Optimal Control of Mass Transport Time-Delay Model in an EGR 2020-01-0251

This paper touches on the mass transport phenomenon in the exhaust gas recirculation (EGR) of a gasoline engine air path. It presents the control-oriented model and control design of the burned gas ratio (BGR) transport phenomenon, witnessed in the intake path of an internal combustion engine (ICE), due to the redirection of burned gases to the intake path by the low-pressure EGR (LP-EGR). Based on a nonlinear AMESim® model of the engine, the BGR in the intake manifold is modeled as a state-space (SS) output time-delay model, or alternatively as an ODE-PDE coupled system, that take into account the time delay between the moment at which the combusted gases leave the exhaust manifold and that at which they are readmitted in the intake manifold. In addition to their mass transport delay, the BGRs in the intake path are also subject to state and input inequality constraints. The objective of the control problem is to track a reference output profile of the BGR in the intake manifold, taking into account the transport delay and the state (output) and input constraints of the system. In this aim, two indirect optimal control approaches are implemented and compared, the discretize-then-optimize approach and the optimize-then-discretize approach. To account for the state inequality constraints, both methods are equipped with techniques for constrained optimization such as the augmented Lagrangian and the UZAWA methods. The necessary conditions of optimality are formulated, in each of both cases, and the resulting equations are solved numerically using the projected gradient-descent method, which ensures the non-violation of the input inequality constraints. The novelty of the work lies in considering the system’s constraints and the infinite-dimensionality of the mass transport phenomenon governing it. The merits of the time-delay model and the model-based control design are illustrated on the nonlinear® AMESim model on which the mathematical model is based.