Model predictive control for automotive time-delay processes: An application to air-to-fuel ratio control ⋆

To meet increasingly stringent emission regulations modern internal combustion engines require highly accurate control of the air-to-fuel ratio. The performance of the conventional air-to-fuel ratio feedback loop is limited by the combustion delay between fuel injection and engine exhaust, and by the transport delay for the exhaust gas to propagate to the air-to-fuel ratio sensor location. The combined delay is variable, since it depends on engine speed and airflow. Drivability, fuel economy and emission requirements result in constraints on the deviations of the air-to-fuel ratio, stored oxygen in the three-way catalyst, and fuel injection. This paper proposes an approach for air-to-fuel ratio control based on Model Predictive Control (MPC). The approach systematically handles both variable time delays and pointwise-in-time constraints. A delay-free model is considered first, which takes into account the dynamic relations between the injected fuel and the air-to-fuel ratio and the dynamics of the oxygen stored in the catalyst. For the delay-free model, the explicit MPC law is computed. Delay compensation is obtained by estimating the delay online from engine operating conditions, and feeding the MPC law with the state predicted ahead over the time interval of the estimated delay. The predicted state is computed by combining measurement filtering with forward iterations of the nonlinear dynamic equations of the model. The achieved performance in tracking the air-to-fuel ratio and the oxygen storage setpoints while enforcing the constraints is demonstrated in simulation using real data profiles.