A modification and the Tustin approximation

The Tustin approximation for determining a discrete-time representation of a continuous-time control system is sufficiently precise. If a sampling interval is chosen properly, it results in some errors in time responses of a plant model, though they are not critical and the static gain value is the same as in the original transfer function. However, this method generally increases the number of coefficients in the numerator of the approximate discrete-time transfer function by one in comparison with the exact transformation. A simple modification of the Tustin approximation that does not have this disadvantage and is far more precise than the original approximation is presented. The additional numerical effort is negligible. Examples of the transformation for three simple continuous systems are presented