FOPID controller tuning for fractional FOPDT plants subject to design specifications in the frequency domain

In this paper, the problem of fractional-order proportional-integral-derivative (FOPID) controller tuning for fractional-order first-order plus dead time plants (FFOPDT) is considered. The designed controller must fulfill the prescribed specifications in the frequency domain. To this end, the fractional orders of the integrator and differentiator components are selected using a set of rules based on the observation of essential plant dynamics, while a numerical optimization algorithm is employed for obtaining the gains of the controller based on three dimensional Newton's method. All the necessary equations for computing the elements of the Jacobian matrix are provided. The proposed algorithm is detailed. It is also implemented and verified on an embedded device. The proposed solution may be useful in developing automatic tuning algorithms for FOPID controllers.