Modeling of a Diesel Engine with VGT and EGR capturing Sign Reversal and Non-minimum Phase Behaviors

A mean value model of a diesel engine with VGT and EGR is developed and validated. The intended model applications are system analysis, simulation, and development of model-based control systems. The goal is to construct a model that describes the dynamics in the manifold pressures, turbocharger, EGR, and actuators with few states in order to have short simulation times. Therefore the model has only eight states: intake and exhaust manifold pressures, oxygen mass fraction in the intake and exhaust manifold, turbocharger speed, and three states describing the actuator dynamics. The model is more complex than e.g. the third order model in [12] that only describes the pressure and turbocharger dynamics, but it is considerably less complex than a GT-POWER model or a Ricardo WAVE model. Many models in the literature, that approximately have the same complexity as the model proposed here, use three states for each control volume in order to describe the temperature dynamics. However, the model proposed here uses only two states for each manifold. Model extensions are investigated showing that inclusion of temperature states and pressure drop over the intercooler only have minor effects on the dynamic behavior and does not improve the model quality. Therefore, these extensions are not included in the proposed model. Model equations and tuning methods are described for each subsystem in the model. In order to have a low number of tuning parameters, flows and efficiencies are modeled using physical relationships and parametric models instead of look-up tables. To tune and validate the model, stationary and dynamic measurements have been performed in an engine laboratory at Scania CV AB. Static and dynamic validations of the entire model using dynamic experimental data show that the mean relative errors are 12.7 % or lower for all measured variables. The validations also show that the proposed model captures the essential system properties, i.e. a non-minimum phase behavior in the channel uegr to pim and a non-minimum phase behavior, an overshoot, and a sign reversal in the channel uvgt to Wc.