Fractional-order PID controllers for stabilization of fractional-order time delay systems based on region stability

Stability is essential to the power system. But a practical system should not only has good steady-state performance, but also need to have good transient performance, such as adjusting the time, overshoot and so on. The transient performance of the system is usually determined by the exact position of the pole .Therefore, the study of regional stability (δ -stability) has more extensive, complex and theoretical and engineering significance. The paper proposed an algorithm for stabilization of fractional-order time delay systems using fractional-order PI
^λ
D
^μ
controllers. This method can be used to find the set of stabilizing controllers that guarantees the biggest δ -stability region needed by the control system. It is based on determining a set of global stability regions in the (k
P
, k
I
, k
D
) -space corresponding to the fractional orders λ and μ in the range of (0, 2) and then choosing the biggest δ - stability region in this set. The algorithm has reliable result which is illustrated by an example, and, hence is practically useful in the analysis and design of feedback control for fractional-order systems having times delays.