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Turbocharger maps measured on a gas stand test bench are commonly used to represent turbine and compressor performance. The maps are useful source of information for mean value modeling, engine calibration optimization, virtual sensing and feedback control design. For some tasks, representing the maps by fitted functional forms can be more convenient than using interpolation of the map data directly. The functional representation usually allows for wider extrapolation ranges and more reliable application of numerical optimization methods. In literature most successful functional forms chosen to represent the compressor flow characteristics are based on rational polynomials of dimensionless head and flow parameters. Turbine flow characteristics, on the other hand, are commonly modeled as orifices or orifices with variable cross-section in case of variable geometry turbines (VGT).

Numerous studies describe the fuel consumption benefits of changing the powertrain temperature based on vehicle operating conditions. Actuators such as electric water pumps and active thermostats now provide more flexibility to change powertrain operating temperature than traditional mechanical-only systems did. Various control strategies have been proposed for powertrain temperature set-point regulation. A characteristic of powertrain thermal management systems is that the operating conditions (speed, load etc) change continuously to meet the driver demand and in most cases, the optimal conditions lie on the edge of the constraint envelope. Control strategies for set-point regulation which rely purely on feedback for disturbance rejection, without knowledge of future disturbances, might not provide the full fuel consumption benefits due to the slow thermal inertia of the system.