Nonlinear Model Predictive Control for Integrated Energy-Efficient Torque-Vectoring and Anti-Roll Moment Distribution

This study applies nonlinear model predictive control (NMPC) to the torque-vectoring (TV) and front-to-total anti-roll moment distribution control of a four-wheel-drive electric vehicle with in-wheel-motors, a brake-by-wire system, and active suspension actuators. The NMPC cost function formulation is based on energy efficiency criteria, and strives to minimize the power losses caused by the longitudinal and lateral tire slips, friction brakes, and electric powertrains, while enhancing the vehicle cornering response in steady-state and transient conditions. The controller is assessed through simulations using an experimentally validated high-fidelity vehicle model, along ramp steer and multiple step steer maneuvers, including and excluding the direct yaw moment and active anti-roll moment distribution actuations. The results show: 1) the substantial enhancement of energy saving and vehicle stabilization performance brought by the integration of the active suspension contribution and TV; 2) the significance of the power loss terms of the NMPC formulation on the results; and 3) the effectiveness of the NMPC with respect to the benchmarking feedback and rule based controllers

On the model-based design of front-to-total anti-roll moment distribution controllers for yaw rate tracking

In passenger cars active suspensions have been traditionally used to enhance comfort through body control, and handling through the reduction of the tyre load variations induced by road irregularities. However, active suspensions can also be designed to track a desired yaw rate profile through the control of the anti-roll moment distribution between the front and rear axles. The effect of the anti-roll moment distribution relates to the nonlinearity of tyre behaviour, which is difficult to capture in the linearised vehicle models normally used for control design. Hence, the tuning of anti-roll moment distribution controllers is usually based on heuristics. This paper includes an analysis of the effect of the lateral load transfer on the lateral axle force and cornering stiffness. A linearised axle force formulation is presented, and compared with a formulation from the literature, based on a quadratic relationship between cornering stiffness and load transfer. Multiple linearised vehicle models for control design are assessed in the frequency domain, and the respective controllers are tuned through optimisation routines. Simulation results from a nonlinear vehicle model are discussed to analyse the performance of the controllers, and show the importance of employing accurate models of the lateral load transfer effect during control design

Search-Based Motion Planning for Performance Autonomous Driving

Driving on the limits of vehicle dynamics requires predictive planning of future vehicle states. In this work, a search-based motion planning is used to generate suitable reference trajectories of dynamic vehicle states with the goal to achieve the minimum lap time on slippery roads. The search-based approach enables to explicitly consider a nonlinear vehicle dynamics model as well as constraints on states and inputs so that even challenging scenarios can be achieved in a safe and optimal way. The algorithm performance is evaluated in simulated driving on a track with segments of different curvatures.Comment: Accepted to IAVSD 201

Optimization of the centre of mass position of a racing motorcycle in dry and wet track by means of the "Optimal Maneuver Method"

The "Optimal Maneuver Method" is an application of the optimal control theory that basically simulates an ideal driver and computes the actions and the trajectory to complete a maneuver in the minimum time. As an application of this method a 125 cc motorcycle and a real race circuit, in both dry and wet conditions, have been simulated, and the validation of the results by means of a comparison with real telemetry data is discussed. Afterwards two significant quantities, the height and the longitudinal position of the centre of mass of the vehicle, have been considered. The influence of variation on the minimum lap time, in the two track conditions discussed above, is presented

Evaluation of optimal yaw rate reference for electric vehicle torque vectoring

This work evaluates the intrinsic contribution of the yaw rate reference to the overall handling performance of an electric vehicle with torque vectoring control - in terms of minimum-time manoeuvring. A range of yaw rate references are compared through optimal control simulations incorporating closed-loop controller dynamics. Results show yaw rate reference has a significant effect on manoeuvre time

