Dr Davide Tavernini



Research interests

My teaching

Courses I teach on


My publications


ARTICLE (2020). Metzler, M., Tavernini, D., Gruber, P. and Sorniotti, A., 2018. On Prediction Model Fidelity in Explicit Nonlinear Model Predictive Vehicle Stability Control. IEEE Transactions on Control Systems Technology. (OPEN ACCESS)
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This study discusses vehicle stability control based on explicit nonlinear model predictive control (NMPC) and investigates the influence of prediction model fidelity on controller performance. The explicit solutions are generated through an algorithm using multiparametric quadratic programming (mp-QP) approximations of the multiparametric nonlinear programming (mp-NLP) problems. Controllers with different prediction models are assessed through objective indicators in sine-with-dwell tests. The analysis considers the following prediction model features: 1) nonlinear lateral tire forces as functions of slip angles, which are essential for the operation of the stability controller at the limit of handling. Moreover, a simple nonlinear tire force model with saturation is shown to be an effective alternative to a more complex model based on a simplified version of the Magic Formula; 2) longitudinal and lateral load transfers, playing a crucial role in the accurate prediction of the lateral tire forces and their yaw moment contributions; 3) coupling between longitudinal and lateral tire forces, which has a significant influence on the front-to-rear distribution of the braking forces generated by the controller; and 4) nonlinear peak and stiffness factors of the tire model, with visible yet negligible effects on the results.
ARTICLE (2020). Parra, A., Tavernini, D., Gruber, P., Sorniotti, A., Zubizarreta, A., Perez, J., 2020. On nonlinear model predictive control for energy-efficient torque-vectoring. IEEE Transactions on Vehicular Technology. (OPEN ACCESS)
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A recently growing literature discusses the topics of direct yaw moment control based on model predictive control (MPC), and energy-efficient torque-vectoring (TV) for electric vehicles with multiple powertrains. To reduce energy consumption, the available TV studies focus on the control allocation layer, which calculates the individual wheel torque levels to generate the total reference longitudinal force and direct yaw moment, specified by higher level algorithms to provide the desired longitudinal and lateral vehicle dynamics. In fact, with a system of redundant actuators, the vehicle-level objectives can be achieved by distributing the individual control actions to minimize an optimality criterion, e.g., based on the reduction of different power loss contributions. However, preliminary simulation and experimental studies - not using MPC - show that further important energy savings are possible through the appropriate design of the reference yaw rate. This paper presents a nonlinear model predictive control (NMPC) implementation for energy-efficient TV, which is based on the concurrent optimization of the reference yaw rate and wheel torque allocation. The NMPC cost function weights are varied through a fuzzy logic algorithm to adaptively prioritize vehicle dynamics or energy efficiency, depending on the driving conditions. The results show that the adaptive NMPC configuration allows stable cornering performance with lower energy consumption than a benchmarking fuzzy logic TV controller using an energy-efficient control allocation layer.
ARTICLE (2020). Shao, L., Karci, A. E. H., Tavernini, D., Sorniotti A. and Cheng, M., 2020. Design Approaches and Control Strategies for Energy-Efficient Electric Machines for Electric Vehicles – A Review, IEEE Access. (OPEN ACCESS)
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The market penetration of electric vehicles (EVs) is going to significantly increase in the next years and decades. However, EVs still present significant practical limitations in terms of mileage. Hence, the automotive industry is making important research efforts towards the progressive increase of battery energy density, reduction of battery charging time, and enhancement of electric powertrain efficiency. The electric machine is the main power loss contributor of an electric powertrain. This literature survey reviews the design and control methods to improve the energy efficiency of electric machines for EVs. The motor design requirements and specifications are described in terms of power density, efficiency along driving cycles, and cost, according to the targets set by the roadmaps of the main governmental agencies. The review discusses the stator and rotor design parameters, winding configurations, novel materials, construction technologies as well as control methods that are most influential on the power loss characteristics of typical traction machines. Moreover, the paper covers: i) driving cycle based design methods of traction motors, for energy consumption reduction in real operating conditions; and ii) novel machine topologies providing potential efficiency benefits.
