The generalized isodamping approach for robust fractional PID controllers design

In this paper we present a novel methodology to design fractional-order proportional-integral-derivative controllers. Based on the description of the controlled system by means of a family of linear models parameterized with respect to a free variable that describes the real process operating point, we design the controller by solving a constrained min-max optimization problem where the maximum sensitivity has to be minimized. Among the imposed constraints, the most important one is the new generalized isodamping condition, that defines the invariancy of the phase margin with respect to the free parameter variations. It is also shown that the well-known classical isodamping condition is a special case of the new technique proposed in this paper. Simulation results show the effectiveness of the proposed technique and the superiority of the fractional-order controller compared to its integer counterpart.