A Simple Mono-Dimensional Approach for Lap Time Optimisation

Lap time minimisation methods have great relevance in the analysis of race tracks, and in the design and optimisation of race vehicles. Several lap time minimisation approaches have been proposed in the literature, which are computationally demanding because they need to either solve differential equations or to implement a forward−backward integration based on an apex-finding method. This paper proposes an alternative method, based on a mono-dimensional quasi-steady-state numerical approach. The proposed approach uses a simplified vehicle model accounting for combined tyre−road interactions, aerodynamic effects, and power limitations. The method exploits the knowledge of the curvature of the trajectory, which is worked out through a rigorous approach that allows for the use trajectories defined with respect to ageneric curve parameter and not necessarily the arc length. An iterative routine is implemented that exploits the vehicle dynamics, without solving differential equations or performing forward−backward integrations from the trajectory apexes. Simulations are carried out on three different tracks and are shown to be computationally efficient. Despite being intentionally simple, the proposed method allows to grasp key aspects of the problem, such as the effect of the combined tyre−road interactions on the acceleration profiles, and the effect of aerodynamic drag and downforce on the position of the braking point on the track and on the speed profile

Gravity balancing of a spatial serial 4-dof arm without auxiliary links using minimum number of springs

The principle of gravity balancing has been studied for a long time. It allows a system to be in indifferent equilibrium regardless of the configuration. In the literature, gravity balancing has often been achieved using appropriate combinations of springs and auxiliary links. Some paper address potential layouts without auxiliary links, but limited to planar mechanisms. This paper proposes a method to passively balance an anthropomorphic arm, with spatial kinematics, avoiding the use of auxiliary links. The approach used in this paper includes the analysis of all the contributions to the potential energy of the arm. It is shown that they are proportional (according to geometrical and inertial parameters) to scalar products between configuration-dependent unit vectors and/or configuration- independent unit vectors. Analysing the potential energy contributions for each combination of unit vectors, it is shown how to minimize the number of springs required to balance the mechanism without additional links. As a result, four possible layouts are developed, all of them using only two springs. Features and design issues of the four layouts are discussed. Finally, one of them is chosen for actual implementation

A state-of-the-art review on torque distribution strategies aimed at enhancing energy efficiency for fully electric vehicles with independently actuated drivetrains

© 2019, Levrotto and Bella. All rights reserved. Electric vehicles are the future of private passenger transportation. However, there are still several technological barriers that hinder the large scale adoption of electric vehicles. In particular, their limited autonomy motivates studies on methods for improving the energy efficiency of electric vehicles so as to make them more attractive to the market. This paper provides a concise review on the current state-of-the-art of torque distribution strategies aimed at enhancing energy efficiency for fully electric vehicles with independently actuated drivetrains (FEVIADs). Starting from the operating principles, which include the "control allocation" problem, the peculiarities of each proposed solution are illustrated. All the existing techniques are categorized based on a selection of parameters deemed relevant to provide a comprehensive overview and understanding of the topic. Finally, future concerns and research perspectives for FEVIAD are discussed

Yaw Rate and Sideslip Angle Control Through Single Input Single Output Direct Yaw Moment Control

Electric vehicles with independently controlled drivetrains allow torque vectoring, which enhances active safety and handling qualities. This article proposes an approach for the concurrent control of yaw rate and sideslip angle based on a single-input single-output (SISO) yaw rate controller. With the SISO formulation, the reference yaw rate is first defined according to the vehicle handling requirements and is then corrected based on the actual sideslip angle. The sideslip angle contribution guarantees a prompt corrective action in critical situations such as incipient vehicle oversteer during limit cornering in low tire-road friction conditions. A design methodology in the frequency domain is discussed, including stability analysis based on the theory of switched linear systems. The performance of the control structure is assessed via: 1) phase-plane plots obtained with a nonlinear vehicle model; 2) simulations with an experimentally validated model, including multiple feedback control structures; and 3) experimental tests on an electric vehicle demonstrator along step steer maneuvers with purposely induced and controlled vehicle drift. Results show that the SISO controller allows constraining the sideslip angle within the predetermined thresholds and yields tire-road friction adaptation with all the considered feedback controllers

A single input single output formulation for yaw rate and sideslip angle control via torque-vectoring