ARTICLE (2020). So, K. M., Gruber, P., Tavernini, D., Karci, A. E., Sorniotti, A. and Motaln,T., 2020, On the Optimal Speed Profile for Electric Vehicles, IEEE Access. (OPEN ACCESS)
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The main question in eco-driving is – what speed or torque profile should the vehicle follow to minimize its energy consumption over a certain distance within a desired trip time? Various techniques to obtain globally optimal energy-efficient driving profiles have been proposed in the literature, involving optimization algorithms such as dynamic programming (DP) or sequential quadratic programming. However, these methods are difficult to implement on real vehicles due to their significant computational requirements and the need for precise a-priori knowledge of the scenario ahead. Although many predictions state that electric vehicles (EVs) represent the future of mobility, the literature lacks a realistic analysis of optimal driving profiles for EVs. This paper attempts to address the gap by providing optimal solutions obtained from DP for a variety of trip times, which are compared with simple intuitive speed profiles. For a case study EV, the results show that the DP solutions involve forms of Pulse-and-Glide (PnG) at high frequency. Hence, detailed investigations are performed to: i) prove the optimality conditions of PnG for EVs; ii) show its practical use, based on realistic electric powertrain efficiency maps; iii) propose rules for lower frequency PnG operation; and iv) use PnG to track generic speed profiles.
ARTICLE (2019). Ricco, M., Zanchetta, M., Cardolini, G., Tavernini, D., Sorniotti, A., Chatzikomis, C., ... & Dhaens, M., 2019. On the design of yaw rate control via variable front-to-total anti-roll moment distribution. IEEE Transactions on Vehicular Technology. (OPEN ACCESS)
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In vehicle dynamics, yaw rate control is used to improve the cornering response in steady-state and transient conditions. This can be achieved through an appropriate anti-roll moment distribution between the front and rear axles of a vehicle with controllable suspension actuators. Such control action alters the load transfer distribution, which in turn provokes a lateral tire force variation. With respect to the extensive set of papers from the literature discussing yaw rate tracking through active suspension control, this study presents: i) A detailed analysis of the effect of the load transfer on the lateral axle force and cornering stiffness; ii) A novel linearized single-track vehicle model formulation for control system design, based on the results in i); and iii) An optimization-based routine for the design of the non-linear feedforward contribution of the control action. The resulting feedforward-feedback controller is assessed through: a) Simulations with an experimentally validated model of a vehicle with active anti-roll bars (case study 1); and b) Experimental tests on a vehicle prototype with an active suspension system (case study 2).
ARTICLE (2019). Zanchetta, M., Tavernini, D., Sorniotti, A., Gruber, P., Lenzo, B., Ferrara, A., Sannen, K., De Smet, J. and De Nijs, W., 2019. Trailer control through vehicle yaw moment control: theoretical analysis and experimental assessment. Mechatronics. (OPEN ACCESS)
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This paper investigates a torque-vectoring formulation for the combined control of the yaw rate and hitch angle of an articulated vehicle through a direct yaw moment generated on the towing car. The formulation is based on a single-input single-output feedback control structure, in which the reference yaw rate for the car is modified when the incipient instability of the trailer is detected with a hitch angle sensor. The design of the hitch angle controller is described, including the gain scheduling as a function of vehicle speed. The controller performance is assessed by means of frequency domain and phase plane analyses, and compared with that of an industrial trailer sway mitigation algorithm. In addition, the novel control strategy is implemented in a high-fidelity articulated vehicle model for robustness assessment, and experimentally tested on an electric vehicle demonstrator with four on-board drivetrains, towing two different conventional single-axle trailers. The results show that: (i) the torque-vectoring controller based only on the yaw rate of the car is not sufficient to mitigate trailer instability in extreme conditions; and (ii) the proposed controller provides safe trailer behaviour during the comprehensive set of manoeuvres, thus justifying the additional hardware complexity associated with the hitch angle measurement.
