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This paper describes a simple engine model at idling and it applies particularly to idle speed control. Through linearization in the neighborhood of the nominal operating points (650 rpm), the engine is expressed as a reduced-order constant coefficient state variable (2 state) model. It was produced through the system order-reduction method. The strategy for controlling idle speed uses the Linear Quadratic and Integral (LQI) optimal control theory. The tracking controller was designed using a state variable engine model, and the performance index was minimized. Since state variables are artificially introduced, they are not directly accessible. Therefore, they must be estimated in accordance with a stored dynamic model (i.e. observer), in which the engine dynamic behavior is estimated on the basis of a state variable model which represents the engine's internal states, in determining controlling values.

It has been reported by several researchers that the L-jetronic fuel injection system offers better idle speed stability than the D-jetronic one in port fuel injection engines. However, the volume between the throttle valve and the intake valves in the L-jetronic system acts as a first order lag element in the system and causes air-fuel ratio fluctuation which, in turn, induces idle speed hunting under certain conditions. This study employs computer simulation to determine the influence of three parameters on idle speed stability: (1) flywheel inertia, (2) intake manifold volume, and (3) air-fuel ratio calibration. It also explores means of improving idle speed stability by controlling the air-fuel ratio and ignition timing. The use of actual engine torque data to estimate the generated torque from the amount of air and fuel in each combustion cycle was the unique feature of this study.