Extremum-seeking control for combined EGR fraction tracking and constrained pumping-loss minimization in Diesel engines

Exhaust gas recirculation (EGR) is an often applied mechanism to suppress the emission of NOx in Diesel engines. EGR however, induces a pumping-loss, which reduces the fuel efficiency of the engine. The corresponding control problem is to track a reference EGR fraction, while simultaneously using the available actuators to minimize pumping-loss. These are conflicting objectives, as the minimum pumping-loss corresponds to zero EGR fraction. In addition, a lower constraint on the air/fuel equivalence ratio is taken into account to prevent high emission of particulate matter (PM). An extension of extremum-seeking (ES) is proposed which combines multivariable proportional-integral (PI) tracking control with optimization, where the conflicting objectives are decoupled by gradient projection. The controller does not rely on parametric models, disturbance knowledge, or explicit optimization, hence it is robust with respect to real-world disturbances and the additional computational effort compared with a standard PI controller is low. The controller is demonstrated in a simulation example using a physics based Diesel engine model.