ARTICLE (2019). Tavernini, D., Vacca, F., Metzler, M., Savitski, D., Ivanov, V., Gruber, P., Karci, A.E.H., Dhaens, M. and Sorniotti, A., 2019. An explicit nonlinear model predictive ABS controller for electro-hydraulic braking systems. IEEE Transactions on Industrial Electronics. (OPEN ACCESS)
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This study addresses the development and Hardware-in-the-Loop (HiL) testing of an explicit nonlinear model predictive controller (eNMPC) for an anti-lock braking system (ABS) for passenger cars, actuated through an electro-hydraulic braking (EHB) unit. The control structure includes a compensation strategy to guard against performance degradation due to actuation dead times, identified through experimental tests. The eNMPC is run on an automotive rapid control prototyping unit, which shows its real-time capability with comfortable margin. A validated high-fidelity vehicle simulation model is used for the assessment of the ABS on a HiL rig equipped with the braking system hardware. The eNMPC is tested in 7 emergency braking scenarios, and its performance is benchmarked against a proportional integral derivative (PID) controller. The eNMPC results show: i) the control system robustness with respect to variations of tire-road friction condition and initial vehicle speed; and ii) a consistent and significant improvement of the stopping distance and wheel slip reference tracking, with respect to the vehicle with the PID ABS.
ARTICLE (2019). Diez, D.R., Velenis, E., Tavernini, D., Smith, E.N., Siampis, E. and Soltani, A., 2019. Front/Rear Axle Torque Vectoring Control for Electric Vehicles. Journal of Dynamic Systems, Measurement, and Control, 141(6), p.061002.
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Vehicles equipped with multiple electric machines allow variable distribution of propulsive and regenerative braking torques between axles or even individual wheels of the car. Left/right torque vectoring (i.e., a torque shift between wheels of the same axle) has been treated extensively in the literature; however, fewer studies focus on the torque shift between the front and rear axles, namely, front/rear torque vectoring, a drivetrain topology more suitable for mass production since it reduces complexity and cost. In this paper, we propose an online control strategy that can enhance vehicle agility and “fun-to-drive” for such a topology or, if necessary, mitigate oversteer during sublimit handling conditions. It includes a front/rear torque control allocation (CA) strategy that is formulated in terms of physical quantities that are directly connected to the vehicle dynamic behavior such as torques and forces, instead of nonphysical control signals. Hence, it is possible to easily incorporate the limitations of the electric machines and tires into the computation of the control action. Aside from the online implementation, this publication includes an offline study to assess the effectiveness of the proposed CA strategy, which illustrates the theoretical capability of affecting yaw moment that the front/rear torque vectoring strategy has for a given set of vehicle and road conditions and considering physical limitations of the tires and actuators. The development of the complete strategy is presented together with the results from hardware-in-the-loop (HiL) simulations, using a high fidelity vehicle model and covering various use cases.
ARTICLE (2018). Tavernini, D., Metzler, M., Gruber, P. and Sorniotti, A., 2018. Explicit Nonlinear Model Predictive Control for Electric Vehicle Traction Control. IEEE Transactions on Control Systems Technology, (99), pp.1-14. (OPEN ACCESS)
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This paper presents a traction control (TC) system for electric vehicles with in-wheel motors, based on explicit nonlinear model predictive control. The feedback law, available beforehand, is described in detail, together with its variation for different plant conditions. The explicit controller is implemented on a rapid control prototyping unit, which proves the real-time capability of the strategy, with computing times on the order of microseconds. These are significantly lower than the required time step for a TC application. Hence, the explicit model predictive controller can run at the same frequency as a simple TC system based on proportional integral (PI) technology. High-fidelity model simulations provide: 1) a performance comparison of the proposed explicit nonlinear model predictive controller (NMPC) with a benchmark PI-based traction controller with gain scheduling and anti-windup features, and 2) a performance comparison among two explicit and one implicit NMPCs based on different internal models, with and without consideration of transient tire behavior and load transfers. Experimental test results on an electric vehicle demonstrator are shown for one of the explicit NMPC formulations.
ARTICLE (2018). Smith, E.N., Velenis, E., Tavernini, D. and Cao, D., 2018. Effect of handling characteristics on minimum time cornering with torque vectoring. Vehicle system dynamics, 56(2), pp.221-248.
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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 TV 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 TV 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 OCP is introduced where a closed-loop TV 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.
ARTICLE (2017). Tavernini, D., Velenis, E. and Longo, S., 2017. Feedback brake distribution control for minimum pitch. Vehicle System Dynamics, 55(6), pp.902-923.
