A new design method of fractional-order proportional-integral controllers is proposed based on fractional calculus and Bode's ideal transfer function for a first-order-plus-dead-time process model. It can be extended to be applied to various dynamic models. Tuning rules were analytically derived to cope with both set-point tracking and disturbance rejection problems. Simulations of a broad range of processes are reported, with each simulated controller being tuned to have a similar degree of robustness in terms of resonant peak to other reported controllers. The proposed controller consistently showed improved performance over other similar controllers and established integer PI controllers.