Stabilization Using Fractional-Order PIDα Controllers for First Order Time Delay System

This brief note considers the problem of stabilizing a first-order plant with dead-time using a fractional order proportional-integral-derivative (PID
^α
) controller. Fractional order controller provides good stability margin than the conventional PID controller. Here, the upper bound of K
_d
value is estimated first for all permissible value of α which is followed by computing the value of K
_c
. Further, the graphic results have been provided to clearly show the range of stabilizing PID
^α
parameters [α, K
_c
, K
_i
and K
_d
]. An example illustrates the applicability of the procedure.