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The distribution of brake forces between front and rear axles of a vehicle is typically specified such that the same level of brake force coefficient is imposed at both front and rear wheels. This condition is known as ‘ideal’  distribution and it is required to deliver the maximum vehicle deceleration and minimum braking distance. For subcritical braking conditions, the deceleration demand may be delivered by different distributions between front and rear braking forces. In this research we show how to obtain the optimal distribution which minimises the pitch angle of a vehicle and hence enhances driver subjective feel during braking. A vehicle model including suspension geometry features is adopted. The problem of the minimum pitch brake distribution for a varying deceleration level demand is solved by means of a model predictive control (MPC) technique. To address the problem of the undesirable pitch rebound caused by a full-stop of the vehicle, a second controller is designed and implemented independently from the braking distribution in use. An extended Kalman filter is designed for state estimation and implemented in a high fidelity environment together with the MPC strategy. The proposed solution is compared with the reference ‘ideal’   distribution as well as another previous feed-forward solution.
ARTICLE (2014). Tavernini, D., Velenis, E., Lot, R. and Massaro, M., 2014. The optimality of the handbrake cornering technique. Journal of Dynamic Systems, Measurement, and Control, 136(4), p.041019.
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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.
ARTICLE (2013). Tavernini, D., Massaro, M., Velenis, E., Katzourakis, D.I. and Lot, R., 2013. Minimum time cornering: the effect of road surface and car transmission layout. Vehicle System Dynamics, 51(10), pp.1533-1547.
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This paper investigates the minimum time/limit handling car manoeuvring through nonlinear optimal control techniques. The resulting ‘optimal driver’ controls the car at its physical limits. The focus is on cornering: different road surfaces (dry and wet paved road, dirt and gravel off-road) and transmission layouts (rear-wheel-drive, front-wheel-drive and all-wheel-drive) are considered. Low-drift paved circuit-like manoeuvres and aggressive/high-drift even counter-steering rally like manoeuvres are found depending on terrain/layout combinations. The results shed a light on the optimality of limit handling techniques.
CONFERENCE (2018). Metzler, M., Tavernini, D., Sorniotti, A. and Gruber, P., 2018, July. An Explicit Nonlinear MPC Approach to Vehicle Stability Control. In Proceedings of The 14th International Symposium on Advanced Vehicle Control. Tsinghua University.
CONFERENCE (2018). Zanchetta, M., Tavernini, D., Sorniotti, A., Gruber, P., Lenzo, B., Ferrara, A., De Nijs, W., Sannen, K. and De Smet, J., 2018, March. On the feedback control of hitch angle through torque-vectoring. In 2018 IEEE 15th International Workshop on Advanced Motion Control (AMC) (pp. 535-540). IEEE.
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This paper describes a torque-vectoring (TV) algorithm for the control of the hitch angle of an articulated vehicle. The hitch angle control function prevents trailer oscillations and instability during extreme cornering maneuvers. The proposed control variable is a weighted combination of terms accounting for the yaw rate, sideslip angle and hitch angle of the articulated vehicle. The novel control variable formulation results in a single-input single-output (SISO) feedback controller. In the specific application a simple proportional integral (PI) controller with gain scheduling on vehicle velocity is developed. The TV system is implemented and experimentally tested on a fully electric vehicle with four on-board drivetrains, towing a single-axle passive trailer. Sinusoidal steer test results show that the proposed algorithm significantly improves the behavior of the articulated vehicle, and justify further research on the topic of hitch angle control through TV.
CONFERENCE (2018). Metzler, Mathias, Davide Tavernini, Aldo Sorniotti, and Patrick Gruber. "Explicit non-linear model predictive control for vehicle stability control." In 9th International Munich Chassis Symposium 2018, pp. 733-752. Springer Vieweg, Wiesbaden, 2019.
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Nonlinear model predictive control is proposed in multiple academic studies as an advanced control system technology for vehicle operation at the limits of handling, allowing high tracking performance and formal consideration of system constraints. However, the implementation of implicit nonlinear model predictive control (NMPC), in which the control problem is solved on-line, poses significant challenges in terms of computational load. This issue can be overcome through explicit NMPC, in which the optimization problem is solved off-line, and the resulting explicit solution, with guaranteed level of sub-optimality, is evaluated on-line. Due to the simplicity of the explicit solution, the real-time execution of the controller is possible even on automotive control hardware platforms with low specifications. The explicit nature of the control law facilitates feasibility checks and functional safety validation. This study presents a yaw and lateral stability controller based on explicit NMPC, actuated through the electrohydraulically controlled friction brakes of the vehicle. The controller performance is demonstrated during sine-with-dwell tests simulated with a high-fidelity model. The analysis includes a comparison of implicit and explicit implementations of the control system.
