A novel volumetric efficiency model for spark ignition engines equipped with variable valve timing and variable valve lift Part I: model development

Estimation of the air charge and the volumetric efficiency is one of the most challenging tasks in the control of internal-combustion engines owing to the intrinsic complexity and the non-linearity of the gas flow phenomena. In particular, with emerging new technologies such as systems with variable valve timing and variable valve lift, the number of effective parameters increases greatly, making the estimation task more complicated. On the other hand, using a three-way catalyst converter needs strict control of the air-to-fuel ratio to around the stoichiometric ratio, and hence more accurate models are required for estimation of the air charge. Therefore, various models have been proposed in the literature for estimation of the volumetric efficiency and the air charge. However, they are either strictly based on physical first principles, making them impractical for conventional applications, or nearly fully empirical and need many experimental data for calibration. In this paper, using a novel approach, a new semiempirical model is proposed for estimation of the volumetric efficiency, which is calibrated with very few experimental data and can be used easily for real-time applications. In addition to the valve timings, the engine speed and the intake manifold pressure, the inlet valve lift is also considered as the model input. The generalizability of the model is proved by applying it to estimate the volumetric efficiency of six different engines. Furthermore, a systematic approach is taken to simplify the proposed model and to strengthen its prediction capability. The result is a simple, practical and generalizable model which can be used for various spark ignition engines, can be trained with very few data and can be utilized for estimating accurately the volumetric efficiency in real-time applications.