This thesis studies the optimal control of vehicular systems, focusing on the solution of minimum-lap-time problems for a Formula 1 car. The basic optimal control theory is summarised as an infinite-dimensional extension of optimisation theory. The relevant numerical techniques for optimisation and integral approximation are compared in view of the application to vehicle systems. The classical brachistochrone problem is revisited from an optimal control perspective, with two vehicle-relevant generalisations. Closed-form solutions are derived for both the optimal trajectory and transit time. Problems involving a steerable disc rolling on the interior surface of a hemisphere are studied. For three-dimensional problems of this type, which involve rolling bodies and nonholonomic constraints, numerical solutions are used. The identification of 3D race track models from measured GPS data is treated as a problem in the differential geometry of curves and surfaces. Curvilinear coordinates are adopted to facilitate optimal control solutions. The track is specified in terms of three displacement-dependent curvatures and two edge variables. The differential model is smoothed using numerical optimal control techniques. The Barcelona track is considered as an illustrative example. The minimum-lap-time problem for a Formula 1 car on a flat track is solved using direct transcription. The driven line and multiple car setup parameters are optimised simultaneously. It is shown that significant lap-time reductions can be obtained from track-specific setup parameter optimisation. Reduced computing times are achieved using a combination of analytical derivatives, model non-dimensionalisation and problem scaling. The optimal control of the car on a 3D track is studied; the results are compared with flat-track solutions. Contemporary kinetic energy-recovery systems are studied and compared with future hybrid kinetic-thermal energy-recovery systems. It is demonstrated that these systems can produce contemporary lap time using approximately two-thirds of the fuel required by present-day vehicles.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:627786 |
| Date | January 2013 |
| Creators | Perantoni, Giacomo |
| Contributors | Limebeer, David J. N. |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:b75fa69c-ebe0-4812-98e9-984d93476d37 |
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