Stability regions of fractional-order PIαDβ controllers with dead-time plant

The aim of this paper is to show the stability areas of fractional order PID controllers to stabilize the first-order system plus time-delay. This is a new approach generalized from the classical case. First-order open-loop stable and unstable system is consider in this paper. Quasi-polynomial characteristic equation produced by the plant having dead-time. Generalization version of the H. Biehler and Pontryagin theorem are applicable to quasi-polynomials. The problem for the solution of fractional order PID controllers stabilization introduced here is based on determine range of controller´s gain for which controller is stable and thus stabilize the plant with dead-time.