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 closedloop 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.

Adaptive and predictive control of fuel injection with time delay consideration for air–fuel ratio regulation of gasoline direct injection engines

“…However, the measurement time delay caused by the location of the UEGO sensor, consisting of combustion cycle delay and exhaust mixing transport delay, becomes an obstacle to the achievable performance by the feedback fuelling control. Various A/F control strategies have been developed to tackle the time delay from the fuel injectors to the A/F output, for example, sliding mode control, 10–14 internal model control, 15–18 gain-scheduling/linear parameter varying (LPV) control, 19–23 model predictive control, 24 the Smith predictor method, 25,26 , the estimate or predict-based method 27–29 and control approaches to systems with input time-delay. 30,31 However, there still exist challenges to more sophisticated and efficient solutions to accurate cylinder air charge estimation and suitable A/F feedback control strategy for online computation and implementation in a real engine regardless of nonlinearities, time-delay and uncertain parameters in engine dynamics.…”