H∞ model matching PID design for fractional FOPDT systems

This paper deals with the H_∞ model matching problem for fractional first-order-plus-dead-time processes. Starting from the analytical solution of the problem, we show that a fractional proportional-integral-derivative controller can be obtained. In this context, the (robust) stability issue is analyzed. Further, guidelines for the tuning of the controller parameters are given in order to address practical issues and to obtain the required performance. Simulation results show that the design methodology is effective and allows the user (on the contrary to the integer-order case) to consider processes with different dynamics in a unified framework.