• Automobile Da Corsa
• Car Model
• Collocazione diretta
• Controllo Ottimo
• Direct Collocation
• Ferrari
• Filtro di Kalman
• Hybrid
• Ibrido
• Kalman Filter
• Lap Time Simulator
• Nonlinear Programming
• Optimal Control
• Racing Car
• Simulazione Giro
• Telemetria
• Telemetry
• Track Model
• Tyre
• Vehicle
• Veicolo

In every racing sport, the main goal of any drivers is to lead a vehicle through an established circuit in the least possible time without going out of the track.
The investigation on which is the manoeuvres which allow reaching this goal and, at the same time, respecting all of the physical constraints is a problem known in the literature as minimum lap time problem.
Racing teams and engineers, which have as principal objective to design and set up a vehicle that allows the driver to complete manoeuvres in minimum time, started to develop mathematical models of the vehicles to use it in numerical optimization method generally called Lap Time Simulator (LapSim).
A LapSim is a tool that allows the engineer not only to predict the lap time but also to set up the configuration of a vehicle in order to obtain the best performance for a given circuit and given working conditions.
This work, developed with the collaboration of Vehicle Performace and Simulation department of Ferrari-Competizioni GT, aims to develop a LapSim of seven-degree freedom (7 DOF) car model, including a nonlinear tire model and a power train model. The method proposed applies the Optimal Control Theory to the Lap time minimization problem. This Optimal Control Problem is solved by a Direct Collocation transcription method using the results of a Quasi Steady State Lap Time Simulation as an initial guess.
A track model based on filtered telemetry data was developed in order to provide a racing line to the LapSim.
This kind of Nonlinear Programming (NLP) problem was implemented by the CasADI optimization software framework in Matlab. The developed tool is then used to study the performance in Paul Ricard Circuit of three different power train models: an endothermic power train, a 2 Wheel-Driving (2WD) hybrid power train, and a 4 Wheel-Driving (4WD) hybrid power train. In particular, three main aspects of the vehicle are investigated: the brake balance, weight distribution and energy management.