A Generalized Compressor Power Model for Turbocharged Internal Combustion Engines With Reduced Complexity

Control-oriented models of automotive turbocharger compressors typically describe the compressor power assumming an isentropic thermodynamic process with a fixed isentropic efficiency and a fixed mechanical efficiency for power transmission between the turbine and compressor. Although these simplifications make the control model tractable, they also introduce additional errors due to unmodeled dynamics, especially when the turbocharger is operated outside its normal operational region. This is also true for map-based approaches, since these supplier-provided maps tend to be sparse or incomplete at the boundary operational regions and often ad-hoc extrapolation is required, leading to large modeling error. Furthermore, these compressor maps are obtained from the steady flow bench tests, which introduce additional errors under pulsating flow conditions in the context of internal combustion engines. In this paper, a physics-based model of compressor power is developed using Euler equations for turbomachinery, where the mass flow rate and compressor rotational speed are used as model inputs. Two new coefficients, speed and power coefficients are defined. This makes it possible to directly estimate the compressor power over the entire compressor operating range based on a single analytic relationship. The proposed modeling approach is validated against test data from standard turbocharger flow bench, steady state engine dynamometer as well as transient simulation tests. The validation results show that the proposed model has adequate accuracy for model-based control design and also reduces the dimension of the parameter space typically needed to model the compressor dynamics.