An IAE optimum control tuned by one parameter

This article proposes an optimal pole placement whose only parameter to tune is the natural frequency of the dominant closed loop pole. This simple tuning is optimal with respect to an IAE criterion for step inputs. In a first stage, the minimum of IAE criterion is studied with respect to reference and disturbance inputs for models whose order are lower than four with one or two zeros. Then, an optimal control strategy is introduced by the adjustment of only one parameter, and relations available for PI and PID controllers are proposed. Lastly, it is shown that such an optimal control provides better results than Ziegler Nichols tuning which is also based on an IAE criterion.