Stability criteria for a generator excitation system with fractional-order controller and time delay

The article studies the influences of time delay on the stability of fractional-order controller on the system of generator exhortation system. The use of measurement devices and communication links for data transfer can cause delays in closed-loop transfer function of the system. The complexity arises because of exponential transcendental term and fractional order in characteristic equation. The stability of time delay is analyzed in an abstract method. A formula will be given to find out the maximum number of time delay that is known with the title of delay margin that this system can tolerate without any loss in its stability. We will present that this process reveals all the possible stability regions analytically in the parametric space of the time delay. It is shown when crossing from certain amount of time delay is occurred the excitation control system becomes unstable. Employing this method which will be shown in this article, first we removed the transcendental terms from the equation and after that we spotted locations in which the axis is an imaginary one. The simulation of time domain of Matlab and Simulink were employed to validate the results of delay margin.