This paper presents a new practical tuning method for fractional order proportional and integral (FO-PI) controller. The plant to be controlled is mainly first order plus delay time (FOPDT). The tuning is optimum in the sense that the load disturbance rejection is optimized yet with a constraint on the maximum or peak sensitivity. We generalized $Ms$ constrained integral (MIGO) based controller tuning method to handle the FO-PI case, called F-MIGO, given the fractional order $α$. The F-MIGO method is then used to develop tuning rules for the FOPDT class of dynamic systems. The final developed tuning rules only apply the relative dead time $τ$ of the FOPDT model to determine the best fractional order $α$ and at the same time to determine the best FO-PI gains. Extensive simulation results are included to illustrate the simple yet practical nature of the developed new tuning rules. The tuning rule development procedure for FO-PI is not only valid for FOPDT but also applicable for other general class of plants.

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