Design and analysis on fractional-order tracking differentiator

The design and analysis on the fractional-order tracking differentiator are investigated in this paper. The optimal-time control conditions are applied to dual integral fractional-order systems to obtain the switching curve. By the aid of the switching curve, the fractional-order optimal-time control scheme is achieved. Like the design method of the integer-order tracking differentiator, the fractional-order tracking differentiator is offered by the replacement in the fractional-order optimal-time controller. The proposed fractional-order tracking differentiator can provide the fractional-order derivative of reference input and arrange a transient profile for the reference input. Finally, two illustrative examples are given to verify the effectiveness of the proposed method.