Robustness analysis of a Fourier-based strategy for cylinder-individual air–fuel ratio control

Abstract

The paper investigates the robustness of a cylinder-to-cylinder air–fuel ratio controller that aims to reduce the exhaust emissions of automotive gasoline engines with spark ignition. A hardware configuration is considered where one wide-range sensor that measures the air–fuel ratio is mounted downstream of the confluence point of an exhaust manifold whose runners are linked to up to five cylinders. An uncertainty analysis is carried out for the closed-loop system with a controller based on Fourier analysis. First, a sensor non-linearity is modelled as an uncertainty and the robustness margins are investigated. With existing observers, the control loop can have a marginal robustness for systems with an even number of cylinders per sensor. For uneven cylinder numbers, however, the loop is always robust. The class of observers considered uses for reconstruction only the necessary number of spectral components of the sensor signal. A modified observer is proposed that also evaluates available redundant spectral information. As a result, the robustness is fully recovered for even numbers of cylinders and further improved for uneven numbers. The robustness is validated on an engine test-bench. Finally, a more complicated case of model uncertainty is investigated where the superimposing signals that originate from the individual cylinders are assumed to be uncertain.