Modeling and Estimation of Unmeasured Variables in a Wastegate Operated Turbocharger

Estimation of relevant turbocharger variables is crucial for proper operation and monitoring of turbocharged (TC) engines, which are important in improving fuel economy of vehicles. This paper presents mean-value models developed for estimating gas flow over the turbine and the wastegate (WG), the wastegate position, and the compressor speed in a TC gasoline engine. The turbine is modeled by an isentropic nozzle with a constant area and an effective pressure ratio calculated from the turbine upstream and downstream pressures. Another physically sensible model is developed for estimating either the WG flow or position. Provided the WG position is available, the WG flow is estimated using the orifice model for compressible fluids. The WG position is predicted considering forces from the WG passing flow and actuator. Moreover, a model for estimating the compressor speed in low and medium compressor pressure ratios is proposed, using the compressor head and efficiency modified by the turbine effective pressure ratio. The estimates of the turbocharger variables match well with the experimentally measured data. The three proposed models are simple in structure, accurate enough to be utilized for engine modeling, and suitable to be validated and calibrated on an internal combustion engine in a test cell.