Variable parameter, fractional order, discrete, inertial transfer function models

In the paper, new, fractional order, variable parameter discrete transfer function models of an elementary inertial plant are proposed. One uses a time variable quasi time constant while the other employs, a variable time quasi constant and variable fractional order. Both models apply the variable fractional order backward difference to approximate the fractional operator. Both variable parameters are described by discrete, bounded functions. The accuracy and stability of the models considered are discussed. Theoretical results are validated by simulations. The proposed models can be applied to the modeling of various physical phenomena, where the constant parameter transfer function is not enough.