Fractional calculus in 13C separation column control

Controller design for an isotope separation column is recognized as a difficult and challenging problem. The dynamics of the isotope separation process is difficult to model precisely using integer order transfer functions; thus, a fractional order approach is preferred. The objective of this work is to design two different PI controllers??a classical one and a fractional order one??and test their closed loop performance under nominal conditions as well as gain uncertainties. Since the process is represented by a fractional order mathematical model, the simplest approach to design both controllers is based on a frequency specification. For the fractional order of the PI controller and its parameters, the authors solve a system of equations that includes a robust performance specification to gain uncertainties. For the classical PI controller, a traditional tuning algorithm based on phase margin specification is implemented. The simulation results show that both controllers meet the design specifications, with the fractional order PI controller behaving more robustly to plant gain variations.