New tuning rules for fractional PIα controllers

This paper describes a new tuning method for fractional PI alpha controllers. The main theoretical contribution of the paper is the analytical solution of a nonlinear function minimization problem, which plays a central role in deriving the tuning formulae. These formulae take advantage of the fractional order alpha to offer an excellent tradeoff between dynamic performances and stability robustness. Finally, a position control is implemented to compare laboratory experiments with computer simulations. The comparison results show the good performance of the tuning formulae.