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.