Many torque-vectoring controllers are based on the concurrent control of yaw rate and sideslip angle through complex multi-variable control structures. In general, the target is to continuously track a reference yaw rate, and constrain the sideslip angle to remain within thresholds that are critical for vehicle stability. To achieve this objective, this paper presents a single input single output (SISO) formulation, which varies the reference yaw rate to constrain sideslip angle. The performance of the controller is successfully validated through simulations and experimental tests on an electric vehicle prototype with four drivetrains

On the passive limited slip differential for high performance vehicle applications

The paper is aimed at a comprehensive revision of the working principles and limitations of the mechanical limited slip differential, the traditional, passive device used to improve traction capabilities and to extend the performance envelope of high performance road cars, racing and rally cars. Its impact on vehicle handling through a yaw moment generated with passive torque distribution across the drive axle is investigated by means of vehicle dynamics simulations

A Real-time Nonlinear Model Predictive Controller for Yaw Motion Optimization of Distributed Drive Electric Vehicles

This paper proposes a real-time nonlinear model predictive control (NMPC) strategy for direct yaw moment control (DYC) of distributed drive electric vehicles (DDEVs). The NMPC strategy is based on a control-oriented model built by integrating a single track vehicle model with the Magic Formula (MF) tire model. To mitigate the NMPC computational cost, the continuation/generalized minimal residual (C/GMRES) algorithm is employed and modified for real-time optimization. Since the traditional C/GMRES algorithm cannot directly solve the inequality constraint problem, the external penalty method is introduced to transform inequality constraints into an equivalently unconstrained optimization problem. Based on the Pontryagin’s minimum principle (PMP), the existence and uniqueness for solution of the proposed C/GMRES algorithm are proven. Additionally, to achieve fast initialization in C/GMRES algorithm, the varying predictive duration is adopted so that the analytic expressions of optimally initial solutions in C/GMRES algorithm can be derived and gained. A Karush-Kuhn-Tucker (KKT) condition based control allocation method distributes the desired traction and yaw moment among four independent motors. Numerical simulations are carried out by combining CarSim and Matlab/Simulink to evaluate the effectiveness of the proposed strategy. Results demonstrate that the real-time NMPC strategy can achieve superior vehicle stability performance, guarantee the given safety constraints, and significantly reduce the computational efforts

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

On the experimental analysis of single input single output control of yaw rate and sideslip angle

Electric vehicles with individually controlled drivetrains allow torque-vectoring, which improves vehicle safety and drivability. This paper investigates a new approach to the concurrent control of yaw rate and sideslip angle. The proposed controller is a simple single input single output (SISO) yaw rate controller, in which the reference yaw rate depends on the vehicle handling requirements, and the actual sideslip angle. The sideslip contribution enhances safety, as it provides a corrective action in critical situations, e.g., in case of oversteer during extreme cornering on a low friction surface. The proposed controller is experimentally assessed on an electric vehicle demonstrator, along two maneuvers with quickly variable tire-road friction coefficient. Different longitudinal locations of the sideslip angle used as control variable are compared during the experiments. Results show that: i) the proposed SISO approach provides significant improvements with respect to the vehicle without torque-vectoring, and the controlled vehicle with a reference yaw rate solely based on the handling requirements for high-friction maneuvering; and ii) the control of the rear axle sideslip angle provides better performance than the control of the sideslip angle at the centre of gravity

A gain scheduled robust linear quadratic regulator for vehicle direct yaw moment control

Yaw moment control systems improve vehicle stability and handling in severe driving manoeuvres. Nevertheless, the control system performance is limited by the unmodelled dynamics and parameter uncertainties. To guarantee robustness of the control system against system uncertainties, this paper proposes a gain scheduling Robust Linear Quadratic Regulator (RLQR), in which an extra control term is added to the feedback of a conventional LQR to limit the closed-loop tracking error in a neighbourhood of the origin of its state-space, despite of the uncertainties and persistent disturbances acting on the plant. In addition, the intrinsic parameter-varying nature of the vehicle dynamics model with respect to the longitudinal vehicle velocity can jeopardize the closed-loop performance of fixed-gain control algorithms in different driving conditions. Therefore, the control gains optimally vary based on the actual longitudinal vehicle velocity to adapt the closed-loop system to the variations of this parameter. The effectiveness of the proposed RLQR in improving the robustness of classical LQR against model uncertainties and parameter variations is proven analytically, numerically and experimentally. The numerical and experimental results are consistent with the analytical analysis proving that the proposed RLQR reduces the ultimate bound of error dynamics