A novel approach towards discrete-time realization of fractional-order proportional integral controller

In this work, a novel approach for realization of the discrete-time fractional-order proportional integral (FOPI) controller has been presented for two fractional-order plant models. The realization of the fractional-order controller has been implemented in two phases. The first phase involves designing the FOPI controller in the continuous-time domain based upon specific frequency domain design criteria through Bode’s ideal transfer function (BITF) and time-delayed Bode’s ideal transfer function methods. In the second phase, a new generating function named Modified Visweswaran-Varshney-Gupta-Schneider-Delta (MV²GSD) approximation has been proposed in the delta domain. The developed generating function undergoes continued fraction expansion (CFE) for discrete-time realization of the controller. The advantage of realizing the discrete-time controller in the delta domain over the conventional $z$-domain has been highlighted, which shows the unification of the discrete-time model with its underlying continuous-time model at a fast sampling rate. Further, simulation studies have been carried out with some benchmark examples to study the effectiveness of the proposed discretization method.