design with fractional-order controllers

This article focuses on H ∞ performance design for fractional-order systems with time-delay, using fractional-order proportional-derivative ( P D μ ) controllers. First, the stabilizing parameters region in proportional-derivative plane of P D μ controller, for a fixed derivative-order, is determined in terms of a graphical stability criterion applicable to fractional-order time-delay systems. Then, in the stabilizing region, the pairs of proportional and derivative gains of P D μ controller are calculated for a range of frequencies, which satisfy the H ∞ -norm constraint of complementary sensitivity function and define the H ∞ boundary curve. Finally, by changing the derivative-order of P D μ controller, we observe the relationship between the H ∞ curve and the derivative-order. Examples are followed to illustrate the design procedure.