The purpose of this paper is to describe an idle speed regulation formula based on a sampled model of a second order type, taken to show the Internal Combustion (IC) engine dynamics from the by-pass idling throttle (RPM vs Duty Cycle). The identification of this reduced model, and the calculation of the desired closed-loop transfer function give the optimal numerical coefficients of the recursive control law. Parametric degrees of freedom are: damping and response time before steady state. Calibration values are calculated in an automatic process by tuning physical parameters. Initial conditions are determined in order to eliminate transient oscillations of the engine speed output.The noticable advantages are: the power of this numerical control law with regard to variable inertia and charge, the good damping obtained on frequency response, and the integrated adaptive form. All kinds of IC engines may be considered and controlled by this law.