Linear Parameter-Varying Control for Air/Fuel Ratio in SI Engines with Parameter Dependent Time Delay

This paper is concerned with the air/fuel ratio control of direct injected, spark ignition (SI) combustion engines. The air/fuel ratio is essential for torque generation together with emissions and requires therefore a precise regulation. The system dynamics are modeled for controller design as a first order linear parameter-varying (LPV) system plus parameter varying time delay where the time delay is approximated by a first order Pade function. The scheduling signals determined by the engine operating point are reduced to a single scheduling parameter. The functional dependence on the plant parameters stored in look-up tables is then approximated by rational functions of this scheduling parameter. For controller synthesis a mixed sensitivity design (four-block) is used with parameter dependent weighting to adjust the requirements to the varying plant dynamics. An LPV controller with guaranteed stability and induced L-2-norm performance is then obtained by solving linear matrix inequalities (LMIs) on a prespecified grid. Simulation results are presented to validate the designed LPV controller. They show performance superior to that of a scheduled PID controller used in serial production cars.