The optimality of the handbrake cornering technique

The paper investigates the optimality of the handbrake cornering, a strategy widespread among rally drivers. Nonlinear optimal control techniques are used to mimic real driver behavior. A proper yet simple cost function is devised to induce the virtual optimal driver to control the car at its physical limits while using the handbrake technique. The optimal solution is validated against experimental data by a professional rally driver performing the handbrake technique on a loose off-road surface. The effects of road surface, inertial properties, center of mass position, and friction coefficient are analyzed to highlight that the optimality of the maneuver does not depend on the particular vehicle data set used. It turns out that the handbrake maneuvering corresponds to the minimum time and minimum (lateral) space strategy on a tight hairpin corner. The results contribute to the understanding of one of the so-called aggressive driving techniques

Effect of handling characteristics on minimum time cornering with torque vectoring

In this paper, the effect of both passive and actively-modified vehicle handling characteristics on minimum time manoeuvring for vehicles with 4-wheel torque vectoring (TV) capability is studied. First, a baseline optimal torque vectoring strategy is sought, independent of any causal control law. An optimal control problem (OCP) is initially formulated considering 4 independent wheel torque inputs, together with the steering angle rate, as the control variables. Using this formulation, the performance benefit using torque vectoring against an electric drive train with a fixed torque distribution, is demonstrated. The sensitivity of TV-controlled manoeuvre time to the passive understeer gradient of the vehicle is then studied. A second formulation of the optimal control problem is introduced where a closed-loop torque vectoring controller is incorporated into the system dynamics of the OCP. This formulation allows the effect of actively modifying a vehicle’s handling characteristic via TV on its minimum time cornering performance of the vehicle to be assessed. In particular, the effect of the target understeer gradient as the key tuning parameter of the literature-standard steady-state linear single-track model yaw rate reference is analysed

On the optimality of handbrake cornering

The aim of this paper is to investigate the optimality of the handbrake cornering technique for a Front Wheel Drive vehicle. Nonlinear Optimal Control theory is used to formulate the problem of optimal cornering and to simulate manoeuvres used by race drivers. Handbrake cornering is optimal with an appropriate selection of the minimization cost. The optimal solution is validated against data collected during the execution of the technique by an expert race driver on a loose off-road surface. Further optimization results considering high adhesion road surface are obtained to show that the optimality of the technique is not affected by the road conditions

Trophic state and seasonal dynamics of phytoplankton communities in two sand-pit lakes at different succesional stages

The seasonal and inter-annual dynamics of phytoplankton in two Italian sand-pit lakes have been analysed over three years (2004-2006). The studied lakes, Ca' Morta (CM) and Ca' Stanga (CS), have a common origin and are contiguous, but are of different ages and have been managed in different ways. CM was created in 2002 and was still being dredged during the study period while sand quarrying in CS began in 1998 and ended at the beginning of the study period These conditions were thought to be of particular interest in assessing the influence of dredging activities on algal assemblages. Physical and chemical water parameters were also analysed to characterise the two lakes and investigate the effects of hydro-chemical features on phytoplankton. CS was stratified from April to October each year during the study period, while CM showed weaker thermal stratification. Conductivity, dissolved nitrate and dissolved reactive silica concentrations were greater in CM than in CS. The mixing depth/euphotic depth ratio was also higher in CM, probably because of water column mixing induced by hydraulic dredging. Overall. 185 phytoplankton taxa were found, of which ca 50% were present in both lakes. No significant diffrences in species richness were observed between lakes, but the decreasing trend of Simpson index values measured in CS showed a reduction in biodiversity after the excavation phose. Phytoplankton biomass was higher in CS than in CM, the latter being oligo-mesotrophic and the former mesotrophic. Diatoms and dinoflagellates were the dominant taxa in both lakes. The main differences in phytoplankton assemblages were related to the persistence of chryptophytes and chlorophytes in CM. Multivariate analyses support the hypothesis that different thermal patterns induced by dredging activities, along with certain physico-chemical parameters of the water, were the major factors shaping phytoplankton communities