CONFERENCE (2016). Smith, E.N., Velenis, E., Cao, D. and Tavernini, D. , Evaluation of optimal yaw rate reference for electric vehicle torque vectoring In: 13th International Symposium on Advanced Vehicle Control (AVEC’16), 13-16 Sep 2016, Munich, Germany.
CONFERENCE (2015). Smith, E.N., Tavernini, D., Claret, C., Velenis, E. and Cao, D. .Optimal yaw rate target for electric vehicle torque vectoring system. In International Symposium on Dynamics of Vehicles on Road and Tracks (IAVSD), 2015.
CONFERENCE (2015). Tavernini, D., Velenis, E. and Assadian, F. .Active Brake Force Distribution for Pitch Angle Minimisation. In International Symposium on Dynamics of Vehicles on Road and Tracks (IAVSD), 2015.
CONFERENCE (2015). Tavernini, D., Velenis, E. and Longo, S., 2015, December. Model-based active brake force distribution for pitch angle minimization. In 2015 54th IEEE Conference on Decision and Control (CDC) (pp. 197-202). IEEE.
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The brake force distribution between front and rear axles of a vehicle is typically specified such that front and rear wheels operate at the same level of brake force coefficient (i.e. equal normalized by axle weight brake forces). It can be shown that this `ideal' distribution is required to deliver the maximum vehicle deceleration and minimum braking distance. In the case of subcritical braking, the deceleration demand may be delivered by different distributions between front and rear braking forces. In this work we obtain the optimal distribution which minimizes the pitch angle and hence enhances driver comfort during braking. This is a unique study in the literature. A vehicle model with appropriate consideration of the suspension geometry is adopted. A feed-forward controller (i.e. quasi-static map) for brake force distribution is generated and tested on a demonstrator vehicle. In addition, to address the problem of the undesirable rebound overshoot caused by a full-stop of the vehicle, an LQR, which can be applied independently from the braking distribution in use, is designed. A second LQR is proposed as an alternative to the feed-forward approach in the calculation of the minimum pitch force distribution.
CONFERENCE (2014). Martínez, C.M., Velenis, E., Tavernini, D., Gao, B. and Wellers, M., 2014, December. Modelling and estimation of friction brake torque for a brake by wire system. In 2014 IEEE International Electric Vehicle Conference (IEVC) (pp. 1-7). IEEE.
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Recent advances in the automotive industry have incorporated the latest technology in vehicle electrification, with the aim to reduce fuel consumption, pollutants emissions, as well as enhance vehicle performance and safety. As a result, Electric Vehicles (EV) and Hybrid Electric Vehicles (HEV) have become the imminent automotive future, establishing important challenges in vehicle systems integration and control. In these vehicles, the regenerative braking is currently the major technique of energy recovery, providing accurate control on the brake torque applied. However regenerative brakes still need the support of conventional friction brakes, mainly due to the battery limitations. Consequently, the coordination of both braking strategies becomes critical for the safe actuation of braking related systems such as: ABS and ESP. Unfortunately, the torque blending between friction and regenerative brakes is a complicated task due to the different systems inputs; the regenerative brakes receive torque inputs, whilst the friction brakes work with pressure inputs. This paper proposes the friction brake torque estimation to simplify the torque blending, and improve the energy recovery and driving safety. The brake torque is estimated not only considering the pressure developed at the calipers, but also the brake disc temperature, and the wheel speed effect on the friction coefficient. The torque is obtained without installing additional sensors in the vehicle platform, considering that only wheel speed sensors are available. The estimation is performed using the extended version of the Kalman Filter. The results obtained are very satisfactory, and can improve the performance of the named systems in a safe way.
CONFERENCE (2013). Tavernini, D., Velenis, E., Lot, R. and Massaro, M., 2013, December. On the optimality of handbrake cornering. In 52nd IEEE Conference on Decision and Control (pp. 2233-2238). IEEE.
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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.
CONFERENCE (2013). Cossalter, V., Lot, R. and Tavernini, D., 2013, February. Optimization of the centre of mass position of a racing motorcycle in dry and wet track by means of the “Optimal Maneuver Method”. In 2013 IEEE International Conference on Mechatronics (ICM) (pp. 412-417). IEEE.
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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.