The tuning of PI controllers by using Ziegler–Nichols methods is a well-known technique. In the fractional case, the FOMCON toolbox for the MATLAB utility program is used for the tuning of FO-PI controllers. In order to obtain the optimal tuning parameters in the fractional case, a number of optimization methods are incorporated in the FOMCON toolbox, both in the frequency range and in the
time domain. In the frequency range, the goal of optimizing the parameters is achieved by obtaining optimal performance in terms of the sensitivity function S(j!) for disturbance rejection for the low and middle frequency range and the rejection of the high frequency noise using the complementary sensitivity function T(j!). In the time domain, the tuning of fractional controllers is carried out by
minimizing optimal criteria, such as the integral absolute error (IAE).
Also, PSO method could be used for optimization of parameters of PI-FO, in usual way, like optimization of any other parameters