Design of variable fractional order differentiator using a modular cascade structure

In this paper, a modular cascade structure is presented to design the variable fractional order differentiator (VFOD). First, a product expansion of exponential function is used to obtain a modular cascade implementation structure of VFOD. This structure is easily implemented by using only one basic modular cell. Then, the digital first order logarithm differentiator designed by the least squares method is applied to realize basic cell in the proposed structure. Finally, several numerical examples are demonstrated to show the effectiveness of the proposed VFOD design method.