A convenient way of modelling turbochargers is based on data maps. These models are easy to put into place, require low CPU charge and are control-oriented. Data relative to compressor and turbine are read from tables: pressure ratio and efficiency are determined as functions of mass flow rate and rotary speed on two distinct data maps. Nevertheless, this type of model has drawbacks:• Usually, only higher turbocharger speed data are mapped (> 90000 rpm ) although the low rpm zone is the most useful zone for normalized driving cycles simulations. Moreover, maps are poorly discretized, leading to the use of specific extra-interpolation methods (many are identified in [5]).• These methods are purely mathematical, which gives inaccurate results in extrapolation zones. Relation between pressure ratio and efficiency is then broken (i.e., if one implements a pumping model for the compressor, the pressure ratio will be affected, but not the efficiency).The present paper develops a new extra/interpolation model incorporating physical laws. An analysis of turbomachinery equations is performed. A new approach for extra-interpolating performance maps, which satisfies the physical laws stated in turbomachinery equations, is derived from this work. Results from this new model are compared with standard methods.The major conclusions drawn from this study are: 1 -The new model improves the simulation accuracy while keeping the same easiness of use and robustness. 2 -Extrapolation in the low rpm zone is derived from physical equations. 3 -This method is applicable to both compressor and turbine. 4 -The pressure ratio and efficiency maps are now linked.

Data maps are easy to put in place and require very low calculation time. As a consequence they are often valued over fully physic-based models. This is particularly true when it is question of turbochargers. However, even if these maps are directly provided by the manufacturer, they usually do not cover the entire engine operating range and are poorly discretized. That's why before implementing them into any model they need to be interpolated and extrapolated.This paper introduces a new interpolation/extrapolation method based on the idea of integrating more physics into the widespread Jensen and Kristensen's method [6]. It essentially relies on the turbo machinery equation analysis performed by Martin during his PhD thesis [9, 10, 11] and the interpolation and extrapolation strategies that he proposed. In most cases the new strategies presented in this paper rely on improvements of the models he proposed. However the major issue here is to associate to each model a robust algorithm to obtain the fully extrapolated data maps from the raw manufacturer's data.The major outcomes of the study are: -new models for compression ratio and turbine flow rate extrapolations androbust and easy to implement algorithms for interpolation and extrapolation to low rotational speeds. These address single stage turbocharging configurations with fixed geometry turbines (in the case of variable geometry turbines, taking each position as a different fixed geometry turbine allow to use the same algorithms).

This paper describes a low-pressure exhaust gas recirculation (LP-EGR) mass flow rate estimation method and a robust air mass fraction observer for a Diesel engine with dualloop EGR system. Both observers operate simultaneously eliminating the need for pressure measurement upstream the LP-EGR valve. A sliding mode observer is designed to estimate the LP-EGR mass flow rate using the standard sensors available in commercial Diesel engines. A robust linear parameter varying Kalman filter is designed for the air mass fraction estimation. The convergence and robustness of the observers are ensured by means of Lyapunov stability and a linear matrix inequality (LMI) framework for the sliding mode observer and robust Kalman filter, respectively. The observers are validated with a Motor Vehicle Emission Group (NMVEG) cycle using an engine model validated on an experimental benchmark as a reference.

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Pollutant emissions and fuel economy objectives have led car manufacturers to develop innovative and more sophisticated engine layouts. In order to reduce time-to-market and development costs, recent research has investigated the idea of a quasi-systematic engine control development approach. Model based approaches might not be the only possibility but they are clearly predetermined to considerably reduce test bench tuning work requirements. In this paper, we present the synthesis of a physics-based nonlinear model predictive control law especially designed for powertrain control. A binary search tree is used to ensure real-time implementation of the explicit form of the control law, computed by solving the associated multi-parametric nonlinear problem.