Optimal Control (OC) is essentially a mathematical extremal problem. The procedure consists on the definition of a criterion to minimize (or maximize), some constraints that must be fulfilled and boundary conditions or disturbances affecting to the system behavior. The OC theory supplies methods to derive a control trajectory that minimizes (or maximizes) that criterion.
This dissertation addresses the application of OC to automotive control problems at the powertrain level, with emphasis on the internal combustion engine. The necessary tools are an optimization method and a mathematical representation of the powertrain. Thus, the OC theory is reviewed with a quantitative analysis of the advantages and drawbacks of the three optimization methods available in literature: dynamic programming, Pontryagin minimum principle and direct methods. Implementation algorithms for these three methods are developed and described in detail. In addition to that, an experimentally validated dynamic powertrain model is developed, comprising longitudinal vehicle dynamics, electrical motor and battery models, and a mean value engine model.
OC can be utilized for three different purposes:
1. Applied control, when all boundaries can be accurately defined. The engine control is addressed with this approach assuming that a the driving cycle is known in advance, translating into a large mathematical problem. Two specific cases are studied: the management of a dual-loop EGR system, and the full control of engine actuators, namely fueling rate, SOI, EGR and VGT settings.
2. Derivation of near-optimal control rules, to be used if some disturbances are unknown. In this context, cycle-specific engine calibrations calculation, and a stochastic feedback control for power-split management in hybrid vehicles are analyzed.
3. Use of OC trajectories as a benchmark or base line to improve the system design and efficiency with an objective criterion. OC is used to optimize the heat release law of a diesel engine and to size a hybrid powertrain with a further cost analysis.
OC strategies have been applied experimentally in the works related to the internal combustion engine, showing significant improvements but non-negligible difficulties, which are analyzed and discussed. The methods developed in this dissertation are general and can be extended to other criteria if appropriate models are available.
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