## 2 Methodologies
### Engine Management System and Control Variables  
An open electronic control unit (ECU) fitted with an Erasable Programmable Read Only Memory (EPROM) emulator module was connected to a personal computer through an ETAS(r) MAC2F interface (ETAS, Stuttgart, Germany). The ETK module was then managed by the INCA(r) software, in order to perform real-time visualization of engine parameters, selection of the required maps stored in the ECU and change of control variables according to the experimental program. Open and closed-loop strategies were available for turbocharger turbine control, according to the engine operating condition. The first option was applied by the ECU at low levels of engine speed and load, setting duty-cycle values of an electro-pneumatic valve (DC\({}_{\mathrm{VNT}}\)), thus obtaining fixed values of variable nozzle turbine opening degree (A\({}_{\mathrm{VNT}}\)), defined in Equation (1). \[\mathrm{A_{VNT}}=[(\mathrm{S_{MAX}}-\mathrm{S})/(\mathrm{S_{MAX}}-\mathrm{S_{ MIN}}]\times 100~{}[\%]. \tag{1}\]  
where S is the displacement of the turbine nozzle ring push rod (measured with a linear potentiometer), while S\({}_{\mathrm{MAX}}\) and S\({}_{\mathrm{MIN}}\) are its maximum and minimum value. A\({}_{\mathrm{VNT}}\) ranges from 0% to 100%, equivalent to the minimum and maximum values of turbine swallowing area. At higher levels of engine speed and load, ECU switched to the closed-loop control scheme, by comparing an intake pressure set point with the measured level, then changing DC\({}_{\mathrm{VNT}}\) to reduce, if necessary, the calculated difference. A closed-loop approach was applied to fuel rail pressure (p\({}_{\mathrm{rail}}\)), through the comparison of the set point (calculated by the ECU according to the engine operating condition or fixed according to the experimental programme) and the level measured by the on board sensor fitted on the common rail. The high-pressure (HP) EGR system was also controlled through a closed-loop scheme, based on the set point for the relative air-fuel ratio (AFR). The actual value was obtained by the measurement of the air mass flow rate, while fuel mass flow rate was calculated by the ECU to match the engine torque requested by the driver. The duty-cycle of the electric HP EGR valve (DC\({}_{\mathrm{EGR}}\)) was then modulated to reduce the difference, thus managing its opening degree and HP EGR mass flow rate. The prototype low-pressure (LP) EGR loop was manually controlled through two different devices. The first was a pneumatic valve, whose opening degree was managed through a vacuum signal. The second was a throttle valve (TV) fitted at the exhaust end [20], whose position allowed us to modify the pressure levels along this circuit (taking into account the absence of a diesel particulate filter) and low-pressure EGR contribution. The conventional approach to define and calculate the EGR rate (f\({}_{\mathrm{EGR}}\)) was applied within the investigation. This term is defined as the ratio between recirculated gas and total engine mass flow rate, which is obtained summing air (M\({}_{\mathrm{a}}\)), fuel (M\({}_{\mathrm{f}}\)) and EGR (M\({}_{\mathrm{EGR}}\)) mass flow rates (Equation (2)). \[\mathrm{f_{EGR}}=[\mathrm{M_{EGR}}/(\mathrm{M_{EGR}}+\mathrm{M_{a}}+\mathrm{ M_{f}})]\times 100~{}[\%] \tag{2}\]  
Measurements of ambient, intake and exhaust carbon dioxide concentrations through NDIR analysers, allowed to calculate the EGR rate [22; 23] according to Equation (3):  
\[\mathrm{f_{EGR}}=[(\mathrm{X_{CO2\,i}}-\mathrm{X_{CO2\,a}})/(\mathrm{X_{CO2\, e}}-\mathrm{X_{CO2\,a}})]\times 100~{}[\%]. \tag{3}\]  
As air and fuel mass flow rates were measured, Equation (2) allowed us to estimate M\({}_{\mathrm{EGR}}\), corresponding to the mass flowing in one circuit when either HP or LP loop was activated or to the total mass of recirculated gases when both were jointly operated.