New results on the synthesis of FO-PID controllers

In this paper a new procedure that allows to define the parameters of fractional order PIλDμPIλDμ controller, designed to stabilize a first-order plant with delay-time, is proposed. Using a version of the Hermite–Biehler theorem applicable to quasipolynomials, the complete set of stabilizing PIλDμPIλDμ parameters is determined. The widespread industrial use of PID controllers and the potentiality of their non-integer order representation justifies a timely interest to PIλDμPIλDμ tuning techniques.