Analytical tuning rules for fractional order proportional integral controllers

A new analytical method based on the fractional calculus and Bode´s ideal transfer function is proposed for the design of fractional-order proportional-integral (FOPI) controllers. On the basis of a first-order-plus-dead-time (FOPDT) process model, the analytical tuning rules are derived by using the frequency domain for achieving the significant improvement in terms of both disturbance rejection and set-point tracking problems. Several illustrative examples are considered to confirm the effectiveness of the proposed algorithm for various dynamic models.