Practical tuning of fractional order proportional and integral controller (I): Tuning rule development

This paper presents a new practical tuning method for fractional order proportional and integral controller (FO-PI). The plant to be controlled is mainly FOPDT (first order plus delay time). 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 MIGO (M-s constrained integral gain optimization) based controller tuning method to handle the FO-PI case, called F-MIGO, given the fractional order a. The F-MIGO method is then used to develop tuning rules for the FOPDT class of dynamic systems. The final developed tuning rules only applies the relative dead time, tau of the FOPDT model to determine the best fractional order a 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. In Part (II) of this companion paper, interesting experimental results in two experimental platforms are reported using the tuning rule of this paper. The tuning rule development procedure for FO-PI is not only valid for FOPDT but also applicable for other general class of plants as illustrated.