# Estimation of the In-Cylinder Air/Fuel Ratio of an Internal Combustion Engine by the Use of Pressure Sensors

University dissertation from Department of Heat and Power Engineering, Lund university

Abstract: This thesis investigates the use of cylinder pressure measurements for estimation of the in-cylinder air/fuel ratio in a spark ignited internal combustion engine.

An estimation model which uses the net heat release profile for estimating the cylinder air/fuel ratio of a spark ignition engine is developed. The net heat release profile is computed from the cylinder pressure trace and quantifies the conversion of chemical energy of the reactants in the charge into thermal energy. The net heat release profile does not take heat- or mass transfer into account. Cycle-averaged air/fuel ratio estimates over a range of engine speeds and loads show an RMS error of 4.1% compared to measurements in the exhaust.

A thermochemical model of the combustion process in an internal combustion engine is developed. It uses a simple chemical combustion reaction, polynomial fits of internal energy as function of temperature, and the first law of thermodynamics to derive a relationship between measured cylinder pressure and the progress of the combustion process. Simplifying assumptions are made to arrive at an equation which relates the net heat release to the cylinder pressure.

Two methods for estimating the sensor offset of a cylinder pressure transducer are developed. Both methods fit the pressure data during the pre-combustion phase of the compression stroke to a polytropic curve. The first method assumes a known polytropic exponent, and the other estimates the polytropic exponent. The first method results in a linear least-squares problem, and the second method results in a nonlinear least-squares problem. The nonlinear least-squares problem is solved by separating out the nonlinear dependence and solving the single-variable minimization problem. For this, a finite difference Newton method is derived. Using this method, the cost of solving the nonlinear least-squares problem is only slightly higher than solving the linear least-squares problem. Both methods show good statistical behavior. Estimation error variances are inversely proportional to the number of pressure samples used for the estimation as predicted by the central limit theorem. CLICK HERE TO DOWNLOAD THE WHOLE DISSERTATION. (in PDF format) 