Control oriented modeling of a radial turbine for a turbocharged gasoline engine

Abstract

This paper presents a control oriented model for predicting turbine major variables in a turbocharged spark ignition engine. The turbine is simulated as a two-nozzle chamber where the pressure ratio over the two nozzles is not the same. A convex nonlinear estimation algorithm is formulated to determine the relation between these pressure ratios. The new model is experimentally validated with transient and steady state data collected from a 1.7 liter gasoline engine. The results show the new model can predict the turbine mass flow with an average error of 1.4%. In addition, the application of the turbine model is illustrated for the design of a nonlinear observer to estimate the turbocharger non-measured variables. The designed observer is tested against experimental data and the results confirm the observer capability to estimate the turbine rotor speed, flow over the compressor and temperature downstream the compressor.

Nonlinear observer design for turbocharger in a SI engine

“…Performance of the designed observer is tested using measured data from a turbocharged 4-cylinder port fuel injected gasoline engine detailed in [13]. Experimental validation of the designed observer is done by applying different step inputs to the engine torque and engine speed using a test procedure shown in Fig.…”

Modeling and extrapolating mass flow characteristics of a radial turbocharger turbine

“…(2) Single-nozzle partial empirical model Jensen et al [18] modeled the mass flow rate of the turbine with the flow equation of an adiabatic nozzle, _ m ffiffiffiffiffiffiffi T 00 p P 00 ¼ (24) where p' crit is the critical pressure ratio of an adiabatic nozzle (for air, p' crit ¼ 0.528). To account for the choked flow condition, the effective nozzle area should be expressed as,…”

“…Similar with Payri's model, Serrano et al [23] deduced a more accurate equation of the intermediate pressure between the stator and the rotor and expanded this model to variable geometry turbines. Eriksson [16] and Salehi et al [24] proposed other simplified expressions of the pressure ratio across the stator. Fang et al [2,25] proposed partial empirical models to predict the mass flow rate and efficiency of inward radial turbines using the Taylor expansion and regression analysis.…”

Research on Control-Oriented Modeling for Turbocharged SI and DI Gasoline Engines

“…In order to design a controller for regulating speed of diesel engine, the nonlinear model was linearized and represented in a state-space form [9]. Reference [10] presented a controloriented model for predicting major turbine variables in a turbocharged spark ignition engine. In the model, the turbine was simulated as a two-nozzle chamber.…”