viscoelastic compounds - constituting the tread and the composite materials of the whole carcass structure - provide the highest interaction force with soil. Moreover, both for tire manufacturing companies and for single track vehicles designers and racing teams, a deep knowledge of the thermodynamic phenomena involved at the ground level is a key factor for the development of optimal solutions and setup. This paper proposes a physical model based on the application of the Fourier thermodynamic equations to a three-dimensional domain, accounting for all the sources of heating like friction power at the road interface and the cyclic generation of heat due to rolling and to asphalt indentation, and for the cooling effects due to air forced convection, to road conduction and to turbulences in the inflation chamber. The complex heat exchanges in the system are fully described and modelled, with particular reference to the management of contact patch position, correlated to camber angle and requiring the adoption of an innovative multi-ribbed and multilayered tire structure. The completely physical approach induces the need of a proper parameterization of the model, whose main stages are described, both from the experimental and identification points of view, with particular reference to non-destructive procedures for thermal parameters definition