Gaussian trajectories in motion control for camless engines

In the last few years, variable engine valve control has attracted a lot of attention because of its ability to reduce pumping losses and increase torque performance over a wider speed and load range. Variable valve timing also allows control of internal exhaust gas recirculation, thus improving fuel economy and reducing NO
_x
emissions. One of the most important issues in this context is to track suitable variable (optimized in terms of engine speed and load) motion profiles for the intake and exhaust valves. This can be achieved using dedicated actuators for the valves instead of a traditional camshaft. This contribution considers a new kind of actuator for this purpose and its control for motion tracking in the context of camless systems. However, this paper's main intention is to introduce a method of generating variable engine valve trajectories that are based on Gaussian curves and exemplarily provide the reader with information on how to exploit their favorable mathematical properties for control design purposes. As a demonstration of this kind of curve's variability, a delay-compensating phase-adaptive feedforward action is derived from a linear model description of the actuator. Simulations show the effectiveness of a simple heuristic delay-estimation algorithm in combination with the mentioned feedforward action.