Turbocharger flow control

1. A method for controlling a turbocharger having a turbine operatively connected to an exhaust of an internal combustion engine and having a compressor operatively connected to an intake of the engine, the method comprising:

determining, via an electronic control unit, engine operating conditions based on air intake flow at at least one of the intake of the engine or a compressor inlet and based on engine exhaust flow at at least one of a turbine inlet or a turbine outlet;

calculating a boost pressure command P i for the compressor from the equation:

<Equation 1: P i >

wherein R is the ideal gas constant, T i is a current temperature at the intake, {dot over (m)} c is a current charge flow command determined by the electronic control unit, n is a determined rotational speed of the engine, D is a displacement of the engine, and η is engine volumetric efficiency, which is calculated as a function of EGRf and the current rotational speed of the engine n, wherein EGRf is an exhaust gas recirculation fraction;

calculating a compressor flow Q c from the equation:

<Equation 2: Q c >

wherein {dot over (m)} a is a determined mass flow to the compressor, T a is atmospheric temperature, and P a is atmospheric pressure;

calculating a compressor pressure ratio P rc from the equation:

<Equation 3: P rc >

wherein, P i is the calculated boost pressure command and P a is atmospheric pressure;

calculating a compressor power E c from the equation:

<Equation 4: E c >

wherein T ex is exhaust temperature, P to is a pressure at an output of the turbine, {dot over (m)} a is the mass flow to the compressor, C p is specific heat of the engine exhaust, T a is atmospheric temperature, a 1 through a 6 are constants specific to the turbocharger, P rc is the calculated pressure ratio across the compressor, and Q c is the calculated compressor flow;

calculating a turbine flow from the equation:

<Equation 5: Q t >

wherein E j is a calculated inertial power and E c is the calculated compressor power; and

commanding the turbocharger to operate at the calculated turbine flow Q t .