Fast extremum seeking for online calibration of engines with variable natural gas composition

THERE is a growing interest worldwide in using alternative fuels, motivated by the potential benefits they can offer regarding emissions and energy security. Among the alternative fuels, natural gas has received special attention due to its vast proven reserves across the world. On the other hand, the composition variation of natural gas poses a challenge for the conventional lookup table-based engine control technology. Recently, Extremum Seeking (ES) theory has been considered by the automotive research community as a solution to cope with the composition variation. Although the existing experimental results have demonstrated improved efficiency by employing ES in steady state operation, yet none of them displays neither fast convergence nor the ability to handle transient engine operation. This thesis addresses these gaps by proposing two extensions to ES theory, namely the fast model-based ES and the multiplexed ES scheme, and experimentally demonstrates the performance improvement achieved in calibration of a CNG-fueled engine. Conventional ES implementations rely on a type of time-scale separation tuning which leads to slow optimization relative to the plant dynamics. While this approach treats the plant as a black box by making no assumption on the plant dynamics, the slow optimization is not desirable in some applications. Recently, two different solutions are proposed to address this issue: the model-based ES approach that uses a parametrized model of the plant to benefit from warm starting the estimation as well as using a large class of optimization algorithms; and the fast ES approach that makes use of partial plant knowledge to accelerate estimation. As the first contribution, this thesis develops a fast model-based ES scheme to combine the advantages of a model-based approach and the accelerated performance of fast ES. Experimental results show improved fuel economy by reducing iii the convergence time of spark timing calibration by an order of magnitude compared with a conventional model-based ES algorithm. Similar results are demonstrated in injection duration calibration using an extension of fast ES developed in this thesis. While the existing ES implementations only consider steady state optimization, in some applications such as the motivating application of this thesis a time-varying extremum must be tracked. This is of particular interest in online calibration of engines over a typical driving cycle. As the second contribution of this thesis, a novel multiplexed ES algorithm is introduced to track the time-varying extremum caused by a measurable disturbance. The experimental results show the successful calibration of spark timing for a CNG-fueled engine over the New European Driving Cycle (NEDC).