Optimal control of manifold filling during VDE mode transitions

During mode transitions in advanced engines and powertrains, actuators (electronic throttle, fuel, spark timing, variable valve timing, etc.) need to be optimally coordinated to obtain the correct state for the next mode. Specific examples of mode changes include cylinder deactivation/reactivation transitions in variable displacement engines, combustion mode transitions in HCCI and DISI engines and clutch transitions between locked and unlocked states in dual clutch transmissions. Mode transitions lead naturally to optimal control problems that can be analyzed using the maximum principle and solved numerically. From this perspective, the paper considers in detail one of the simplest problems of its kind (which to the authors' knowledge has not been treated), the optimal control of intake manifold filling using the electronic throttle. This problem is relevant to variable displacement engines and to the fuel economy that these engines can achieve. The analysis of minimum time and Nonlinear Quadratic (NLQ) optimal control problems is presented for the nonlinear manifold filling dynamics based on the maximum principle and simulated optimal trajectories are reported. Then a recently proposed Iterative Model and Trajectory Refinement (IMTR) strategy for solving trajectory optimization problems is validated using the intake manifold pressure filling as a case study. Specifically, we demonstrate the convergence of IMTR to trajectories that are close enough to the trajectories obtained from the maximum principle.