Variable-, Fractional-Order RST/PID Controller Transient Characteristics Calculation

In the paper we propose a method of the variable-fractional-order (VFO) discrete-time linear system response calculation applied to the VFO RST/PID controllers response. To such controllers we cannot directly apply the commonly known one-sided Z-Transform method. Treating the VFO-PID controller as a special case of the RST controller we show that using classical methods we can derive the dynamical properties of the VFO-PID controller.