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In modern engine control applications, there is a distinct trend towards model-based control schemes. There are various reasons for this trend: Physical models allow deeper insights compared to heuristic functions, controllers can be designed faster and more accurately, and the possibility of obtaining an automated application scheme for the final engine to be controlled is a significant advantage. Another reason is that if physical effects can be separated, higher order models can be applied for different subsystems. This is in contrast to heuristic functions where the determination of the various maps poses large problems and is thus only feasible for low order models. One of the most important parts of an engine management system is the air-to-fuel control. The catalytic converter requires the mean air-to-fuel ratio to be very accurate in order to reach its optimal conversion rate. Disturbances from the active carbon filter and other additional devices have to be compensated.

In this paper the fuel path of a sequentially injected gasoline engine is discussed. Since a fraction of the injected fuel suffers a delay due to the wall-wetting phenomenon, in transient phases a significant deviation of the air-to-fuel ratio from its setpoint can arise. The amount of fuel on the manifold wall and its rate of evaporation cannot be measured directly. Therefore, the effects of the wall-wetting on exhaust lambda and engine torque have to be considered for the identification of the dynamics. The dynamics of the exhaust-gas-oxygen (EGO) sensor is not negligible for the interpretation of the lambda measurement. Since both the dynamics and the statics of a ZrO2 Sensor are very nonlinear, a normal EGO-sensor is not suitable for these investigations. On the other hand, the engine torque is a good measure for the cylinder lambda when all other effects which lead to torque changes can be eliminated.

Today's engine management systems for SI engines consist of static and dynamic control algorithms. The static functions of the engine management guarantee the correct stationary operation of the engine in all the possible operating points. The static functions are contained mainly in two lookup tables, one for the spark advance and one for the metered depending on engine speed and load. Usually these lookup tables are determined with experiments on the engine test bench. In this paper, a model-based method for the evaluation of the fuel-optimal maps for spark advance and metered fuel is described. The method can be divided into several steps: 1. Measurement and identification of all the engine parameters in a reference point (including the pressure in one cylinder) Calculation of the burn-through function (progress of the combustion) Iterative calculation of the amount of residual exhaust gas Approximation of the definitive burn-through function with the Vibe equation 2.

Modern model-based control schemes and their application on different engines need mathematical models for the various dynamic subsystems of interest. Here, the fuel path of an SI engine is investigated. When the engine speed and the throttle angle are kept constant, the fuel path is excited only by the fuel injected. Taking the NO concentration of the exhaust gas as a measure for the air/fuel ratio, models are derived for the wall-wetting dynamics, the gas mixture, as well as for the air/fuel ratio sensor. When only the spark advance is excited, the gas flow dynamics can be studied. A very fast NO measurement device is used as reference. Its time constant is below the segment time of one single cylinder (180° crank angle for a 4-cylinder engine), therefore its dynamics are much faster than the time constants of the systems investigated. A model structure considering the muliplexing effects of the discrete operation of an engine is given for the fuel path of a BMW 1.8 liter engine.